Force = G m M / d^2
m is small one, M is big one
the attractive force is the same on both
If there is no outside force on the system, they must move around the center of gravity of the 2 body system. When the big one is huge, that point is close to the center of the big one. (so actually the earth does not revolve around the sun, but the center of gravity of the earth sun system is so close to the center of the sun that we do not worry about that.) (same sort of argument for earth and moon, center close to earth center.
NOW if the force F = G m M/d^2 is pulling them togeter, whydon't they crash?
It is because the net force on the little one = its mass m times its acceleration A
F = G m M /d^2 = m A
luckily that A is centripetal acceleration if we are revolving around the sun. If we stipped rotaning in our orbit, we would accelerate straight into the sun
A = v^2/d for tangential orbit speed v
so
G m M /d^2 = m v^2/d if the gravity is balanced by the centripetal acceleration
so
G M = v^2 d
and
v^2 = G M/d
so to stick in orbit at distance d we need tangential speed = sqrt [ G M/d }
1.Explain why the Earth orbits the Sun, but the moon orbits the Earth.
2.How does size impact gravitational force?
3. How do the Sun’s gravity and the Earth’s inertia keep us orbiting in the solar system?
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