What is the minimum initial velocity necessary for an object to leave Earth?

The problem can be easily solved using energy formulas. The only force that acts on the departing object is the gravitational force, which is conservative. Therefore the total energy is conserved on the trajectory:E=mv2/2-GmM/r=ct.The energy on the surface of the planet is:E=mv2i/2-GmM/R where vi is the initial velocity and R is the radius of Earth.At infinity(where the objects eventually gets since it leaves Earth):E=mv2f/2 where vf is the final velocity, which will be set to 0 in order to minimise the initial velocity.Equating the energies of the two positions we get:mv2i/2-GmM/R=0vi=(2GM/R)1/2 After introducing the values for the gravitational constant, mass and radius of Earth we get the final velocity:vi=11.2 km/s

Answered by Leontica S. Physics tutor

1736 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

What is the definition of the photoelectric effect?


A yacht is sailing through water that is flowing due west at 2m/s. The velocity of the yacht relative to the water is 6m/s due south. The yacht has a resultant velocity of V m/s on a bearing of theta. Find V and theta


Topic - force as rate of change of momentum; (i) force on a wall due to water from a hose, (ii) force on a table as a rope is dropped onto it.


What's the difference between inertial and gravitational mass?


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