Newton connected the dots between Kepler’s third law (about planetary motion) and the concept of gravity. He realized

• A planet's gravitational force keeps a satellite circling it.

Real-World Analogy: Think of gravity as an invisible string tied between a planet and a satellite, constantly pulling them together. Without this string, the satellite would fly off!

Imagine a cannon on a really tall mountain

• Scenario A: The cannon fires its ball horizontally. Because Earth isn’t flat (it’s a big round ball), the cannonball doesn’t just drop straight down. It travels a bit before being pulled down by gravity. Like throwing a stone!

• Scenario B: If we shoot the cannonball even faster, it'll go even further before dropping.

• Scenario C: At a SUPER high speed, the cannonball will go around Earth without touching it. It's now an orbiting satellite!

Real-World Analogy: Think of swinging a ball on a string around you. The string keeps the ball from flying off. Similarly, gravity is the "invisible string" keeping satellites in orbit!

• The gravitational pull (FG) acts as the centripetal force (FC) that keeps the satellite in its orbit.

• They gave this relationship
  FC = FG = mω2 r = GMEm/r2

• But, because math is magic, some symbols cancel out, and we get
  ω2 r = GME/r2

Fun Fact: Here ω is the satellite’s orbital speed, ME is Earth's mass, and m is the satellite's mass. And, G is a universal gravitational constant.