Answer:
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
