You Have Discovered a New Asteroid, Which Has a Moon

Multiple Choice

You have discovered a new asteroid, which has a moon in an elliptical orbit around it. From a series of observations, you establish that the closest approach occurs when the moon is 51,000 m from the asteroid, the furthest separation is 102,000 m, and the speed of the moon at the point of closest approach is 7.50 m/s. What is the mass of the asteroid? G = 6.67 x 10^-11 N·m²/kg².

A) 4.25 × 10¹⁶ kg
B) 9.87 × 10¹⁶ kg
C) 3.22 × 10¹⁶ kg
D) 2.04 × 10¹⁶ kg
E) 5.05 × 10¹⁶ kg