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?

  1. 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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