Therefore, r is the distance between the centers of mass of the two objects. For
objects with uniform density, this is merely the distance from center to center.
The force of gravity is very small unless at least one of the objects is large, like a
planet or moon. Let’s try a problem that explores this.
- The Sun has a mass of 2 × 10^30 kg and Mars has a mass of 6 ×
1023 kg. How does the acceleration of the Sun due to Mars compare
to the acceleration of Mars due to the Sun?
Here’s How to Crack It
The force on the Sun is F = mSaS, and the force on Mars is F = mMaM. Since F is
the same in both of these equations—because F is their mutual gravitational
attraction—we can write
So, the acceleration of the Sun is much smaller than that of Mars; it’s only 3 × 10−7
times as much. Because of Mars’s much smaller mass, it’s affected more by the
gravitational force, which is why Mars orbits the Sun and not the other way around.
To Do What You’re Told,
Do What You Need
If the radius of the Sun
and Mars had been given,
you’d have been able
to calculate the accelerations
for each, but that
would have been far more
complicated. On the SAT
Physics Subject Test, you
will always be able to
solve the problem with the
information given, so try
to figure out how to manipulate
the formulas you
know to solve the problem