MYTUTOR SUBJECT ANSWERS

851 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

47 SUBJECT SPECIALISTS

£24 /hr

Ashleigh H.

Degree: Physics (Masters) - University College London University

Subjects offered: Physics, Science+ 2 more

Physics
Science
Maths
Chemistry

“ I believe tutoring isn't just about helping a student get to grips with the content of their course, but also building their confidence and exam technique”

£30 /hr

Louis S.

Degree: Mathematics (Bachelors) - Cambridge University

Subjects offered: Physics, Maths+ 6 more

Physics
Maths
Further Mathematics
Extended Project Qualification
.STEP.
.MAT.
-Personal Statements-
-Oxbridge Preparation-

“ second year undergraduate at the University of Cambridge, studying for a B.A. in Mathematics, having received A*s in A-Level Mathematics, Further Mathematics (Edexcel) and Physics (AQA)”

£20 /hr

Hafsah K.

Degree: Mechanical Engineering (Masters) - Nottingham University

Subjects offered: Physics, Maths+ 1 more

Physics
Maths
Chemistry

“About Me:  I study Mechanical Engineering at the University of Nottingham. Maths and science have always been my favourite subjects, and I hope to share my passion for them with you! I have hadprevious experience in tutoring with two ...”

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

If the highest frequency a song is 10 kHz and it is encoded at 16 bits per sample what is the minimum number of bytes needed to encode the 3 minute song?

What is the Doppler Effect?

Why is Kinetic Energy mv^2/2?

How can an object be accelerating if it does not change in speed?

View A Level Physics tutors

Cookies:

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

mtw:mercury1:status:ok