Question

What is the acceleration of Earth produced by the Moon's

gravity, relative to the acceleration of the Moon produced by Earth's gravity? (You can give a *ratio* of masses and/or any other relevant variables)

Answer 1

the acceleration of earth's tides caused by the moons gravity is related to the acceleration of the moon caused by earths gravity.

Step-by-step explanation:

1. the moons gravity pulls on the earths oceans, creating a tidal force. this force causes the water in the oceans to bulge, resulting in high and low tides.

the gravitational force between the moon and the earth is proportional to the masses of both objects and inversely proportional to the square distance of the between them. since the moon has a much smaller mass than the earth, the gravitational force exerted by the moon on the earth is revelatory small compared to the gravitational force exerted by the earth on the moon.

newtons second law of motion states that force is equal to mass multiplied by acceleration therefore the acceleration experienced by the earth due to the moons gravity can be calculated by dividing the tidal force by the mass of the earth.

similarly, the acceleration of the moon caused by earths gravity can be calculated by dividing the gravitational force exerted by the earth on the moon by the mass of the moon.

it is important to note that the acceleration of the moon caused by earths gravity is signifiganctly greater than the accerlation of the earth caused by the moons gravity. this is because the mass of the earth is much larger than the mass of the moon.

in summary the accerlation of the earths tides caused by the moons gravity is related to the accerlation of the moon caused by eraths gravity however the maghnitude of the acceleration experiemced by each object is differnt due to the difference in their masses.

Answer 2

The acceleration of Earth by the Moon's gravity is less than the acceleration of the Moon by Earth's gravity, due to the inverse ratio of their masses. Tides on Earth are predominantly affected by the Moon instead of the Sun because of the gravitational gradient and the Moon's closer proximity to Earth.

Step-by-step explanation:

The acceleration of Earth produced by the Moon's gravity, relative to the acceleration of the Moon produced by Earth's gravity, is directly proportional to the ratio of their masses due to Newton's second law (F = ma) and Newton's law of universal gravitation (F = G(Mm/r2)). Given that mass of Earth (ME) is significantly greater than the mass of the Moon (MM), the acceleration produced on the Moon by Earth's gravity is greater in magnitude than the acceleration produced on Earth by the Moon's gravity. Specifically, the ratio is equal to the inverse ratio of their masses (aEarth / aMoon = MM / ME).

The reason tides are predominantly due to the Moon, despite the greater acceleration Earth experiences from the Sun, is largely due to the differential force, or the gravitational gradient, that results from the Moon being much closer to Earth relative to the Sun. The differential force exerted by the Moon falls off more slowly with distance than that from the Sun, hence causing more significant tidal effects.