When the distance between the center of an orbiting satellite and the center of the Earth is doubled, the gravitational attraction experienced by the satellite decreases significantly. This relationship is described by Newton’s law of universal gravitation, which states that the gravitational force (F) between two objects is inversely proportional to the square of the distance (r) between them.
Mathematically, this is expressed as:
F = G * (m1 * m2) / r²
Here, F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects (the Earth and the satellite), and r is the distance between their centers. When we double the distance (2r), the equation becomes:
F' = G * (m1 * m2) / (2r)²
This simplifies to:
F' = G * (m1 * m2) / (4r²)
As a result, the new gravitational force F’ is one-fourth (1/4) of the initial gravitational force F. This means that doubling the distance reduces the gravitational attraction by a factor of four. So, the satellite will feel significantly less pull from the Earth, affecting its orbit and stability.