What is gravitational potential and how can gravitational potential energy be used to estimate the escape velocity of a planet of mass m and radius r?

The graviational potential at a point in space is the work done to move a unit mass from infinite (very far away) to the point in question. The gravitational potential V at a point outside a single spherically-symmetric planet is calculated by V = -GM/r, where G is Newton's gravitational constant = 6.67x10^-11 Nm^2kg^-2, M is the mass of the planet and r is the distance from the centre of the planet.
The escape velocity is the speed an object must have so that it can escape a planet's gravitational field from its surface. By conservation of energy, we know that KE1 + PE1 = KE2 + PE2 (KE = kinetic energy, PE = potential energy). The (gravitational) potential energy of an object is the gravitational potential multiplied by its mass (m), so PE = -GMm/r. It's kinetic energy is KE (1/2)mv^2, as usual. KE1 and PE1 are the energies at the surface of the planet (i.e. a distance r from its centre) while KE2 and PE2 are the energies at infinite distance. PE2 is 0 by definition, since no work is required to move the object to infinite from infinite. For the object to escape, KE2 must be at least 0 (not less than 0), so(1/2)m (v_esc)^2 + -GMm/r = 0 + 0This solves to v_esc = (2GM/r)^(1/2).

Answered by Physics tutor

5169 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

Describe energy transformations in a oscillating pendulum, which undergoes simple harmonic motion. How this implies the velocity at critical (lowest and highest) points?


From the 2016 OCR B paper A ball is thrown at an angle of 30 Degrees to the horizontal. The initial kinetic energy of the ball is K. Air resistance is negligible. What is the kinetic energy of the ball at the maximum height.


If a bulb has a current of 20mA and voltage of 5V, and the current cost of electricity is £3 for a kW/hour. How much money would you spend to power the bulb for 8 hours? Are these good estimates for the current, voltage and cost of electricity?


The Large Hadron Collider (LHC) of circumference 27km uses magnetic fields to accelerate a proton repeatedly in a circular path. Calculate the flux density of a uniform magnetic field required for the proton to travel at a tenth of the speed of light.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning