Gravitational interaction between three bodies

[Ranku]

If there are three bodies A, B, and C arranged linearly, and B is free falling towards C, will the gravitational presence of A affect the rate of free fall of B towards C?

 

[jbriggs444]

If there are three bodies A, B, and C arranged linearly, and B is free falling towards C, will the gravitational presence of A affect the rate of free fall of B towards C?

Why not set up a situation and calculate it? Put B in the middle at coordinate zero, A on the left at coordinate -1 and C on the right at coordinate 1. Give them all the same mass.

Decide what you want to calculate. The rate at which the distance between B and C decreases?

Calculate. First with A present then with A absent.

Hint: Tides.

 

[Ranku]

Why not set up a situation and calculate it? Put B in the middle at coordinate zero, A on the left at coordinate -1 and C on the right at coordinate 1. Give them all the same mass.

Decide what you want to calculate. The rate at which the distance between B and C decreases?

Calculate. First with A present then with A absent.

Hint: Tides.

What formulas do I use and in what order?

 

[jbriggs444]

What formulas do I use and in what order?

Newton's second law:$$F=ma$$That'll let you compute the acceleration $a$ of an object of mass $m$ when subject to a force $F$.

Newton's universal law of gravitation:$$F=G\frac{m_1m_2}{r^2}$$That'll let you compute the force $F$ on an object of mass $m_1$ from an object of mass $m_2$ a distance $r$ away.

It should be enough to look at the accelerations, but you might choose to look at the resulting velocities. You get that from Calculus or the SUVAT equations. In particular:$$v=at$$That'll give you the velocity $v$ of an object with uniform acceleration $a$ after duration $t$ when starting from rest.

 

[HallsofIvy]

The answer to your query is that total gravitational force on a given mass by several other masses is the (vector) sum of the forces due to the individual masses. One mass does not "interfere" with the affect of another mass.