A. Use the relation 2

m
m
m
GM
g
R
ƒ­ to find the acceleration due to gravity on the surface
of the Moon. You can use the following data:
Mass of the Moon m M = 7.35 ¡Ñ 1022 kg. Radius of the Moon m R = 1.74 ¡Ñ 106 m.
B. How does this value compare with the acceleration due to gravity g ƒ­ 9.8m s2 on
the Earth¡¦s surface?
C. The center-to-center distance between the Earth and the Moon is 3.85 ¡Ñ 108 m.
Calculate the orbital speed of the Moon as it revolves round the Earth.
Also estimate the period of Moon¡¦s orbit from the given data. Express your
answer in days for this part.
(Mass of the Earth E M = 5.97 ¡Ñ 1024 kg.)

5.87

A. To find the acceleration due to gravity on the surface of the Moon, we can use the formula:

g = (GM) / (R^2)

where G is the universal gravitational constant, M is the mass of the Moon, and R is the radius of the Moon.

Given data:
Mass of the Moon, M = 7.35 × 10^22 kg
Radius of the Moon, R = 1.74 × 10^6 m
Universal gravitational constant, G = 6.67 × 10^(-11) Nm^2/kg^2

Substituting the values into the equation, we get:

g = (6.67 × 10^(-11) Nm^2/kg^2 * 7.35 × 10^22 kg) / (1.74 × 10^6 m)^2

Simplifying the equation, we can cancel out the units and calculate the value of g.

B. To compare the acceleration due to gravity on the Moon with that on Earth's surface, we need to calculate the value of g on Earth.

Given data:
Acceleration due to gravity on Earth, g = 9.8 m/s^2

Compare the value of g on the Moon obtained in part A with the value of g on Earth to see how they differ. Keep in mind that the units are different, so make sure to compare them accordingly.

C. To calculate the orbital speed of the Moon as it revolves around the Earth, we can use the formula:

v = √(GM / r)

where G is the universal gravitational constant, M is the mass of the Earth, and r is the center-to-center distance between the Earth and the Moon.

Given data:
Center-to-center distance between the Earth and the Moon, r = 3.85 × 10^8 m
Universal gravitational constant, G = 6.67 × 10^(-11) Nm^2/kg^2
Mass of the Earth, M = 5.97 × 10^24 kg

Substitute the values into the formula and calculate the orbital speed, v.

To estimate the period of the Moon's orbit, we can use the formula:

T = (2πr) / v

where r is the center-to-center distance between the Earth and the Moon, and v is the orbital speed of the Moon.

Substitute the values into the formula and calculate the period, T. Then convert the result to days by dividing by the number of seconds in a day (24 hours * 60 minutes * 60 seconds).