Beings on spherical asteroid Î have observed that a large rock is approaching th

Question

Beings on spherical asteroid Î have observed that a large rock is approaching their asteroid in a collision course. At 5747 km from the center of the asteroid, the rock has a speed of 201 m/s and later at 1507 km it has a speed of 370 m/s. Use energy conservation to find the mass of asteroid Î . You can neglect any effects due to the parent star of the asteroid. (G = 6.67 × 10-11 N · m2/kg2)

A. 1.478 × 10^20 kg

B. 2.956 × 10^27 kg

C. 1.972 × 10^28 kg

D. 1.478 × 10^21 kg

Thank you! Please show all work and specify the correct answer choice at the end.

Explanation / Answer

by conservation of energy

initial energy = final energy

gravitational potential energy + kinetic energy = gravitational potential energy + kinetic energy

gravitational potential energy = -G * m1 * m2 / r

so,

-G * m1 * m2 / r1 + 0.5 * m1 * v1^2 = -G * m1 * m2 / r2 + 0.5 * m1 * v2^2

-G * m2 / r1 + 0.5 * v1^2 = -G * m2 / r2 + 0.5 * v2^2

6.67 * 10^-11 * m2 / (5747 * 10^3) + 0.5 * 201^2 = 6.67 * 10^-11 * m2 / (1507 * 10^3) + 0.5 * 370^2

m2 = 1.478 * 10^21 kg

mass of asteroid = 1.478 * 10^21 kg

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