Mass Radius Orbital Radius Orbital Period Moon 1 2.5x1015 kg Unknown 5x1010 m 5

Question

Mass

Radius

Orbital Radius

Orbital Period

Moon 1

2.5x1015 kg

Unknown

5x1010 m

5 earth years

Moon 2

1.5x1014 kg

3 million km

8x1013 m

Unknown

Zeus is a celestial body that I just made up. Zeus is orbited by two satellites, whose characteristics are described below. Provided Zeus has a radius of 100,000 km, what is the gravitational acceleration (gZeus) on the surface this body? (G = 6.67x10-11 N·m2/kg2)

Mass

Radius

Orbital Radius

Orbital Period

Moon 1

2.5x1015 kg

Unknown

5x1010 m

5 earth years

Moon 2

1.5x1014 kg

3 million km

8x1013 m

Unknown

Explanation / Answer

on moon 2 :

gravitational accleration g = GM/R^2

here R = 3e 9 + 1 e8 = 3.1 e 9 m

so

g on moon1 = (6.67e -11 * 1.5 e 14)/(3.1e 9*3.1 e 9)

g = 1.04*10^-14m/s^2

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