Physics
posted by Crystal
So this is the problem:
A comet is in an elliptical orbit around our Sun. At its point of closest approach, it is moving at 6.3x10^4 m/s and is 4.2x10^10m away from the sun. When it is at the farthest distance, 7.5x10^12m away, how fast is it going?
This is what I did
K1+U1=K2+U2 (since energy should be conserved)
so...
1/2m1v1^2 + Gm1m2/r1 = 1/2m1v2^2 + Gm1m2/r2
the m1 cancel since all of them have it
1/2v1^2 + Gm2/r1 = 1/2v2^2 + Gm2/r2
then I rearranged to get v2 by itself
1/2v1^2 + Gm2/r1 + Gm2/r2 = 1/2v2^2
*2 *2
(v1)^2 +2Gm2/r1 + 2Gm2/r2 = (v2)^2
(v1)^2 + 2Gm2/r2 2Gm2/r1 = (v2)^2
simplified it
(v1)^2 + (2Gm2 (1/r2  1/r1))= (v2)^2
and then square root for the final equation to be
((v1)^2 + (2Gm2 (1/r2  1/r1)))^.5 = (v2)
Then I plugged in the numbers
v1 = 6.3x10^4
G= 6.67x10^11
r2= 7.5x10^11
r1= 4.2x10^10
m2 (mass sun) = 2x10^30
But when I plugged all this in to solve for v2 I got a negative number under the square root. Where did I go wrong? Is my math right? Did I set up the equations right?

Damon
How about we write +  as just 
:)
whoops typo = ten times further
r2= 7.5x10^11
should be
r2= 7.5x10^12
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