You throw a rock with an initial horizontal velocity and it hits the ground at x

Question

You throw a rock with an initial horizontal velocity and it hits the ground at x meters away from your feet. What if:

(a) You throw the same stone with the same initial conditions but instead you do this on a another planet with a mass 3 times the mass of the earth. With what factor will x change?

(b) You throw the same stone with the same initial conditions but instead you do this on a another planet with a radius 7 times the radius of the earth. With what factor will x change?

AND

You are making a trip in a space shuttle, and your friend Jimmy is in another space shuttle. He shares the same circular orbit with you, which is 410 km above the Earth, but he is 22 km ahead of you.

(a) How long will it take you to catch up with your friend if you reduce your orbital radius by 0.8 km? ("Catch up" here means to lie along a line that passes through the center of the earth.)

(b) By how much must you reduce your orbital radius to catch up in 10 hours?

Explanation / Answer

g=GM/r

x=u2/2g

if M is 3 times,g is 3 times, x reduces 3 times

if r is 7 times, g reduces 7 times, x increase 7 times

v=square root of GM/r

a) T2+24/v2=T1

T=2*pi*square root of r3/Gm

b) in this case T2+v2+6=T1

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