What role does gravity and inertia play in our Solar System?

It keeps the planets in orbit.

Inertia is what keeps an object moving (in the same direction). Gravity is the pull of an object to another.

The planets have reached the perfect medium to where inertia keeps the planets moving (instead of remaining completely still in space), and gravity pulls them toward the sun so that they move around it instead of moving straight past it or straight into it.

This is also true about the Earth and the moon.

This is also true with satellites in orbit.