Planets A B and C are all in one line where planets A and C are the same distance apart from planet B. Planet A has a mass of m. a planet B has a mass of m. Planet C has a mass of 4 m. Why does Planet A experience a gravitational force by Planet C that is equal to that by Planet B
According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
For Planet A, the distance to Planet B is equal to the distance to Planet C because they are in a straight line.
Let's suppose the distance between Planet A and B (AB) is equal to the distance between Planet A and C (AC), denoted as d.
The gravitational force between Planet A and B (FAB) can be expressed as: FAB = G * (m * m) / (d^2)
Similarly, the gravitational force between Planet A and C (FAC) can be expressed as: FAC = G * (m * 4m) / (d^2)
We can simplify the expressions above to compare the forces:
FAB = G * m^2 / (d^2)
FAC = G * 4m^2 / (d^2)
Dividing FAC by FAB:
FAC / FAB = (G * 4m^2 / (d^2)) / (G * m^2 / (d^2))
The G, d^2, and (1/d^2) terms cancel out:
FAC / FAB = (4m^2) / (m^2)
Simplifying the right side:
FAC / FAB = 4
Therefore, Planet A experiences a gravitational force by Planet C that is four times greater than the gravitational force by Planet B.