Correct question:
The acceleration due to gravity at the surface of the moon is 1.6 m/s2. If the radius
of the moon is 1.74 x 10^6 m, calculate the mass of the moon
Answer:
M = 7.3 × 10^22
Step-by-step explanation:
Given the following :
Acceleration due to gravity (g) at surface of the moon = 1.6m/s^2
Radius of the moon (r) = 1.7 × 10^6 m
The acceleration due to gravity of large bodies such as the moon is calculated using the formula :
g = GM / r^2
Where;
g = acceleration due to gravity
G = the universal gravitational constant, G = (6.673 x 10^-11)
M = mass
r = the distance from the center of mass of the body
Therefore, to calculate mass M from the formula :
M = gr^2 / G
Inputting our values :
M = [1.6 × (1.7×10^6)^2] / 6.673 x 10^-11
M = [1.6 × (3.0276×10^12)] / 6.673 x 10^-11
M = (4.84416 × 10^12) / 6.673 × 10^-11
M = 0.7259 × 10^(12+11)
M = 0.7259 × 10^23
M = 7.259 × 10^23
M = 7.3 × 10^22