What is the escape velocity for a body on the surface of a planet on which the acceleration

Artist’s conception of NASA’s Space Launch System (NASA).

Why do a baseball and a rocket need the same launch speed to get from Earth into space? It has to do with physics and gravitational force.

In early 2018, Elon Musk made headlines by launching his Tesla Roadster into space, playing David Bowie’s “Starman” on repeat as it made its slow journey through space. This was a fun publicity stunt. But how the Roadster got to space is an even cooler story.

The Roadster hitched a ride on the newest SpaceX rocket, the Falcon Heavy, as it made its maiden voyage into space. At the time of its launch, the Falcon Heavy was the most powerful operational rocket in the world (though not in history).

Did you know?

The Falcon Heavy weighs almost 1.5 million kilograms! 

How do you launch something into space?

You might be wondering about how hard it is to launch something that large. How fast does it need to go? Surprisingly, getting anything into deep space (beyond the Earth’s orbit) from the surface of the Earth—the Falcon Heavy, a Roadster, or even a baseball—requires the same launch speed. This speed is called escape velocity, since it’s just enough speed to escape the gravitational pull of the Earth. 

But why is the escape velocity the same, no matter the mass of the object? The reason is that mass and escape velocity are not related. For example, say you wanted to drive 100 km in an hour. It would not matter if you were driving a tiny car or a big transport truck. You would still need to drive at a speed of 100 km/h to reach this goal.

So what exactly is the escape velocity from the surface of the Earth? It is a whopping 11.2 km/s (kilometres per second). That’s more than 40 000 km/h. At that speed, you could travel from the North Pole to the South Pole in about 21 minutes!

Misconception Alert

Going into Space vs. Escape Velocity

Most satellites and spacecraft sent into space do not reach escape velocity! Space is usually considered to start at an altitude of 100 km (this is known as the Kármán line). If a rocket goes fast enough and high enough to enter space but does not reach escape velocity, it will enter orbit around the Earth. The International Space Station and many satellites orbit the Earth.

How do you calculate escape velocity?

Escape velocity depends on a number of factors. Let’s take a step back for a moment. Scientists have determined that the escape velocity for any large object (such as a planet or star) can be calculated from the following equation:

ve = √(2GM/r)

The M in the equation represents the mass of the planet. Planets with more mass are harder to escape than planets with less mass. This is because the more mass a planet has, the stronger its force of gravity. For example, when you watch footage of astronauts jumping on the Moon, it looks effortless. This is because the Moon’s mass (and therefore its gravity) is much less than Earth’s. 

Did you know?

As of 2019, only 24 humans have ever reached escape velocity. They were the crews of the Apollo missions that flew to the Moon between 1968 and 1972.

The r in the equation represents radius, which is the distance between the centre of the planet and the object that is trying to escape. In other words, radius is the distance between the centre of the planet and its surface. As an object moves away from the planet, the planet’s gravitational pull will have less of an influence on it. If the object moves far enough away, it feels almost no attraction. When this happens, the escape velocity will basically be zero! 

Finally, the G in the equation is a constant. Specifically, it is Newton’s universal constant of gravity. For the moment, all you need to know is that we need this constant to make the equation work. G is approximately equal to 6.67 × 10–11 metres3/(kg)(second)2.

Now, let’s plug in some numbers to determine the escape velocity from the surface of the Earth. For M, we use the mass of the Earth, which is approximately 5.97 × 1024 kg.

For r, since we are calculating the escape velocity from the surface of the Earth, we can use the Earth’s radius, which is approximately 6.37 × 106 m.

We can now calculate the escape velocity for the Earth:

Escape velocity equals the square roots of 2GM over r which equals the square root of 2 times 6.67 times ten to the minus eleven times 5.97 times ten to the twenty fourth over 6 378 000, which equals approximately 11.2 kilometers per second.

You can calculate the escape velocity from any body in space as long as you know its radius and its mass. For example, using the above equation, we can calculate the escape velocity of the Moon. From its equator, the Moon has a radius of 1 738 km. It also has an estimated mass of 7.342 × 1022 kg. This means that the Moon’s escape velocity is 2.38 km/s. That is much less than the 11.2 km/s it takes to get off the Earth. In the future, perhaps rockets will be built on and take off from the Moon rather than from Earth!

The escape velocity of Mars is 4.25 km.s. The escape velocity of Earth is 11.19 km/s. The escape velocity of Venus is 10.36 km/s. The escape velocity of Mars is 5.03 km/s. The escape velocity of Saturn is 36.09 km/s. The escape velocity of Uranus is 21.38 km/s. The escape velocity of Neptune is 23.56 km/s. The escape velocity of Jupiter is 60.20 km/s.

We’ve taken a first glimpse at the rocket science needed to get the Falcon Heavy (and a Roadster playing David Bowie) into space. All we need to do is accelerate the rocket to 11.2 km/s and point it upwards. As the scientists and engineers at SpaceX know well, acceleration and pointing the rockets are the hard part! 

Did you know?

As of 2019, the most powerful rocket ever made was NASA’s Saturn V. It was the rocket used to get astronauts to the Moon in the 1960s and 1970s.

• Have you watched a rocket launch before? Have you heard the launch team talk about boosters firing and boosters falling away? What do you think is the purpose of boosters? 
• If you could launch something into space, what would you choose? Why?
•  

• What would be the advantage, from an escape velocity perspective, of sending spacecraft to Mars from the Moon or a space station?
• What are the advantages and disadvantages of reusable rocket boosters like the Falcon Heavy compared to older rockets like the Saturn V for sending spacecraft beyond Earth orbit?
• What would the advantages and disadvantages of launching spacecraft to the Moon or Mars from low Earth orbit (e.g., from the International Space Station) vs. from the surface of the Earth? Would the benefits outweigh the costs?
•  

• What is escape velocity? Is escape velocity actually a velocity? Explain.
• How does the size of planetary body impact on its escape velocity?
• Does there come a point where a mass is too large to get off the Earth? Explain.
•  

• Is the cost and risk of sending spacecraft beyond Earth orbit justified by the scientific gains?

• What media you seen heard or read about the Falcon Heavy? What types of media were used by SpaceX to promote the lift-off event? What audiences is the company targeting? How does the media from SpaceX differ from the media produced by NASA? 
• Does a media stunt such as launching a car into space help raise awareness of and support of space exploration?

• This article and embedded video can be use for Physics and Space Science teaching and learning related to planetary science. Concepts introduced include rocket, escape velocity, mass (M), radius (r), center, distance and Newton’s universal constant of gravity (G). 
• After reading this article, teachers could have students consolidate their understanding of escape velocity using a Concept Definition Web learning strategy. Ready-to-use Concept Definition Web reproducibles are available in [Google doc] and [PDF] formats.
• For a math and physics focus and follow-up to reading this article, teachers could have students calculate the escape velocity for the other planets, given their mass and radius measurements. Their answers could be checked using the graphic in the article titled Escape Velocities from Planets in our Solar System.

• Have you watched a rocket launch before? Have you heard the launch team talk about boosters firing and boosters falling away? What do you think is the purpose of boosters? 
• If you could launch something into space, what would you choose? Why?
•  

• What would be the advantage, from an escape velocity perspective, of sending spacecraft to Mars from the Moon or a space station?
• What are the advantages and disadvantages of reusable rocket boosters like the Falcon Heavy compared to older rockets like the Saturn V for sending spacecraft beyond Earth orbit?
• What would the advantages and disadvantages of launching spacecraft to the Moon or Mars from low Earth orbit (e.g., from the International Space Station) vs. from the surface of the Earth? Would the benefits outweigh the costs?
•  

• What is escape velocity? Is escape velocity actually a velocity? Explain.
• How does the size of planetary body impact on its escape velocity?
• Does there come a point where a mass is too large to get off the Earth? Explain.
•  

• Is the cost and risk of sending spacecraft beyond Earth orbit justified by the scientific gains?

• What media you seen heard or read about the Falcon Heavy? What types of media were used by SpaceX to promote the lift-off event? What audiences is the company targeting? How does the media from SpaceX differ from the media produced by NASA? 
• Does a media stunt such as launching a car into space help raise awareness of and support of space exploration?

• This article and embedded video can be use for Physics and Space Science teaching and learning related to planetary science. Concepts introduced include rocket, escape velocity, mass (M), radius (r), center, distance and Newton’s universal constant of gravity (G). 
• After reading this article, teachers could have students consolidate their understanding of escape velocity using a Concept Definition Web learning strategy. Ready-to-use Concept Definition Web reproducibles are available in [Google doc] and [PDF] formats.
• For a math and physics focus and follow-up to reading this article, teachers could have students calculate the escape velocity for the other planets, given their mass and radius measurements. Their answers could be checked using the graphic in the article titled Escape Velocities from Planets in our Solar System.