Question

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.

Answer 1

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

Which is our required answer.