Question

# The distance between the center of the moon and the center of the earth is is...

The distance between the center of the moon and the center of the earth is is 4.0*10^6 m. The moon is also regarded as a point mass situated at its center. The orbit period of the moon about the earth is 2.4*10^6s.

(a) Calculate the orbital speed of the moon?

(b) Using your answer above and what you know about energy. Calculate the value of the Gravitational potential due to earth at a distance of 4.0*10^9m from its center.

Here we have given that,

The distance between the center of the moon and the center of the earth r = 4.0*10^6 m.

The orbit period of the moon about the earth T= 2.4*10^6s.

(a) so that the orbital speed of the moon is given as

V = 2pie×r/T = 2 × 3.14 × 4×10^6/2.4×10^6

V = (10.47197551197) m/s which is the required orbital speed of moon.

(b) now using the above relation the energy associated with moon here will be,

Um = -GMm/r

Where M is the mass of earth

m is the mas of moon

r is the distance betweens then earth and moon center.

now to Calculate the value of the Gravitational potential due to earth at a distance of 4.0*10^9m from its center will be given as,

Ve = - GMe/r = - 6.67 ×10^-11×6×10^24/ 4×10^9 =

Ve = - 100050 V