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Escape Velocity Definition and Formula

Escape Velocity

Escape velocity is a fundamental concept in astrophysics and aerospace engineering, crucial for understanding the mechanics of space travel and celestial mechanics. Here is the definition of escape velocity, its nature as a speed rather than a velocity, its applications, the formula governing it, and a table of values for various celestial bodies.

What Is Escape Velocity?

Escape velocity is the minimum speed an object must reach to break free from the gravitational pull of a body without further propulsion. This means that a spacecraft, for instance, must attain this speed to escape the Earth’s gravitational field without needing additional energy input, such as from rockets.

Speed vs. Velocity: Why Escape Velocity Is a Speed

While often referred to as a “velocity,” escape velocity is technically a scalar quantity , which means it has magnitude but no specific direction. In contrast, “velocity” is a vector quantity, encompassing both magnitude and direction. Therefore, the term “escape speed” is more accurate. What matters in overcoming a body’s gravitational pull is the object’s speed (how fast it’s moving), not the direction of its movement.

Uses and Applications

Knowing the escape velocity of a body has several applications:

  • Space Travel : The most direct application is in determining the initial speed required for spacecraft to leave a planet or moon.
  • Astrophysics : Knowing the escape speed helps in understanding the behavior of celestial objects, like the conditions necessary for an atmosphere to remain bound to a planet.
  • Planetary Science : The calculation assists in studying the gravitational fields of planets and moons, which is crucial for landing and takeoff of space missions.

The Escape Velocity Formula

The formula for escape velocity derives from the law of conservation of energy :

v e ​ = (2 GM /r​​) 1/2

  • v e ​ is the escape velocity.
  • G is the gravitational constant (6.674×10−11 Nm 2 /kg 2 ).
  • M is the mass of the celestial body.
  • r is the radius of the celestial body from its center to the point of escape

Escape Velocity for Earth

For Earth, the values are:

  • M Earth ​= 5.972×10 24 kg
  • r Earth ​ = 6.371×10 6 m

Plugging in the values and performing the calculation:

v e ​= (2 × 6.674×10 −11 Nm 2 /kg 2 × 5.972×10 24 kg ​​/ 6.371×10 6 m) 1/2

Remember, 1 N = 1 kg⋅m/s 2

So, the escape velocity for Earth is approximately 11,185.7311,185.73 meters per second or 11.2 m/s.

Escape Velocity Table for Celestial Bodies

This table provides the mass, radius, and calculated escape velocity for various celestial bodies, including the Sun, Mercury, Venus, Earth, Moon, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto.

The escape velocity of the Milky Way galaxy is between 492 and 594 km/s. Meanwhile, the intense gravitational pull of a black hole is so high that its escape velocity is faster than the speed of light !

Deriving the Formula for Escape Velocity

The escape velocity formula comes from the principle of conservation of energy, based on two states of the system: one when the object is at the surface of the celestial body (like a planet) and the other when the object is at an infinite distance away, having just escaped the gravitational pull of the body.

Object on the Surface

At this state, the object at the surface has the following energies:

  • Gravitational Potential Energy (U) : U 1 ​ = − GMm / r​
  • Kinetic Energy (K) : K 1 ​ = 1/2 mv 2 (where v is the velocity of the object)

The total energy at state 1 (E1) is the sum of kinetic and potential energy:

E 1 ​= K 1​ + U 1 ​= 1/2​ mv 2 − GMm / r ​

Object at an Infinite Distance

At infinite distance, the gravitational potential energy becomes zero because the object is no longer within the gravitational influence of the celestial body. Also, for the object to just escape, we assume its kinetic energy reduces to zero (i.e., it escapes but eventually comes to rest). So:

  • Gravitational Potential Energy (U) : U 2 ​ = 0
  • Kinetic Energy (K) : K 2 ​=0

Therefore, the total energy at state 2 (E 2 ) is: E 2 ​= K 2 ​+ U 2 ​ = 0

Conservation of Energy

According to the law of conservation of energy, the total mechanical energy of the system remains constant if only conservative forces (like gravity) are doing work. Therefore, E 1 ​ = E 2 ​.

Setting the total energies equal to each other: 1/2​ mv 2 − GMm ​ /r = 0

Solving for Escape Velocity

Now, we solve for v , the escape velocity:

1/2 mv 2 = GMm / r ​

mv 2 = 2 GMm / r

v 2 = 2 GM / r

v = (2 GM / r ) 1/2 ​​​​

Here, G is the gravitational constant, M is the mass of the celestial body, m is the mass of the object, and r is the distance from the center of the celestial body to the object (typically the radius of the body). Mass cancels out, showing that escape velocity is independent of the mass of the escaping object.

Why Launches Are Close to the Equator

Rockets achieve escape velocity (or orbital velocity, if the goal is to orbit rather than escape) through sustained acceleration. They do not need to reach escape velocity instantly; instead, they gradually increase their speed over time using their engines. Launching spacecraft close to the equator takes advantage of the Earth’s rotation, giving the craft a boost toward achieving escape velocity and offering additional advantages:

1. Rotational Speed of the Earth

The Earth rotates faster at the equator than at any other latitude . This means that a location on the equator is moving eastward at a higher speed compared to locations further north or south. When a spacecraft launches from the equator, it benefits from this additional rotational speed of the Earth. The extra speed provided by the Earth’s rotation means the rocket requires less fuel to reach the necessary orbital velocity, making the launch more efficient. Also, although the effect is minor, planets are slightly flattened, so the equator is slightly further from the center of the planet than the poles.

3. Direct Access to Geostationary Orbit

Geostationary orbits are directly above the equator. Launching from the equator allows for a more direct and fuel-efficient path to this type of orbit, which is important for communication and weather satellites.

4. Flexibility in Launch Azimuth

Launching from near the equator offers more flexibility in choosing a launch azimuth (the angle of the launch relative to North). This flexibility is crucial for efficiently reaching different types of orbits, especially equatorial and geostationary orbits.

5. Energy Efficiency

The rotational boost and the direct path to certain orbits mean that rockets can carry more payload for the same amount of fuel, or the same payload with less fuel. This efficiency is crucial for cost-effective space missions.

  • Bate, Roger R.; Mueller, Donald D.; White, Jerry E. (1971). Fundamentals of Astrodynamics (Illustrated ed.). Courier Corporation. ISBN 978-0-486-60061-1.
  • Giancoli, Douglas C. (2008). Physics for Scientists and Engineers with Modern Physics . Addison-Wesley. ISBN 978-0-13-149508-1.
  • Smith, Martin C.; Ruchti, G. R.; Helmi, A.; Wyse, R. F. G. (2007). “The RAVE Survey: Constraining the Local Galactic Escape Speed”. Proceedings of the International Astronomical Union . 2 (S235): 755–772. doi: 10.1017/S1743921306005692
  • Teodorescu, P. P. (2007). Mechanical Systems, Classical Models . Springer, Japan. ISBN 978-1-4020-5441-9.

Related Posts

What is escape velocity?

Escape velocity is the speed that an object needs to be traveling to break free of a planet or moon's gravity well and leave it without further propulsion. For example, a spacecraft leaving the surface of Earth needs to be going 7 miles per second, or nearly 25,000 miles per hour to leave without falling back to the surface or falling into orbit.

space travel escape speed

Since escape velocity depends on the mass of the planet or moon that a spacecraft is blasting off of, a spacecraft leaving the moon's surface could go slower than one blasting off of the Earth, because the moon has less gravity than the Earth. On the other hand, the escape velocity for Jupiter would be many times that of Earth's because Jupiter is so huge and has so much gravity.

One reason that manned missions to other planets are difficult to plan is that a ship would have to take enough fuel into space to blast off of the other planet when the astronauts wanted to go home. The weight of the fuel would make the spaceship so heavy it would be hard to blast it off of Earth!

What is gravity? How do we put a spacecraft into orbit? Once a ship is in orbit, do we have to do anything to keep it there? How did DS1 get into space? Could NASA use ion propulsion to put a ship into space?
What is mass? Why is it a good idea to launch a ship into orbit from near the equator? Why is mass important? How does a multi-stage rocket like the Delta II work? Why does it take so much energy to launch DS1?
Why do mass and distance affect gravity? What's a gravity well?

Space Travel Calculator

Table of contents

Ever since the dawn of civilization, the idea of space travel has fascinated humans! Haven't we all looked up into the night sky and dreamed about space?

With the successful return of the first all-civilian crew of SpaceX's Inspiration4 mission after orbiting the Earth for three days, the dream of space travel looks more and more realistic now.

While traveling deep into space is still something out of science fiction movies like Star Trek and Star Wars, the tremendous progress made by private space companies so far seems very promising. Someday, space travel (or even interstellar travel) might be accessible to everyone!

It's never too early to start planning for a trip of a lifetime (or several lifetimes). You can also plan your own space trip and celebrate World Space Week in your own special way!

This space travel calculator is a comprehensive tool that allows you to estimate many essential parameters in theoretical interstellar space travel . Have you ever wondered how fast we can travel in space, how much time it will take to get to the nearest star or galaxy, or how much fuel it requires? In the following article, using a relativistic rocket equation, we'll try to answer questions like "Is interstellar travel possible?" , and "Can humans travel at the speed of light?"

Explore the world of light-speed travel of (hopefully) future spaceships with our relativistic space travel calculator!

If you're interested in astrophysics, check out our other calculators. Find out the speed required to leave the surface of any planet with the escape velocity calculator or estimate the parameters of the orbital motion of planets using the orbital velocity calculator .

One small step for man, one giant leap for humanity

Although human beings have been dreaming about space travel forever, the first landmark in the history of space travel is Russia's launch of Sputnik 2 into space in November 1957. The spacecraft carried the first earthling, the Russian dog Laika , into space.

Four years later, on 12 April 1961, Soviet cosmonaut Yuri A. Gagarin became the first human in space when his spacecraft, the Vostok 1, completed one orbit of Earth.

The first American astronaut to enter space was Alan Shepard (May 1961). During the Apollo 11 mission in July 1969, Neil Armstrong and Buzz Aldrin became the first men to land on the moon. Between 1969 and 1972, a total of 12 astronauts walked the moon, marking one of the most outstanding achievements for NASA.

Buzz Aldrin climbs down the Eagle's ladder to the surface.

In recent decades, space travel technology has seen some incredible advancements. Especially with the advent of private space companies like SpaceX, Virgin Galactic, and Blue Origin, the dream of space tourism is looking more and more realistic for everyone!

However, when it comes to including women, we are yet to make great strides. So far, 566 people have traveled to space. Only 65 of them were women .

Although the first woman in space, a Soviet astronaut Valentina Tereshkova , who orbited Earth 48 times, went into orbit in June 1963. It was only in October 2019 that the first all-female spacewalk was completed by NASA astronauts Jessica Meir and Christina Koch.

Women's access to space is still far from equal, but there are signs of progress, like NASA planning to land the first woman and first person of color on the moon by 2024 with its Artemis missions. World Space Week is also celebrating the achievements and contributions of women in space this year!

In the following sections, we will explore the feasibility of space travel and its associated challenges.

How fast can we travel in space? Is interstellar travel possible?

Interstellar space is a rather empty place. Its temperature is not much more than the coldest possible temperature, i.e., an absolute zero. It equals about 3 kelvins – minus 270 °C or minus 455 °F. You can't find air there, and therefore there is no drag or friction. On the one hand, humans can't survive in such a hostile place without expensive equipment like a spacesuit or a spaceship, but on the other hand, we can make use of space conditions and its emptiness.

The main advantage of future spaceships is that, since they are moving through a vacuum, they can theoretically accelerate to infinite speeds! However, this is only possible in the classical world of relatively low speeds, where Newtonian physics can be applied. Even if it's true, let's imagine, just for a moment, that we live in a world where any speed is allowed. How long will it take to visit the Andromeda Galaxy, the nearest galaxy to the Milky Way?

Space travel.

We will begin our intergalactic travel with a constant acceleration of 1 g (9.81 m/s² or 32.17 ft/s²) because it ensures that the crew experiences the same comfortable gravitational field as the one on Earth. By using this space travel calculator in Newton's universe mode, you can find out that you need about 2200 years to arrive at the nearest galaxy! And, if you want to stop there, you need an additional 1000 years . Nobody lives for 3000 years! Is intergalactic travel impossible for us, then? Luckily, we have good news. We live in a world of relativistic effects, where unusual phenomena readily occur.

Can humans travel at the speed of light? – relativistic space travel

In the previous example, where we traveled to Andromeda Galaxy, the maximum velocity was almost 3000 times greater than the speed of light c = 299,792,458 m/s , or about c = 3 × 10 8 m/s using scientific notation.

However, as velocity increases, relativistic effects start to play an essential role. According to special relativity proposed by Albert Einstein, nothing can exceed the speed of light. How can it help us with interstellar space travel? Doesn't it mean we will travel at a much lower speed? Yes, it does, but there are also a few new relativistic phenomena, including time dilation and length contraction, to name a few. The former is crucial in relativistic space travel.

Time dilation is a difference of time measured by two observers, one being in motion and the second at rest (relative to each other). It is something we are not used to on Earth. Clocks in a moving spaceship tick slower than the same clocks on Earth ! Time passing in a moving spaceship T T T and equivalent time observed on Earth t t t are related by the following formula:

where γ \gamma γ is the Lorentz factor that comprises the speed of the spaceship v v v and the speed of light c c c :

where β = v / c \beta = v/c β = v / c .

For example, if γ = 10 \gamma = 10 γ = 10 ( v = 0.995 c v = 0.995c v = 0.995 c ), then every second passing on Earth corresponds to ten seconds passing in the spaceship. Inside the spacecraft, events take place 90 percent slower; the difference can be even greater for higher velocities. Note that both observers can be in motion, too. In that case, to calculate the relative relativistic velocity, you can use our velocity addition calculator .

Let's go back to our example again, but this time we're in Einstein's universe of relativistic effects trying to reach Andromeda. The time needed to get there, measured by the crew of the spaceship, equals only 15 years ! Well, this is still a long time, but it is more achievable in a practical sense. If you would like to stop at the destination, you should start decelerating halfway through. In this situation, the time passed in the spaceship will be extended by about 13 additional years .

Unfortunately, this is only a one-way journey. You can, of course, go back to Earth, but nothing will be the same. During your interstellar space travel to the Andromeda Galaxy, about 2,500,000 years have passed on Earth. It would be a completely different planet, and nobody could foresee the fate of our civilization.

A similar problem was considered in the first Planet of the Apes movie, where astronauts crash-landed back on Earth. While these astronauts had only aged by 18 months, 2000 years had passed on Earth (sorry for the spoilers, but the film is over 50 years old at this point, you should have seen it by now). How about you? Would you be able to leave everything you know and love about our galaxy forever and begin a life of space exploration?

Space travel calculator – relativistic rocket equation

Now that you know whether interstellar travel is possible and how fast we can travel in space, it's time for some formulas. In this section, you can find the "classical" and relativistic rocket equations that are included in the relativistic space travel calculator.

There could be four combinations since we want to estimate how long it takes to arrive at the destination point at full speed as well as arrive at the destination point and stop. Every set contains distance, time passing on Earth and in the spaceship (only relativity approach), expected maximum velocity and corresponding kinetic energy (on the additional parameters section), and the required fuel mass (see Intergalactic travel — fuel problem section for more information). The notation is:

  • a a a — Spaceship acceleration (by default 1   g 1\rm\, g 1 g ). We assume it is positive a > 0 a > 0 a > 0 (at least until halfway) and constant.
  • m m m — Spaceship mass. It is required to calculate kinetic energy (and fuel).
  • d d d — Distance to the destination. Note that you can select it from the list or type in any other distance to the desired object.
  • T T T — Time that passed in a spaceship, or, in other words, how much the crew has aged.
  • t t t — Time that passed in a resting frame of reference, e.g., on Earth.
  • v v v — Maximum velocity reached by the spaceship.
  • K E \rm KE KE — Maximum kinetic energy reached by the spaceship.

The relativistic space travel calculator is dedicated to very long journeys, interstellar or even intergalactic, in which we can neglect the influence of the gravitational field, e.g., from Earth. We didn't include our closest celestial bodies, like the Moon or Mars, in the destination list because it would be pointless. For them, we need different equations that also take into consideration gravitational force.

Newton's universe — arrive at the destination at full speed

It's the simplest case because here, T T T equals t t t for any speed. To calculate the distance covered at constant acceleration during a certain time, you can use the following classical formula:

Since acceleration is constant, and we assume that the initial velocity equals zero, you can estimate the maximum velocity using this equation:

and the corresponding kinetic energy:

Newton's universe — arrive at the destination and stop

In this situation, we accelerate to the halfway point, reach maximum velocity, and then decelerate to stop at the destination point. Distance covered during the same time is, as you may expect, smaller than before:

Acceleration remains positive until we're halfway there (then it is negative – deceleration), so the maximum velocity is:

and the kinetic energy equation is the same as the previous one.

Einstein's universe — arrive at the destination at full speed

The relativistic rocket equation has to consider the effects of light-speed travel. These are not only speed limitations and time dilation but also how every length becomes shorter for a moving observer, which is a phenomenon of special relativity called length contraction. If l l l is the proper length observed in the rest frame and L L L is the length observed by a crew in a spaceship, then:

What does it mean? If a spaceship moves with the velocity of v = 0.995 c v = 0.995c v = 0.995 c , then γ = 10 \gamma = 10 γ = 10 , and the length observed by a moving object is ten times smaller than the real length. For example, the distance to the Andromeda Galaxy equals about 2,520,000 light years with Earth as the frame of reference. For a spaceship moving with v = 0.995 c v = 0.995c v = 0.995 c , it will be "only" 252,200 light years away. That's a 90 percent decrease or a 164 percent difference!

Now you probably understand why special relativity allows us to intergalactic travel. Below you can find the relativistic rocket equation for the case in which you want to arrive at the destination point at full speed (without stopping). You can find its derivation in the book by Messrs Misner, Thorne ( Co-Winner of the 2017 Nobel Prize in Physics ) and Wheller titled Gravitation , section §6.2. Hyperbolic motion. More accessible formulas are in the mathematical physicist John Baez's article The Relativistic Rocket :

  • Time passed on Earth:
  • Time passed in the spaceship:
  • Maximum velocity:
  • Relativistic kinetic energy remains the same:

The symbols sh ⁡ \sh sh , ch ⁡ \ch ch , and th ⁡ \th th are, respectively, sine, cosine, and tangent hyperbolic functions, which are analogs of the ordinary trigonometric functions. In turn, sh ⁡ − 1 \sh^{-1} sh − 1 and ch ⁡ − 1 \ch^{-1} ch − 1 are the inverse hyperbolic functions that can be expressed with natural logarithms and square roots, according to the article Inverse hyperbolic functions on Wikipedia.

Einstein's universe – arrive at destination point and stop

Most websites with relativistic rocket equations consider only arriving at the desired place at full speed. If you want to stop there, you should start decelerating at the halfway point. Below, you can find a set of equations estimating interstellar space travel parameters in the situation when you want to stop at the destination point :

Intergalactic travel – fuel problem

So, after all of these considerations, can humans travel at the speed of light, or at least at a speed close to it? Jet-rocket engines need a lot of fuel per unit of weight of the rocket. You can use our rocket equation calculator to see how much fuel you need to obtain a certain velocity (e.g., with an effective exhaust velocity of 4500 m/s).

Hopefully, future spaceships will be able to produce energy from matter-antimatter annihilation. This process releases energy from two particles that have mass (e.g., electron and positron) into photons. These photons may then be shot out at the back of the spaceship and accelerate the spaceship due to the conservation of momentum. If you want to know how much energy is contained in matter, check out our E = mc² calculator , which is about the famous Albert Einstein equation.

Now that you know the maximum amount of energy you can acquire from matter, it's time to estimate how much of it you need for intergalactic travel. Appropriate formulas are derived from the conservation of momentum and energy principles. For the relativistic case:

where e x e^x e x is an exponential function, and for classical case:

Remember that it assumes 100% efficiency! One of the promising future spaceships' power sources is the fusion of hydrogen into helium, which provides energy of 0.008 mc² . As you can see, in this reaction, efficiency equals only 0.8%.

Let's check whether the fuel mass amount is reasonable for sending a mass of 1 kg to the nearest galaxy. With a space travel calculator, you can find out that, even with 100% efficiency, you would need 5,200 tons of fuel to send only 1 kilogram of your spaceship . That's a lot!

So can humans travel at the speed of light? Right now, it seems impossible, but technology is still developing. For example, a photonic laser thruster is a good candidate since it doesn't require any matter to work, only photons. Infinity and beyond is actually within our reach!

How do I calculate the travel time to other planets?

To calculate the time it takes to travel to a specific star or galaxy using the space travel calculator, follow these steps:

  • Choose the acceleration : the default mode is 1 g (gravitational field similar to Earth's).
  • Enter the spaceship mass , excluding fuel.
  • Select the destination : pick the star, planet, or galaxy you want to travel to from the dropdown menu.
  • The distance between the Earth and your chosen stars will automatically appear. You can also input the distance in light-years directly if you select the Custom distance option in the previous dropdown.
  • Define the aim : select whether you aim to " Arrive at destination and stop " or “ Arrive at destination at full speed ”.
  • Pick the calculation mode : opt for either " Einstein's universe " mode for relativistic effects or " Newton's universe " for simpler calculations.
  • Time passed in spaceship : estimated time experienced by the crew during the journey. (" Einstein's universe " mode)
  • Time passed on Earth : estimated time elapsed on Earth during the trip. (" Einstein's universe " mode)
  • Time passed : depends on the frame of reference, e.g., on Earth. (" Newton's universe " mode)
  • Required fuel mass : estimated fuel quantity needed for the journey.
  • Maximum velocity : maximum speed achieved by the spaceship.

How long does it take to get to space?

It takes about 8.5 minutes for a space shuttle or spacecraft to reach Earth's orbit, i.e., the limit of space where the Earth's atmosphere ends. This dividing line between the Earth's atmosphere and space is called the Kármán line . It happens so quickly because the shuttle goes from zero to around 17,500 miles per hour in those 8.5 minutes .

How fast does the space station travel?

The International Space Station travels at an average speed of 28,000 km/h or 17,500 mph . In a single day, the ISS can make several complete revolutions as it circumnavigates the globe in just 90 minutes . Placed in orbit at an altitude of 350 km , the station is visible to the naked eye, looking like a dot crossing the sky due to its very bright solar panels.

How do I reach the speed of light?

To reach the speed of light, you would have to overcome several obstacles, including:

Mass limit : traveling at the speed of light would mean traveling at 299,792,458 meters per second. But, thanks to Einstein's theory of relativity, we know that an object with non-zero mass cannot reach this speed.

Energy : accelerating to the speed of light would require infinite energy.

Effects of relativity : from the outside, time would slow down, and you would shrink.

Why can't sound travel in space?

Sound can’t travel in space because it is a mechanical wave that requires a medium to propagate — this medium can be solid, liquid, or gas. In space, there is no matter, or at least not enough for sound to propagate. The density of matter in space is of the order 1 particle per cubic centimeter . While on Earth , it's much denser at around 10 20 particles per cubic centimeter .

Dreaming of traveling into space? 🌌 Plan your interstellar travel (even to a Star Trek destination) using this calculator 👨‍🚀! Estimate how fast you can reach your destination and how much fuel you would need 🚀

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ol{padding-top:0;}.css-1dtpypy ul:not(:first-child),.css-1dtpypy ol:not(:first-child){padding-top:4px;} Spaceship and destination 👩‍🚀👨‍🚀

Spaceship acceleration

Spaceship mass

Mass of spaceship excluding fuel.

Destination

Select a destination from the list or type in distance by hand.

Which star/galaxy?

If you want to input your own distance, select the 'Custom destination' option in the 'Which star/galaxy?' field.

Calculation options

Do you want to stop at destination point? If yes, the spaceship will start decelerating once it reaches the halfway point.

Calculations mode

You can compare Einstein's special relativity with non-relativistic Newton's physics. Remember that at near-light speeds only the former is correct!

Travel details 🚀

Time passed in spaceship

Time passed on Earth

Time passed in the resting frame of reference. It could be an observer on Earth.

Required fuel mass

Assuming 100% efficiency.

Maximum velocity

Note that our calculator may round velocity to the speed of light if it is really close to it.

Additional parameters

Fuel energy equivalent

Required fuel mass multiplied by c².

Maximum kinetic energy

Beta parameter for the maximum velocity.

γ [1/√(1 - β²)]

Lorentz factor for the maximum velocity.

Companion site to the textbook by Dale A. Ostlie, Oxford University Press, 2022

Escape Speed

$$v_\text{escape} = \sqrt{\frac{2GM\phantom{)}}{R}}\quad[\text{Eq. (6.7)}]\quad\text{or}\quad v_\text{escape} = 11.2~\text{km}/\text{s}\times\sqrt{\frac{M_\text{Earth}}{R_\text{Earth}}}$$

Note: If you feel uncomfortable with working with variables, fractions, percentages, or scientific notation, you should review the following tutorials before working through this tutorial:

  • Percentages
  • Scientific notation

Introduction

  • Quiz yourself

The escape speed equation is the result of asking the question: How fast must an object travel straight up in order to escape from a body of mass \(M\) that has a radius of \(R\) (note that we are ignoring any air resistance)? To answer the question it first gets converted into a conservation of energy equation: What must the kinetic energy \(\frac{1}{2}mv^2\) of the object be in order to overcome the change in potential energy due to gravity in going straight up from the surface of the body to infinitely far away, or \(\frac{1}{2}mv_\text{escape}^2 = \text{change in gravitational potential energy}\).

Advance d: For the curious, the change in gravitational potential energy that goes on the right-hand side of the expression derives directly from the force equation that is Newton’s universal law of gravitation [Equation (5.7)] : \(\text{change in gravitational potential energy} = GMm/R\). The 2 on the right-hand side of Equation (6.7) comes from the \(\frac{1}{2}\) in the kinetic energy expression the little \(m\)s cancel, and the square root comes from solving for \(v_\text{escape}\). BTW, whenever you see Big G (\(G\)) you know gravity is involved.

The alternate form of the escape speed equation comes from using the “trick” used many times in the textbook: divide the general equation by the same equation using specific values of a well-known object or system. The obvious “well-known” object that is used here is Earth. Substituting the mass of Earth (\(\text{M}_\text{Earth}\)), the radius of Earth (\(\text{R}_\text{Earth}\)), and the value of Big G , tells us that the escape speed from Earth is \(11.2~\text{km}/\text{s}=\sqrt{2G\text{M}_\text{Earth}/\text{R}_\text{Earth}}\). Dividing the general equation [(Equation (6.7)] by this last equation produces the alternate form of the escape speed, where the mass and radius MUST be expressed in terms of the mass and radius of Earth (the Earth subscripts are meant to remind you of this requirement in using the alternate form).

  • Venus is very similar in size to Earth. Its mass is \(81\%\) of Earth’s mass and its radius is \(95\%\) of Earth’s radius. What is the escape speed from the surface of Venus? $$v_\text{escape} = 11.2~\text{km}/\text{s}\times \sqrt{\frac{0.81}{0.95}} = 11.2~\text{km}/\text{s}\times\sqrt{0.85} = 11.2~\text{km}/\text{s}\times 0.92 = 10.3~\text{km}/\text{s}.$$
  • The Sun’s mass is \(\text{333,000}\) times the mass of Earth and its radius \(109\) times Earth’s radius. What is the Sun’s escape speed? $$v_\text{escape} = 11.2~\text{km}/\text{s}\times\sqrt{\frac{\text{333,000}}{109}} = 11.2~\text{km}/\text{s}\times \sqrt{3055} = 11.2~\text{km}/\text{s}\times55.3=619~\text{km}/\text{s}.$$
  • Ceres is located in the asteroid belt and is classified as both an asteroid and a dwarf planet. It’s mass is \(0.000\,16\) times the mass of Earth, and its radius is only \(0.075\) times Earth’s radius. What is its escape speed? $$v_\text{escape}=11.2~\text{km}/\text{s}\times\sqrt{\frac{0.000\,16}{0.075}} = 11.2~\text{km}/\text{s}\times\sqrt{0.0021}=11.2~\text{km}/\text{s}\times0.046=520~\text{m}/\text{s}$$.
  • Mimas, a small moon of Saturn, has a mass estimated to be \(6.3 \times 10^{-6}\) times the mass of Earth, and a radius of \(198~\text{km}\) (the radius of Earth is \(6378~\text{km}\)). Calculate the escape speed of Mimas. $$v_\text{escape} = 11.2~\text{km}/\text{s}\times \sqrt{\frac{6.3\times 10^{-6}}{198/6378}} = 11.2~\text{km}/\text{s}\times \sqrt{\frac{6.3\times 10^{-6}}{0.031}} =160~\text{m}/\text{s}.$$

Quiz Yourself

Try the following exercises to make sure that you really do understand the material just presented. By the way, computers and many calculators write scientific notation in “computer-speak,” where \(10\) raised to an integer (either positive or negative) replaces \(\times 10^\text{exponent}\) with \({\rm E(exponent)}\) or \({\rm e(exponent)}\); in other words, \(3.14159 \times 10^9\) is represented by \(3.14159\text{E}9\). If your calculator has the \(\Large{\hat{ }}\) symbol, then you would enter the number as \(3.14159 \times 10{\Large{\hat{ }}}9\). If your calculator has a \(10^x\) button then you would enter the number as \(3.14159\times9\,\,10^x\). If you have having problems with entering numbers in scientific notation, read the manual or help screens, or ask your instructor.

( Answers are available below. )

  • Suppose that Earth’s mass magically increased by a factor of 9 without any change in its radius. Would its escape speed increase or decrease, and by what factor?
  • Suppose that Earth’s mass increases by a factor of 2 while its radius decreases by a factor of 8. What would the new value of Earth’s escape speed be?
  • Jupiter has a mass of \(318~\text{M}_\text{Earth}\) and a radius of \(11.2~\text{R}_\text{Earth}\). What is the escape speed from the “surface” of Jupiter. (Actually Jupiter is a gas giant and doesn’t have a solid surface.)
  • You land on a planet with twice Earth’s radius and eight times Earth’s mass. Determine the planet’s escape speed. (You shouldn’t need to use a calculator for this one.)
  • The mass of Mimas, one of Saturn’s moons, is \(0.000\,0063~\text{M}_\text{s}\) and its radius is \(198~\text{km}.\) The radius of Earth is \(6378~\text{km}\). What is the escape speed of Mimas?
  • Bennu is a near-Earth asteroid with an estimated mass of \(7.3\times 10^{10}~\text{kg}\) and an average radius of \(245~\text{m}\). Earth’s mass and radius are \(5.97\times 10^{24}~\text{kg}\) and \(6378~\text{km}\), respectively. (a) What is the escape speed from the surface of Bennu? (b) A major-league fastball is about \(45~\text{m}/\text{s}\); the world record top running speed is \(12.4~\text{m}/\text{s}\); a human typically walks at roughly \(2~\text{m}/\text{s}\). Which one of these speeds is the escape speed of Bennu closest to, and how many times faster or slower is Bennu’s escape speed? (c) Could someone jump off of Bennu’s surface? (A space mission has traveled to Bennu to retrieve some of its surface material to return to Earth.)
  • Sirius B is a star that has roughly the radius of Earth, but has a mass that is close to the mass of the Sun (about 333,000 times the mass of Earth). What is the escape speed of Sirius B?
  • The escape speed would increase by a factor of 3.
  • \(5.6\text{ km}/\text{s}\)
  • \(59.7~\text{km}/\text{s}\)
  • \(22.4~\text{km}/\text{s}\)
  • \(0.16~\text{km}/\text{s}\)
  • (a) \(0.0002~\text{km}/\text{s} = 0.2~\text{m}/\text{s}\). (b) Bennu’s escape speed is 10 times slower than typical walking speed. (c) Yes, and easily!
  • \(6500\text{ km}/\text{s}\) (about 4040 miles per hour)

Science Digest

Science Digest

Escape Velocity Calculator – Calculate Launch Speed

Escape velocity is the speed needed to break free from a planet or star’s gravity. It is crucial for spacecraft to launch successfully. Our Escape Velocity Calculator figures out this speed. It uses a formula based on the planet’s mass, size, and the pull of gravity, like 6.674×10−11N⋅m²/kg².

Known as the second cosmic velocity , it’s based on the energy conservation law. This law talks about balancing potential and kinetic energy at launch. You can find the escape velocity by adding the planet’s mass and size to this equation: v=√(2GM/R). For Earth, this velocity is about 11.2 km/s. Check out our space travel calculator and physics velocity calculator for exact gravitational pull calculations . They’re designed for your space journey needs.

Escape Velocity Calculator

Understanding escape velocity.

When getting ready for space travel, knowing about escape velocity is super important. It’s the speed needed for something to leave a planet without engines.

What is Escape Velocity?

Escape velocity is the speed needed to beat a planet’s gravity. It lets objects fly away without constant power. To find this speed, we use info about the planet’s size and mass. It’s interesting that the object’s own weight doesn’t matter for this.

Basic Concepts of Escape Velocity

The formula to find escape velocity is v=√(2GM/R). It includes the gravitational constant (G), the planet’s mass (M), and its radius (R). For Earth, this speed is about 11.2 kilometers per second.

The Importance of Escape Velocity in Space Travel

Knowing escape velocity is more than just a complicated math problem. It’s key to launching spacecraft safely. By figuring out this speed, we can send missions into space without them crashing back to Earth.

How to Use the Escape Velocity Calculator

The escape velocity calculator is easy to use. It helps find the speed rockets need to leave Earth or other planets. First, you need to have the planet’s mass and radius. For example, Earth’s mass is 5.9723×10 24 kg, and the radius is 6,371 km. Enter these numbers into the calculator.

This calculator uses a known formula to figure out escape speed. After entering the planet’s mass and radius, it shows the escape speed. For Earth, this speed is about 11.2 km/s.

It’s key to understand what the escape velocity calculator shows us. Knowing the right launch speed is crucial for space missions. This way, the rocket can leave Earth’s pull and fly beyond its atmosphere. So, accurate planet data in the calculator leads to successful space trips.

The Science Behind the Escape Velocity Formula

Knowing the escape velocity formula helps us understand how things leave big space objects’ gravitational pull. This formula combines potential and kinetic energy at launch. It’s key for space travel progress.

Breaking Down the Escape Velocity Equation

The escape velocity equation comes from the energy conservation rule, written as v=√(2GM/R) . In this, v is the velocity needed to escape, G is gravity’s constant, M means the body’s mass, and R stands for its radius. This equation tells us how much energy is needed to escape a planet’s or star’s pull, linking kinetic and potential energy exactly.

The Role of Mass and Radius in Escape Velocity

Escape velocity depends on a cosmic body’s weight and size. Bigger planets need more escape speed because they pull harder. But, if a planet is larger, the needed speed goes down. This shows us how a planet’s features change how fast we need to go to escape it.

Gravitational Constants and Their Influences

The gravitational constant (G) is a key part of the escape velocity formula. It’s about 6.674×10−11N⋅m²/kg² . It shows the small, but always there, gravity force in space. Understanding G helps us know the fine balance needed to fly from a planet, proving gravity calculations are complex.

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  • Introduction To Motion

Escape Speed

Escape speed is the minimum speed required to escape a planet’s gravitational pull.

A spacecraft leaving the earth’s surface should be going at a speed of about 11 kilometres (7 miles) per second to enter the outer orbit. Here, in this article, let us dig deeper into the concept of escape speed.

What Is Escape Speed?

Escape speed is the minimum speed with which a mass should be projected from the Earth’s surface in order to escape Earth’s gravitation field. Escape speed, also known as escape velocity is defined as:

The minimum speed that is required for an object to free itself from the gravitational force exerted by a massive object.

Escape Speed

For example, if we consider earth as a massive body. The escape velocity is the minimum velocity that an object should acquire to overcome the gravitational field of earth and fly to infinity without ever falling back. It purely depends on the distance of the object from the massive body and the mass of the massive body. More the mass it will be higher, similarly, the closer distance, higher will be the escape velocity.

For any massive bodies such as planets, stars which are spherically symmetric in nature, the escape speed for any given distance is mathematically expressed as:

  • v e is the escape speed
  • G is the universal gravitational constant (G≅6.67×10 -11 m 3 kg -1 s -2 )
  • M is the mass of the massive body(the body from which the object is to be escaped from)
  • r is the distance from the centre of the massive body to the object

Here we can notice that the above-mentioned relation is independent of the mass of the object which will be escaping from the massive body.

You may also want to check out these topics given below!

  • The escape velocity of earth
  • Potential energy
  • Equivalence principle

Derivation of Escape Speed

In general escape, speed is achieved when the object moves with a velocity at which the arithmetic sum of the object’s gravitational potential energy and its Kinetic energy equates to zero. That is, the object should possess greater kinetic energy than the gravitational potential energy to escape to infinity.

  • The simplest way of deriving the formula is by using the concept of conservation of energy. Let us assume that the object is trying to escape from a planet (which is uniform circular in nature) by moving away from it.
  • The prime force acting on such an object will be the planet’s gravity. As we know, Kinetic energy(K) and the Gravitational Potential Energy(U g ) are the only two kinds of energies associated here.

By the principle of conservation of energy, we can write:

  • \(\begin{array}{l}K=\frac{1}{2}mv^{2}\end{array} \)
  • \(\begin{array}{l}U=\frac{GMm}{r}\end{array} \)

Here U gf is zero as the distance is infinity and K f will also be zero as final velocity will be zero. Thus, we get:

The minimum velocity required to escape from the gravitational influence of massive body is given by:

The escape speed of the earth at the surface is approximately 11.186 km/s. That means “ an object should have a minimum of 11.186 km/s initial velocity to escape from earth’s gravity and fly to infinite space.”

Ideally, If you can jump with initial velocity 11.186 km/s you can tour outer space! Isn’t it interesting? For more such brain-twisting concepts do follow the links given below.

Unit Of Escape Speed

Unit of escape speed or the escape velocity is metre per seconds (m.s -1 ) which is also the SI unit of escape speed.

Dimensional Formula:

Read More: Principle of Conservation of Energy

Frequently Asked Questions

1) Is it better to launch a ship into orbit from near or away from the equator?

Ans: It is better to launch a ship from the equator because the radius is greater at the equator than at the poles. This lowers the escape velocity.

2) Compute the escape velocity for the indicated planet. Use G = 6.67 x 10 -11 N-m 2 /kg 2

a) Mars: Mass 6.46 x 10 23 kg; Radius 3.39 x 10 6 m

The formula to find the escape speed is as follows:

Substituting the values in the equation, we get

The escape speed for earth is approximately equal to 5.04 x 10 3 m/s.

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Escape Velocity of Earth

Most recent answer: 10/22/2007

(published on 10/22/2007)

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  • How many spacecraft have been to Saturn?
  • Has a spacecraft ever landed on Venus?
  • When was the first rocket launched into space?
  • When did we first land a spacecraft on Mars?
  • How many spacecraft have been to Mercury?
  • Will we ever travel to the stars?
  • How long would it take a spacecraft to reach the nearest galaxy?
  • How much space debris is orbiting Earth?
  • How much did the Space Shuttle weigh?

How fast does a rocket have to travel to get into space?

  • What was the first man-made object to reach another world?

This really depends on what you mean by "into space." If you just want to get into orbit around the Earth, you need to reach speeds of at least 4.9 miles per second, or about 17,600 miles per hour. If you want to completely escape Earth's gravity and travel to another moon or planet, though, you need to be going even faster - at a speed of at least 7 miles per second or about 25,000 miles per hour.

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Expert Voices

Is Interstellar Travel Really Possible?

Interstellar flight is a real pain in the neck.

Artist’s illustration of a Breakthrough Starshot probe arriving at the potentially Earth-like planet Proxima Centauri b. A representation of laser beams is visible emanating from the corners of the craft’s lightsail.

Paul M. Sutter is an astrophysicist at The Ohio State University , host of Ask a Spaceman and Space Radio , and author of " Your Place in the Universe. " Sutter contributed this article to Space.com's Expert Voices: Op-Ed & Insights . 

Interstellar space travel . Fantasy of every five-year-old kid within us. Staple of science fiction serials. Boldly going where nobody has gone before in a really fantastic way. As we grow ever more advanced with our rockets and space probes, the question arises: could we ever hope to colonize the stars? Or, barring that far-flung dream, can we at least send space probes to alien planets, letting them tell us what they see?

The truth is that interstellar travel and exploration is technically possible . There's no law of physics that outright forbids it. But that doesn't necessarily make it easy, and it certainly doesn't mean we'll achieve it in our lifetimes, let alone this century. Interstellar space travel is a real pain in the neck. 

Related: Gallery: Visions of Interstellar Starship Travel

Voyage outward

If you're sufficiently patient, then we've already achieved interstellar exploration status. We have several spacecraft on escape trajectories, meaning they're leaving the solar system and they are never coming back. NASA's Pioneer missions, the Voyager missions , and most recently New Horizons have all started their long outward journeys. The Voyagers especially are now considered outside the solar system, as defined as the region where the solar wind emanating from the sun gives way to general galactic background particles and dust.

So, great; we have interstellar space probes currently in operation. Except the problem is that they're going nowhere really fast. Each one of these intrepid interstellar explorers is traveling at tens of thousands of miles per hour, which sounds pretty fast. They're not headed in the direction of any particular star, because their missions were designed to explore planets inside the solar system. But if any of these spacecraft were headed to our nearest neighbor, Proxima Centauri , just barely 4 light-years away, they would reach it in about 80,000 years.

I don't know about you, but I don't think NASA budgets for those kinds of timelines. Also, by the time these probes reach anywhere halfway interesting, their nuclear batteries will be long dead, and just be useless hunks of metal hurtling through the void. Which is a sort of success, if you think about it: It's not like our ancestors were able to accomplish such feats as tossing random junk between the stars, but it's probably also not exactly what you imagined interstellar space travel to be like.

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Related: Superfast Spacecraft Propulsion Concepts (Images)

Speed racer

To make interstellar spaceflight more reasonable, a probe has to go really fast. On the order of at least one-tenth the speed of light. At that speed, spacecraft could reach Proxima Centauri in a handful of decades, and send back pictures a few years later, well within a human lifetime. Is it really so unreasonable to ask that the same person who starts the mission gets to finish it?

Going these speeds requires a tremendous amount of energy. One option is to contain that energy onboard the spacecraft as fuel. But if that's the case, the extra fuel adds mass, which makes it even harder to propel it up to those speeds. There are designs and sketches for nuclear-powered spacecraft that try to accomplish just this, but unless we want to start building thousands upon thousands of nuclear bombs just to put inside a rocket, we need to come up with other ideas.

Perhaps one of the most promising ideas is to keep the energy source of the spacecraft fixed and somehow transport that energy to the spacecraft as it travels. One way to do this is with lasers. Radiation is good at transporting energy from one place to another, especially over the vast distances of space. The spacecraft can then capture this energy and propel itself forward.

This is the basic idea behind the Breakthrough Starshot project , which aims to design a spacecraft capable of reaching the nearest stars in a matter of decades. In the simplest outline of this project, a giant laser on the order of 100 gigawatts shoots at an Earth-orbiting spacecraft. That spacecraft has a large solar sail that is incredibly reflective. The laser bounces off of that sail, giving momentum to the spacecraft. The thing is, a 100-gigawatt laser only has the force of a heavy backpack. You didn't read that incorrectly. If we were to shoot this laser at the spacecraft for about 10 minutes, in order to reach one-tenth the speed of light, the spacecraft can weigh no more than a gram.

That's the mass of a paper clip.

Related: Breakthrough Starshot in Pictures: Laser-Sailing Nanocraft to Study Alien Planets

A spaceship for ants

This is where the rubber meets the interstellar road when it comes to making spacecraft travel the required speeds. The laser itself, at 100 gigawatts, is more powerful than any laser we've ever designed by many orders of magnitude. To give you a sense of scale, 100 gigawatts is the entire capacity of every single nuclear power plant operating in the United States combined.

And the spacecraft, which has to have a mass no more than a paper clip, must include a camera, computer, power source, circuitry, a shell, an antenna for communicating back home and the entire lightsail itself.  

That lightsail must be almost perfectly reflective. If it absorbs even a tiny fraction of that incoming laser radiation it will convert that energy to heat instead of momentum. At 100 gigawatts, that means straight-up melting, which is generally considered not good for spacecraft. 

Once accelerated to one-tenth the speed of light, the real journey begins. For 40 years, this little spacecraft will have to withstand the trials and travails of interstellar space. It will be impacted by dust grains at that enormous velocity. And while the dust is very tiny, at those speeds motes can do incredible damage. Cosmic rays, which are high-energy particles emitted by everything from the sun to distant supernova, can mess with the delicate circuitry inside. The spacecraft will be bombarded by these cosmic rays non-stop as soon as the journey begins.

Is Breakthrough Starshot possible? In principle, yes. Like I said above, there's no law of physics that prevents any of this from becoming reality. But that doesn't make it easy or even probable or plausible or even feasible using our current levels of technology (or reasonable projections into the near future of our technology). Can we really make a spacecraft that small and light? Can we really make a laser that powerful? Can a mission like this actually survive the challenges of deep space?

The answer isn't yes or no. The real question is this: are we willing to spend enough money to find out if it's possible?

  • Building Sails for Tiny Interstellar Probes Will Be Tough — But Not Impossible
  • 10 Exoplanets That Could Host Alien Life
  • Interstellar Space Travel: 7 Futuristic Spacecraft to Explore the Cosmos

Learn more by listening to the episode "Is interstellar travel possible?" on the Ask A Spaceman podcast, available on iTunes and on the Web at http://www.askaspaceman.com . Thanks to @infirmus, Amber D., neo, and Alex V. for the questions that led to this piece! Ask your own question on Twitter using #AskASpaceman or by following Paul @PaulMattSutter and facebook.com/PaulMattSutter .  

Follow us on Twitter @Spacedotcom or Facebook . 

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: [email protected].

Paul M. Sutter is an astrophysicist at SUNY Stony Brook and the Flatiron Institute in New York City. Paul received his PhD in Physics from the University of Illinois at Urbana-Champaign in 2011, and spent three years at the Paris Institute of Astrophysics, followed by a research fellowship in Trieste, Italy, His research focuses on many diverse topics, from the emptiest regions of the universe to the earliest moments of the Big Bang to the hunt for the first stars. As an "Agent to the Stars," Paul has passionately engaged the public in science outreach for several years. He is the host of the popular "Ask a Spaceman!" podcast, author of "Your Place in the Universe" and "How to Die in Space" and he frequently appears on TV — including on The Weather Channel, for which he serves as Official Space Specialist.

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space travel escape speed

space travel escape speed

Hamblen Co. tortoise opens enclosure, leads owner on days-long slow-speed escape

A 15-year-old tortoise made a great escape from its home in Hamblen County recently, but the 120 lbs. reptile is now back with its owner.

According to one of the owners, he was going about his nightly routine when he noticed the gate had been opened, and Delbert was nowhere to be found.

The cunning tortoise was able to push the gate open himself, and his owners had no luck in their attempts to find him. Delbert's owners then made a post on social media, drawing in hundreds of people who offered to look for him. 

A post on social media by Renee Johnson asked people who had seen him to give him some fruit or lettuce and then to call her. 

"This will help keep him in one spot for a while and give us a chance to run over to get him," Johnson said. 

Soon after, Johnson issued an update that Delbert's whereabouts had been narrowed down. She also said he moves fast but was most likely hunkered down for the night under thick brush off Cain Mill. 

On Tuesday around 10:30 a.m., Johnson posted another update that Delbert had been brought home safely.

"He was found walking down the middle of Three Springs Rd," Johnson said on social media. "I think he was headed to Morristown to look for a mate!"

Johnson also thanked the men who saw Delbert and moved him out of the road. The men also stayed with him to be sure he didn't make another daring escape and called the sheriff who then called Johnson to get the missing tortoise. 

According to Johnson's husband, Charles, the two had Delbert for six years — ever since they rescued him in California. 

Backfill Image

Hurricane Beryl lashes Jamaica as its center brushes past island coast

Hurricane Beryl lashed Jamaica with strong winds and a deluge of rain and powerful waves before the Category 4 storm pulled away on a path that will take it near the Cayman Islands, officials said.

Beryl had maximum sustained winds of 140 mph as its center skirted the southern coast of the Caribbean nation of 2.8 million Wednesday afternoon, and by 11 p.m. its center was past the island and continuing west in the Caribbean,  the National Hurricane Center said .

The storm, which had made history as the strongest hurricane ever recorded in July before it was downgraded from Category 5 to Category 4, has been blamed for at least seven deaths as it devastated parts of the Windward Islands and caused flooding and damage in Venezuela.

No deaths have been reported in Jamaica, Prime Minister Andrew Holness said. He said the hurricane was moving quickly, "which is good for us. The quicker it moves, the better."

"Generally, I would say that we have not seen the worst of what could possibly happen," Holness said. "We still have a few hours to go."

Around 500 people in Jamaica were in shelters, Holness said. Authorities in the Cayman Islands also opened shelters.

The hurricane, with maximum sustained winds of around 130 mph, was forecast to pass just south of the Cayman Islands overnight into Thursday, the hurricane center said.

Meanwhile, in the U.S., with Beryl's path uncertain, state authorities in Texas have warned people in coastal areas to be prepared and "weather aware" over the holiday weekend in case tropical weather reaches the U.S.' Gulf Coast.

Gov. Greg Abbott on Wednesday directed the Texas Division of Emergency Management to issue a hurricane advisory notice to the Texas Emergency Management Council.

Abbott said the state "stands ready to deploy all available resources and support to our coastal communities."

Hurricane Beryl passes Dominican Republic

The storm has destroyed homes and devastated farms on islands across the Caribbean.

The small island nation of St. Vincent and the Grenadines was badly hit, with at least one person dead and more casualties feared. In Grenada, where at least three people have died, Prime Minister Dickon Mitchell said many homes had been destroyed and called the storm's effect "Armageddon-like." Venezuela was hit by heavy flooding, and at least three people have died there, with four more missing, President Nicolás Maduro said.

In Barbados, the fishing community and coastline were hit hard, Prime Minister Mia Mottley said. In a video shared on X, large waves crashed over a hotel balcony in Dover Beach.

On Monday, Beryl strengthened to a Category 5 hurricane, and early Tuesday its maximum sustained winds reached a record-breaking 165 mph, according to the National Hurricane Center, making it the strongest July hurricane on record.

Beryl has weakened as it has moved west across the Caribbean Sea toward the Gulf of Mexico — but it is still forecast to be at or near major hurricane status when it passes south of the Cayman Islands.

While the storm weakened slightly as it approached Jamaica, authorities made it clear that it is a major weather event that should not be taken lightly.

"If you live in a low-lying area, an area that is historically prone to flooding and landslide, or if you live on the banks of a river ... I implore you to evacuate to a shelter or to safer ground," Holness, Jamaica's prime minister, said in a video statement Tuesday.

Casey and Warner Haley, of Knoxville, Tennessee, were enjoying their honeymoon after they were married Saturday when they were told they needed to hunker down at their resort in Montego Bay.

"Yesterday morning it was perfect weather. We went snorkeling and we went kayaking, and by the time we got back, the forecast had changed," Casey, 23, said in a phone interview Wednesday.

The couple said they immediately contacted their travel agent but were told no flights were available. At the airport, they were told the same.

"It was quite literally doomsday-type level scenery," Casey said. "We went to all the flight counters, just saying, ‘Hey can you get us anywhere at all, particularly in the U.S., but literally just anywhere?’ And they all said, ‘No, we’re all booked.'"

The local grocery was packed, Casey said, describing it as "an absolute frenzy" with lines reaching to the back.

A mandatory evacuation has not been ordered at the resort, but a conference room has been opened for guests to ride out the hurricane.

Hurricane Beryl makes its way through the Caribbean

Holness said the country's security forces had plans to stop looting and other opportunistic crime once the hurricane has passed.

Fisherman Courtney Howell, of Kingston, told Reuters that Jamaicans were used to hurricanes.

"Well, this one is more dangerous than the one before. But this one, I mean, I’m not scared, because I’m used to them and I’ve been through many. So this one now coming is just another experience," he said.

Residents look out at a fallen tree after Hurricane Beryl hit St. James, Barbados.

By 11 p.m., the hurricane’s center was about 160 miles southeast of Grand Cayman, and the storm was moving west-northwest at 21 mph, the national hurricane center said.

“The Cayman Islands are sort of next in line for seeing significant impacts,” National Hurricane Center Director Michael Brennan said in a video update Wednesday afternoon.

Storm surge there could raise water levels by as much as 2 to 4 feet above normal tide levels, and rainfall totals could range from 4 to 6 inches, the hurricane center said.

The storm is projected to be a hurricane as it crosses the Yucatán Peninsula on Friday, the agency said, and it will then move into the Gulf of Mexico and threaten Mexico or southern Texas.

space travel escape speed

Patrick Smith is a London-based editor and reporter for NBC News Digital.

Minyvonne Burke is a senior breaking news reporter for NBC News.

space travel escape speed

Phil Helsel is a reporter for NBC News.

IMAGES

  1. Escape Speed

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  2. an image of the earth and space shuttles with caption that reads escape

    space travel escape speed

  3. relation between escape speed and orbital speed with a illustration

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  4. PPT

    space travel escape speed

  5. Escape Velocity

    space travel escape speed

  6. Escape Velocity: Rocket Leaving Earth into Outer Space Stock

    space travel escape speed

VIDEO

  1. Time travel escape room game level 39

  2. Time Travel Escape Level 2

  3. 45 уровень

  4. Time Travel Escape Level 15

  5. Time Travel Escape Level 8

  6. Time Travel Escape Level 1

COMMENTS

  1. Escape velocity

    Calculation. Escape speed at a distance d from the center of a spherically symmetric primary body (such as a star or a planet) with mass M is given by the formula = = where: G is the universal gravitational constant (G ≈ 6.67×10 −11 m 3 ·kg −1 ·s −2); g = GM/d 2 is the local gravitational acceleration (or the surface gravity, when d = r).; The value GM is called the standard ...

  2. Escape Velocity Definition and Formula

    Escape velocity is a fundamental concept in astrophysics and aerospace engineering, crucial for understanding the mechanics of space travel and celestial mechanics. Here is the definition of escape velocity, its nature as a speed rather than a velocity, its applications, the formula governing it, and a table of values for various celestial bodies.

  3. Escape velocity

    escape velocity, in astronomy and space exploration, the velocity needed for a body to escape from a gravitational centre of attraction without undergoing any further acceleration.The escape velocity v esc is expressed as v esc = Square root of √ 2GM / r, where G is the gravitational constant, M is the mass of the attracting mass, and r is the distance from the centre of that mass.

  4. Escape Velocity: Unraveling the Cosmic Speed Limit in Detail

    Understanding Escape Velocity. Escape velocity is a fundamental concept in physics that plays a crucial role in space travel and exploration. It refers to the minimum speed required for an object to break free from the gravitational pull of a celestial body, such as a planet or a star, and enter into space.In this article, we will delve into the definition of escape velocity, explore the ...

  5. Escape Velocity Calculator

    Follow these steps to calculate escape velocity: Take the gravitational constant (G=6.674 ×10 −11 N⋅m 2 ⋅kg -2) and multiply it by the mass of the celestial object you're trying to escape; Multiply the result by 2; Divide the result by the distance from the center of that mass; and. Put the result under a square root.

  6. What is escape velocity?

    Escape velocity is the speed that an object needs to be traveling to break free of a planet or moon's gravity well and leave it without further propulsion. For example, a spacecraft leaving the surface of Earth needs to be going 7 miles per second, or nearly 25,000 miles per hour to leave without falling back to the surface or falling into ...

  7. Learn How Escape Velocity Works and How to Calculate ...

    The speed required to break free of an orbit is known as escape velocity. It takes a certain level of velocity for an object to achieve orbit around a celestial body such as Earth. It takes even greater velocity to break free of such an orbit. When astrophysicists design rockets to travel to other planets—or out of the solar system entirely ...

  8. Space Travel Calculator

    Explore the world of light-speed travel of (hopefully) future spaceships with our relativistic space travel calculator! If you're interested in astrophysics, check out our other calculators. Find out the speed required to leave the surface of any planet with the escape velocity calculator or estimate the parameters of the orbital motion of ...

  9. PDF Lecture 14: Gravitational potential energy and space travel

    Example: Escape speed from orbit =1.99 × 10 30 kg = 1.50 × 10 11 m = 6.67 × 10 -11 N m2/kg2 𝑐= 2 𝐸 =42,000 / Speed necessary to escape gravitational field of the Sun when object is launched from Earth:

  10. Escape Speed

    (A space mission has traveled to Bennu to retrieve some of its surface material to return to Earth.) Sirius B is a star that has roughly the radius of Earth, but has a mass that is close to the mass of the Sun (about 333,000 times the mass of Earth). What is the escape speed of Sirius B? Answers. The escape speed would increase by a factor of 3.

  11. Escape Velocity Calculator

    Escape velocity is the speed needed to break free from a planet or star's gravity. It is crucial for spacecraft to launch successfully. Our Escape Velocity Calculator figures out this speed. It uses a formula based on the planet's mass, size, and the pull of gravity, like 6.674×10−11N⋅m²/kg². Known as the second cosmic velocity, it ...

  12. Escape Speed

    The escape speed of the earth at the surface is approximately 11.186 km/s. That means "an object should have a minimum of 11.186 km/s initial velocity to escape from earth's gravity and fly to infinite space." Ideally, If you can jump with initial velocity 11.186 km/s you can tour outer space!

  13. orbital mechanics

    Solar system's orbital velocity is estimated at roughly 220 km/s, and galactic escape velocity for our vicinity at about 537 km/s. So in the direction of Solar system's velocity vector, velocity required to escape Milky Way is ~ 317 km/s. And much more, if this Solar system's own orbital momentum cannot be used to full extent and a launch in ...

  14. Escape Velocity of Earth

    The official name for this speed is called the "escape velocity". If a spacecraft is launched from a pad on the surface of the earth with this speed or greater, it will escape the Earth's gravitational field. The escape velocity can be calculated from the Earth's mass, its radius, and Newton's gravitational constant G: v_esc=sqrt(2*G*M/R).

  15. How fast does a rocket have to travel to get into space?

    This really depends on what you mean by "into space." If you just want to get into orbit around the Earth, you need to reach speeds of at least 4.9 miles per second, or about 17,600 miles per hour. If you want to completely escape Earth's gravity and travel to another moon or planet, though, you need to be going even faster - at a speed of at ...

  16. forces

    You're absolutely correct - objects do not need to ever reach earth's escape velocity of 11.2 km/s, and many spacecraft that leave orbit, don't.. That being said, note that escape velocity depends on where you are: the velocity that a cannonball 1000 km above the earth's surface would need to escape is substantially lower than that needed by a cannonball on the surface.

  17. Escape Speed

    Escape Speed. If you throw an object up in the air, it generally comes back down. How fast would you have to throw it so it never came back down? Ignore air resistance. The minimum speed required to escape from a planet's gravitational pull is known as the escape speed.

  18. Interstellar travel

    Interstellar travel is the hypothetical travel of spacecraft from one star system, solitary star, or planetary system to another. Interstellar travel is expected to prove much more difficult than interplanetary spaceflight due to the vast difference in the scale of the involved distances. Whereas the distance between any two planets in the Solar System is less than 55 astronomical units (AU ...

  19. Is Interstellar Travel Really Possible?

    Once accelerated to one-tenth the speed of light, the real journey begins. For 40 years, this little spacecraft will have to withstand the trials and travails of interstellar space. It will be ...

  20. interstellar travel

    Travel on land requires the constant burning of fuel to be able to replace the speed lost to friction, air resistance, etc. Travel in space doesn't work the same way, it doesn't require a constant burning, it requires you burn enough fuel to propel the mass to that initial speed, then enough to burn in reverse to slow itself down at its ...

  21. Delbert's Daring Dash

    A 15-year-old tortoise made a great escape from its home in Hamblen County recently, but the 120 lbs. reptile is now back with its owner. According to one of the owners, he was going about his ...

  22. Hurricane Beryl lashes Jamaica as its center brushes past island coast

    Hurricane Beryl lashed Jamaica with strong winds and a deluge of rain and powerful waves before the Category 4 storm pulled away on a path that will take it near the Cayman Islands, officials said ...