The radius of the moon is R.A satellite orbiting the moon in a circular orbit has an acceleration due to the moon's gravity of 0.14 m/s².The acceleration due to gravity at the moon's surface is 1.62 m/s².The height of the satellite above the moon's surface is A)3.4R B)0.42R C)11R D)2.4R E)1.7R

Question

Quizplus · Accepted Answer

Using the formula for the acceleration due to gravity in a circular orbit:

a = GM/r^2

where a is the acceleration due to gravity, G is the gravitational constant, M is the mass of the moon, and r is the distance between the center of the moon and the center of the satellite.

We can solve for r:

r = sqrt(GM/a)

At the surface of the moon, a = 1.62 m/s^2 and R = 1738 km = 1.738 x 10^6 m

So,

r = sqrt((6.67 x 10^-11 N(m/kg)^2) * (7.34 x 10^22 kg) / (1.62 m/s^2))

r = 1.74 x 10^6 m

The height of the satellite above the surface of the moon is:

r - R = 1.74 x 10^6 m - 1.738 x 10^6 m = 2 x 10^3 m = 2 km

So, the height of the satellite above the moon's surface is 2.4 times the radius of the moon:

2 km = 2.4R

Therefore, the answer is (D) 2.4R.

The Radius of the Moon Is R