21. A meteoroid fragment is in circular orbit around moon B at a small altitude

Question

21. A meteoroid fragment is in circular orbit around moon B at a small altitude h above the surface. The altitude h is a very small fraction of the radius of the moon. What is the speed of the fragment? Note: The constant of universal gravity (G) equals 6.674 × 10-11 N m2/kg2.

440 m/s

220 m/s

320 m/s

640 m/s

880 m/s

Moon

Mass

Radius

Orbital radius

Orbital period

A

4.0 × 1020 kg

2.0 × 108 m

4.0 × 10 6 s

B

1.5 × 1020 kg

2.0 × 10 5 m

3.0 × 108 m

440 m/s

220 m/s

320 m/s

640 m/s

880 m/s

Moon

Mass

Radius

Orbital radius

Orbital period

A

4.0 × 1020 kg

2.0 × 108 m

4.0 × 10 6 s

B

1.5 × 1020 kg

2.0 × 10 5 m

3.0 × 108 m

Explanation / Answer

By Kepler’s third law,

T^2 = [(4^2)/(GM)]*r^3

T^2 = [(4*3.14^2)/(6.67*10^-11*1.5*10^20)]*(2.0*10^5)^3

Simplifying T = 5616 s

v= 2r/T = (2*3.14*2.0*10^5)/ 5615.6 = 223.6 m/s = 220 m/s

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