If you know the mass of a star and a planet

Question

Question

Answer 1

Answer #1

conservation of angular momentum:

L1 = L2

==> m r1 v1 = m r2 v2

==> r1 v1 = r2 v2

==> r2 = r1 v1/v2 = 5.1e10 * 7e4/v2 = 3.57e15/v2

conservation of energy:

1/2 m v1^2 + G M m/r1 = 1/2 m v2^2 + G M m/r2

==> 1/2 v1^2 + G M/r1 = 1/2 v2^2 + G M/r2

==> 1/2 v1^2 + G M/r1 = 1/2 v2^2 + G M/(3.57e15/v2)

==> 1/2 * 7e4 * 7e4 + 6.673e-11*1.9891e30/5.1e10 = 1/2 * (v2)^2 + 6.673e-11*1.9891e30/(3.57e15/(v2))

==> 5052600843 = 1/2 * (v2)^2 + 37180 (v2)

==> v2 = 70000.00787 m

==> v2 = 7.0 x 10^4 m

Answer 2

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