Calculate the acceleration of the moon moving around the earth in a circle, the distance between the centers

| November 25, 2020 | education

Calculate the acceleration of the moon moving around the earth in a circle, the distance between the centers of the earth and the moon is taken equal to 400000 km; the radius of the earth is 6400 km (g3 = 10m / s)

Rlz = 400000 km = 4 * 10 ^ 8 m.
Rz = 6400 km = 64 * 10 ^ 5 m.
g3 = 10 m / s ^ 2.
a -?
Let’s write 2 Newton’s law for the Moon: ml * a = G * ml * Ms / Rls ^ 2.
The acceleration of the moon will be determined by the formula: a = G * Ms / Rls ^ 2.
Let’s write 2 Newton’s law for the Moon if the moon rotated around the surface of the Earth: ml * g3 = G * ml * Mz / Rz ^ 2.
g3 = G * M3 / R3 ^ 2.
G * Mz = g3 * Rz ^ 2.
a = g3 * R3 ^ 2 / Rs ^ 2.
a = 10 m / s ^ 2 * (64 * 10 ^ 5 m) ^ 2 / (4 * 10 ^ 8 m) ^ 2 = 0.256 m / s ^ 2.
Answer: the acceleration of the Moon is a = 0.256 m / s ^ 2.



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