# The two-body problem: What is force between them?

Two bodies with similar/different mass orbiting around a common barycenter.

• What is force between them, where $F_{12}$ is the force on mass 1 due to its interactions with mass 2 and $F_{21}$ is the force on mass 2 due to its interactions with mass 1?
• What is relation between $F_{12}$ and $F_{21}$?
• What is total force between them?
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is there anybody out there!? – baloteli Jun 28 '12 at 20:27
Newton say: "$F_{12}=-F_{21}$". – kηives Jun 28 '12 at 20:37
Did you do a search for two-body problem? – Edu Jun 28 '12 at 21:23
Suggest close exact duplicate: physics.stackexchange.com/questions/6616/… – Argus Jun 28 '12 at 22:40
This looks like (very easy) homework, except for "total force"--- I don't know what that means. – Ron Maimon Jul 29 '12 at 6:16

According to Newton's Law of Universal Gravitation, the magnitude of the force between the two bodies can be calculated by the following equation:

$F$ = $G$*$m_{1}$*$m_{2}$/$r^2$

where:

$G$ is the gravitational constant
$m_{1}$ is the mass of the first body
$m_{2}$ is the mass of the second body
$r$ is the distance between the centers of the masses

As for the relation between the two forces, according to Newton's 3rd Law:

$F_{12}$ = $-F_{21}$

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This is given by Newton's law of gravitation: $$F_{12} = F_{21} = G\frac{m_1m_2}{r^2},$$ where $G$ is the universal gravitational constant, $m_1$ and $m_2$ are the masses of the two bodies, and $r$ is the distance between them. The two forces have equal magnitude but point in opposite directions. (That's Newton's third law.)

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