MULTIPLE CHOICE: In another solar system, Star X has twice the mass of our sun.

Question

MULTIPLE CHOICE: In another solar system, Star X has twice the mass of our sun. A planet the same size and mass of earth is in orbit around Star X at the same orbital distance from star X that earth is from the sun. The orbital speed of this planet around Star X relative to that of earth around the sun is as follows.

b. The planet will orbit at 2 times that of the earth

c. The planet will orbit at the same as that of the earth.

d. The planet will orbit at 1/2 times that of the earth

e. Need to know the mass of the planet relative to earth.

PLEASE EXPLAIN THE ANSWER

Explanation / Answer

Fx = G 2 M m / R^2    the gravitational attraction
Fe = G M m / R^2
Fx / Fe = 2
Fx = m Vx^2 / R       the centripetal force
Fe = m Ve^2 / R
Vx^2 / Ve^2 = Fx / Fe = 2
Vx = 2^1/2 Ve

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