🧩 Adventure 14 — Activity 1

2) Key Equations and Derivation

The Moon stays in orbit because gravity provides the inward force required for circular motion.

Newton’s gravitational force:   F = GMm / R²

where G is the gravitational constant, M is Earth’s mass, m is the Moon’s mass, and R is the Earth–Moon distance.

Circular motion requirement:   F = mv² / R

Since gravity is the force that keeps the Moon in circular motion, we set the two expressions equal:

GMm / R² = mv² / R

Cancel m and multiply both sides by R:

GM / R = v²

Therefore the orbital speed is:

v = √(GM / R)

3) Compute the Moon’s Orbital Speed

Use these values:

• G = 6.67 × 10⁻¹¹ N·m²/kg²
• M = 5.97 × 10²⁴ kg
• R = 3.84 × 10⁸ m

Substitute into v = √(GM/R) and compute the Moon’s speed in m/s.

Convert your result to km/s.

4) Compute the Orbital Period

The Moon travels one full circle in one orbit, so first compute the circumference:

distance = 2πR

Now use:

time = distance / speed

Orbital period in seconds:

Convert the result into days.

5) Interpretation

Why does the Moon not crash into Earth?

What would happen if the Moon moved more slowly?

What would happen if the Moon moved more quickly?

1) The Big Idea

Complete the sentence in your own words:

The Moon stays in orbit because