The gravitational field | POINT classical mechanics
The gravitational field
The law of universal gravitation states that the gravitational force between two material bodies is inversely proportional to the square of the distance between the centers of the two bodies. Therefore, the gravitational force decreases as the distance between the two bodies increases until the distance between their centers reaches a distance at which the gravitational forces between them almost disappear. Within this distance, there is a space in which the gravitational force appears, and this space is called the gravitational field
Deducing the Strength of the Earth's Gravitational Field:
Assuming that a body with a mass of 1kg is placed in the Earth's gravitational field and at a distance of r from the center of the Earth, then the force of gravity of the Earth on the body is:
① F= mg = 1×g = g
By applying the law of universal gravitation:
② F= GMm/r² = GM/r²
from ①,②: g = GM/r²
Where (M) is the mass of the Earth (5.98×10²⁴kg)
If the body is on the surface of the Earth, then: g = GM/R²
if the body is at a height of h above the surface of the Earth, then: g = GM/(R+h)²
Where (R) is the radius of the Earth (approximately 6378 km)
From the above, we note that the strength of the Earth's gravitational field at a point is numerically equal to the acceleration due to the Earth's gravity at that point.
Earth's gravitational field strength: the force of Earth's gravitation to a body of mass 1kg at a given point.
The strength of the gravitational field on the Earth's surface varies slightly due to the difference in its radius from one location to another, as the Earth is not perfectly spherical but rather flattened at the poles.This results from the effect of the centripetal force due to the Earth's rotation around itself.