What happens to gravitational force when a satellite is twice as far from the center of the Earth?

• A. Increases four times
• B. Decreases to one-half
• C. Decreases to one fourth
• D. Remains the same

Answer: (C)

When a satellite is moved to a distance that is twice as far from the center of the Earth, the gravitational force acting on it decreases to one fourth of what it was at its original position. This can be understood through Newton's law of universal gravitation, which states that the gravitational force between two masses is inversely proportional to the square of the distance between their centers.

Mathematically, this law can be expressed as:

[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} ]

where ( F ) is the gravitational force, ( G ) is the gravitational constant, ( m_1 ) and ( m_2 ) are the masses of the two objects (in this case, the Earth and the satellite), and ( r ) is the distance between their centers.

When the distance ( r ) is doubled (meaning the satellite is now at a distance of ( 2r )), the gravitational force can be recalculated as follows:

[ F' = \frac{G \cdot m_1 \cdot m_2}{(2r)^2} = \frac{G \cdot m_1 \cdot