Question

In: Physics

The mass of Earth is 5.972 * 1024 kg, and the radius of Earth is 6,371...

The mass of Earth is 5.972 * 10²⁴ kg, and the radius of Earth is 6,371 km. The mass of the moon is 7.348 * 10²² kg, and the radius of the moon is 1,737 km. The centers of the Earth and the moon are separated by 384,400 km.
(3A) What is the magnitude of the gravitational acceleration (in m/s²) due to the moon at the near-side surface of Earth? (Hint: The correct answer is between 0.000001 and 5).
(3B) How does the gravitational acceleration due to the moon at the near-side surface of Earth compare to the gravitational acceleration due to Earth at the surface of Earth (i.e., what value is g_{moon at surface of
Earth} / g_{Earth at surface of Earth})?
(3C) What is the magnitude of the gravitational acceleration (in m/s²) due to the moon at the surface of the moon? (Hint: The correct answer is between 0.1 and 50).
(3D) What is the magnitude of the gravitational acceleration (in m/s²) due to Earth at the near-side surface of the moon? (Hint: The correct answer is between 0.0001 and 5).
(3E) How does the gravitational acceleration due to Earth at the near-side surface of the moon compare to the gravitational acceleration due to the moon at the surface of the moon (i.e., what value is g_{Earth at
surface of moon} / g_{moon at surface of moon})? (Hint: The correct answer is between 0.00001 and 5).
(3F) Which force is stronger, the gravitational force due to the moon at the near-side surface of Earth, or the gravitational force due to Earth at the near-side surface of the moon?

Solutions

Expert Solution

Radius of earth , Radius of moon , Distance between the center of earth and moon

Mass of earth , mass of moon

Gravitational acceleration due to moon at the near side surface of earth is

Gravitational acceleration due to earth at the surface of earth is

Gravitational acceleration due to moon at the surface of moon is

Gravitational acceleration due to earth at the near side surface of moon is

That is , the gravitational force due to Earth at the near-side surface of the moon is stronger.

genius_generous answered 1 year ago

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