Determine the modules of speed and centripetal acceleration of the Moon moving around the Earth.

| January 24, 2021 | education

Determine the modules of speed and centripetal acceleration of the Moon moving around the Earth. Consider the radius of the Moon’s orbit equal to R = 384 * 10 ^ 3 km, and the period of its rotation T = 28 days.

R = 384 * 10 ^ 3 km = 384 * 10 ^ 6 m.

T = 28 days = 2419200 s.

V -?

a -?

The period T is the time of one complete revolution. During this time, the Moon travels a path equal to the circumference of a circle of radius R.

The speed V is the ratio of the traversed path S to the time of its passage t: V = S / t.

The circumference is determined by the formula: S = 2 * P * R, t = T.

V = 2 * P * R / T.

V = 2 * 3.14 * 384 * 10 ^ 6 m / 2419200 s = 996.82 m / s.

a = V ^ 2 / R.

a = (996.82 m / s) ^ 2/2419200 s = 0.00258 m / s ^ 2.

Answer: V = 996.82 m / s, a = 0.00258 m / s ^ 2.



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