Asteroid Orbits: Finding r with Kepler's Laws

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sya deela
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Homework Statement


An asteroid of mass m is in circular orbit of radius r around the sun with speed v.It has an impact with another asteroid of mass M and is kicked into a new circular orbit with a speed 1.5v.What is the radius of the new orbit in terms r?[/B]

Homework Equations

(v1)^2/(v2)^2 = (r2)^2 / (r1)^2[/B]

The Attempt at a Solution

is it using equations based on kepler's second law or third law.[/B]
 
Hi sya, and welcome to Physics Forums!

You need to provide a more detailed attempt and show your work. Let us assume that your idea is correct, how would you use that to find the new radius?
 
is it correct?i used based on kepler's third law.
 
Attachments
  • Handwritten derivation on white paper: v_new = 1.5v, r_new = ?, F = ma with a = v^2/r, then GMm/r^2 = mv^2/r, simplifying to GM/r^2 = v^2/r, then GM/r = v^2, giving v^2 = 1/r with GM constant.
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  • Handwritten derivation on lined paper: v_new squared over v squared equals (1/r_new) over (1/r), then v_new squared over v squared equals r over r_new, then 1.5 squared times v squared over v squared equals r over r_new, giving 2.25 = r over r_new, so r_new = r over 2.25 = 0.44 r.
    2014-11-14 22.16.43.jpg
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What you have used is Newton's gravitational law, not Kepler's laws. Also, we generally do not allow posting problems or attempted solutions as image attachments or links as it requires significantly more efforts from helpers. If you want people to help you, you should make the minimal effort of typing out the full problem and your full attempt at a solution in-forum. Please refer to the Guidelines for Students and Helpers as well as the Physics Forums General Guidelines for more information.