Using Newton's law of gravitation, derive a suitable formula for the escape velocity of an object at Earth's surface.

Newton's law of gravitation is;
F = GMm/(r2)
Where G is the Universal Gravitational constant, M is the mass of Earth, m is the mass of the object and r is the radius of Earth (no values are needed for this as we are simply deriving a formula, not working out a solution)
We can equate this force to the centripetal force experienced by an object at Earth's surface. This is because the centripetal force is what keeps an object in circular motion, acting towards the centre of the circle. It can be thought of as the force pulling us in toward the centre of the Earth, which we know is gravity so therefore is the same as the force given in Newtons law.
F = m(v2)/r (centripetal force)
Therefore;
GMm/(r2) = m(v2)/r
Dividing by m and multiplying by r
GM/r = (v2)
v = (GM/r)1/2where v is the escape velocity

Answered by Charlie M. Physics tutor

4753 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

What is the general equation for the alpha-decay of a nucleus X, with nucleon number A and proton number Z, into nucleon Y??


Using Newton's law of universal gravitation, show that T^2 is proportional to r^3 (where T is the orbital period of a planet around a star, and r is the distance between them).


With the help of a suitably labelled graph, explain what is meant by resonance of a mechanical system.


How can we explain the standing waves on a string?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences