(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A package with mass m sits on an airless asteroid of mass M and radius R. We want to launch a package straight up in such a way that its speed drops to zero when it is a distance 4R away from the center of the asteroid, where it's picked up by a waiting ship before it can fall back down. We have a powerful spring whose stiffness is Ks. How much must we compress the spring?

2. Relevant equations

I'm not quite sure what equations to use, except I'm almost positive we're going to use U(spring)= 1/2*Ks*s^2, where s is the abs value of the stretch/compression.

Maybe also use:

F(grav)=-G((M*m)/(|r21|^2))*rhat, where |r21| is the magnitude of the difference of locations between these two objects

or:

U(grav)=-G(M*m)/|r21|

3. The attempt at a solution

I know that the answer is: stretch=sqrt((3*G*m*M)/(2*R*Ks))

I just can't figure out how to get there. I assumed that the way we got the "3" on the top was due to the actual distance between them was 3R (since 1R was the actual radius of the asteroid.

please help!

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# Compression of a Spring on an Asteroid?

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