What is the total energy of a spaceship of mass m, orbiting a planet of mass M in a circular orbit with radius r? The ship and the planet are taken to be an isolated system.

 In the non-inertial frame of reference of the spaceship, a centrifugal and a gravitational force acts on the spaceship. If its mass is m and the positive direction is radially outwards, we have:

F= -GmM/r2 -  gravitational force(G is the gravitational constant)

F= mv2/r - centrifugal force(v is the spaceship's velocity)

the spaceship's orbit is of fixed radius, so it doesn't move radially, thus there is no radial acceleration, when all forces are taken into account. From Newton's second law we have:

F+ F= ma = 0 - here a is the acceleration of the ship

=> mv2/r - GmM/r= 0

v= GM/r      (1)

The ship has kinetic and potential energies, which are given by the equations:

E= mv2/2 = GmM/2r - kinetic energy with the substitution from equation (1)

E= -GmM/r - potential energy, which is only the gravitational potential energy, since there are no other force fields

The total energy is then:

E = E+ E= GmM/2r -  GmM/r = -GmM/2r

Answered by Ivan D. Physics tutor

2249 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

Use the kinetic theory of gases to explain why the pressure inside a container increases when the temperature of the air inside it rises. Assume that the volume of the container remains constant.


A truck with mass 1200kg is moving at 8m/s when it collides head-on with a stationary car of mass 800kg. As they collide, the vehicles move together with the same velocity, v. Calculate this velocity.


What is the maximum height a pole vaulter could reach?


A satellite is in a stationary orbit above a planet of mass 8.9 x 10^25 kg and period of rotation 1.2 x 10^5 s. Calculate the radius of the satellite's orbit from the centre of the planet.


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