A science question about mavity

Relative mass isn't the only contributing factor, their velocities would have to be considered as well. If a football-sized object approached the Earth at a high enough speed or at the wrong angle, it wouldn't enter an orbit despite the gravitational attraction. If the momentum was just right, that same object would orbit a single neutron - assuming, for the same of the argument, that neutron is held in a static frame of reference.
 
The equation for Universal Gravitation is F = GMm/R2

F = Force
G = Gravitational constant N-m2/kg2
Mm = Mass of two objects
R = Distance

For example using the formula above, the gravitational force between a football(0.5kg) and a tennis ball(0.1kg) within 1 meter apart would be: 3.3350e-12
 
Any two massive objects will have a gravitational effect on one another. Whether they will orbit each other has nothing to do with their size, mass, or separation. Depending on their relative velocities, their motion will be either radial, hyperbolic, parabolic, elliptic, or circular. It's all described by the so-called eccentricity of the orbit.

Note that radial, parabolic, and circular orbits are very special cases where the system must have a precise configuration (i.e. the eccentricity must be either 0 or 1 exactly). In reality, pretty much all orbits are either elliptic or hyperbolic. This includes planetary orbits, which are actually elliptic, even though they look circular :)
 
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