1. mars has a mean diameter of 4200 mi (the earth's is 7900 mi). the mass of mars is .11 times the mass of the earth. what is the value of g on mars?
2. what is the escape velocity on the moon?
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1. 3.8 m/s²

2. 2400 m/s

Explanation:

1. Acceleration due to gravity can be found with Newton's law of gravitation:

g = GM / R²

where g is the acceleration at the surface,

G is the universal gravitational constant,

M is the mass of the planet,

and R is the radius of the planet.

If we say M is the mass of the Earth and R is the radius of the Earth, then we know:

9.8 = GM / R²

Mars has a mass of 0.11 M and a radius of (4200/7900) R = 0.53 R.  So the acceleration is:

g = G (0.11 M) / (0.53 R)²

g = 0.39 GM / R²

g = 0.39 (9.8)

g = 3.8

So the value of g on Mars is 3.8 m/s².

2. The escape velocity is the velocity at which the kinetic energy of an object at the surface equals its gravitational potential energy.

½ m v² = m (GM / r²) r

½ v² = GM / r

v² = 2GM / r

v = √(2GM / r)

The mass of the moon is 7.35×10²² kg, and the radius of the moon is 1.74×10⁶ m.

v = √(2 (6.67×10⁻¹¹) (7.35×10²²) / (1.74×10⁶))

v = 2400 m/s

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