escape velocity from a planet?

Question

I need some help trying to figure out how to find the escape velocity from a planet. If i have the radius of the planet, and the gravitational acceleration speed yet no masses of the planet or the object to be fired upwards, which equations should i be using to find the escape velocity ?
Thanks.

Answer 1

I never memorize the formula, but it's easy to derive.

Kinetic Energy = Gravitational Potential Energy

1/2mv^2 = GmM/r

cancel m (the mass of the object) and get v = sqrt (2GM/r).

Now, you have no M, but you do have g (acceleration due to gravity) and r, so you can solve for M.

Gravitational acceleration = GmM/r^2 = mg

Once again, cancel m and M = gr^2/G. plus that into the equation for escape velocity.

= sqrt (2GM/r)=sqrt(2gr).

Answer 2

permit Earth's get away velocity be v = eleven.2E3 mps = sqrt(Gm/r) and V = ? = sqrt(G4m/2r) be the get away velocity on that different planet. m and r are Earth's mass and radius. G is the gravitational consistent. Then V = sqrt(G4m/2r//Gm/r) v = sqrt(2)*eleven.2E3 = 15839.2 mps. ANS. hint. while comparing like aspects, the right innovations-set is to apply the ratio, like V/v. That way distinctive aspects will cancel out, like G, m, and r to that end.

Answer 3

Use with calculus Newton's laws of motion and Newton's law of universal gravitation

Answer 4

Here's the formula. Use it.

http://en.wikipedia.org/wiki/Escape_velocity#Calculating_an_escape_velocity