How many times is the first cosmic speed for the Moon less than the first cosmic speed for the Earth

| August 18, 2021 | education

How many times is the first cosmic speed for the Moon less than the first cosmic speed for the Earth, if it is known that the acceleration of gravity on the surface of the Moon is 6 times less than the acceleration of free fall on the surface of the Earth?

To calculate the ratio of the first cosmic velocities of the Earth and the Moon, we use the formula: k = Vs1 / Vl1 = √ (gz * Rz) / √ (gl * Rl) = √ (gz * Rz / (gl * Rl)).

Constants and variables: gz / gl – the ratio of gravitational accelerations (gz / gl = 6); Rz – radius of the Earth (Rz = 6371 km); Rl is the radius of the moon (Rl = 1737.1 km).

Let’s calculate: k = √ (gz * Rz / (gl * Rl)) = √ (6 * 6371 / 1737.1) = 4.691 rubles.

Answer: According to the calculation, the first cosmic speed of the Moon is 4.691 times less.



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