MYTUTOR SUBJECT ANSWERS

1736 views

Derive the escape velocity from the surface of a planet with radius, r, and mass, M.

This question is about converting kinetic energy into gravitational potential energy. Escape velocity is the speed required to leave the gravitational field of a mass, in this case it's a planet. In other words the body has to be moving at such a velocity that it will reach a point infinitely far away from the planet.

The gravitational potential energy (PE) at any given point is given as:

PE = -GMm/r

Where G is Newton's gravitational constant; M is the mass of the planet; m is the mass of the body moving away from the planet and r is the distance from the centre of the planet/gravitational field.

Using this formula the potential energy at a distance infinitely far away (infinity) is 0. At the surface of the planet the potential energy is:

-GMm/r

This means that in order to get from the surface to infinity there will be a gain of

GMm/r

This will come from the kinetic energy of the body escaping.

Kinetic Energy (KE) is given as:

KE = mv2/2 

Where m is the mass of the moving body and v is it's velocity.Now we have all we need to solve this problem

If we set the kinetic and potential energy equal to each other:

KE = PE

mv2/2 = GMm/r 

Divide by m on both sides, this gets rid of all mentions of m. That means the final answer will not depend on the mass leaving the planet at all! 

v2/2 = GM/r 

Rearrange: 

v = sqrt(2GM/r)

sqrt() means take the square root of what is inside the bracket.

Interesting related fact: 

A black hole is an object that has an escape velocity that is greater than the speed of light. This means not even light can escape the gravitational pull of a black hole!!!

Thomas R. Uni Admissions Test -Oxbridge Preparation- tutor, A Level P...

2 years ago

Answered by Thomas, who tutored A Level Physics with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

81 SUBJECT SPECIALISTS

Timothy N. A Level Design & Technology tutor, GCSE Design & Technolog...
£26 /hr

Timothy N.

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Physics, Science+ 3 more

Physics
Science
Maths
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my years of experience tutoring, we will be able to surpass the grades you want!”

£30 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Physics, Maths+ 1 more

Physics
Maths
Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£24 /hr

James T.

Degree: Chemical Engineering (Masters) - Bath University

Subjects offered:Physics, Maths+ 2 more

Physics
Maths
Chemistry
-Personal Statements-

“Second year Engineer. I love problem-solving and hard work! Everyone works differently and I will find the best way for you to learn and make sessions fun!”

About the author

£20 /hr

Thomas R.

Degree: Physics (Bachelors) - Oxford, Magdalen College University

Subjects offered:Physics, Maths+ 1 more

Physics
Maths
Further Mathematics

“Oxford physics student at Magdalen College. Here to help with Physics and Maths all the way up to A level.”

MyTutor guarantee

You may also like...

Other A Level Physics questions

How to solve horizontally-launched projectile motion problems using equations of motion?

How would you integrate ln(x)

A student is measuring the acceleration due to gravity, g. They drop a piece of card from rest, from a vertical height of 0.75m above a light gate. The light gate measures the card's speed as it passes to be 3.84 m/s. Calculate an estimate for g.

An electrical heater supplies 500J of heat energy to a copper cylinder of mass 32.4g Find the increase in temperature of the cylinder. (Specific heat capacity of copper = 385 J*kg^-1*Celsius^-1

View A Level Physics tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok