Caption: A cartoon illustrating the Sun and a general (Solar System) planet in an elliptical orbit.
Note that planets orbit the Sun in elliptical orbits is historically speaking Kepler's 1st law of planetary motion.
Features:
This situation is what the cartoon illustrates.
See the Sun dominator in the figure below (local link / general link: sun_dominator.html).
To put the last statement in other words,
the gravitational force
explicitly obeys
Newton's 3rd law of motion:
for every
force there is an equal
(in magnitude) and opposite (in direction)
force.
However, the Sun's
dominance in mass means the
sum of the all the planet
gravitational forces
on the Sun is just
a gravitational perturbation.
Now solar mass M_☉ = 1.98855*10**30 kg
is so much larger than any planet
mass
that (M_1 * M_2) for
Sun
and planet
is much larger than (M_1 * M_2) for
any planet
and planet.
Thus, the gravitational force
between Sun
and planet
is much larger than for
any planet
and planet.
In fact, the gravitational force
between any planet
and planet.
is negligible
to 1st order.
If the Sun
suddenly vanished, the planets
would fly away from each other in space
and NEVER meet again because
the major source of gravity was gone:
gravity is proportional to mass.
Yours truly can---if yours truly---do
a demonstration with a swirling object.
The moons
would stay gravitationally bound to the planets, of course.
If the planets suddenly vanished, the
Sun
would barely notice.
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G * M_1 * M_2
F = --------------- ,
r**2
where
F is size of the pulling gravitational force
each object exerts on the other,
gravitational constant G=6.67430(15)*10**(-11) (MKS units),
(M_1 * M_2) is the product of the object
masses,
and r is their separation for point masses
or their
center-to-center separation for
spherically symmetric bodies.