Gravitational Relationships Between the Sun, Earth and Moon

1. What Is Gravitational Relationship

Gravitation is a mutual attractive force between any two masses in the universe.

According to Newton’s Law of Universal Gravitation:

F = G(m1*m2/r^2)

Where:

• F = gravitational force
• G = gravitational constant
• m1,m2​ = masses of the two objects
• r = distance between their centers

More mass = Stronger gravity
More distance = Weaker gravity

2. The Three-Body System: Sun–Earth–Moon

The Sun, Earth and Moon form a gravitationally bound three-body system where each body influences the others.

Mass comparison:

• Sun > Earth > Moon
• The Sun has ~99.86% of the solar system’s mass

This mass hierarchy explains who dominates whom gravitationally.

3. Sun–Earth Gravitational Relationship

Why Earth Orbits the Sun

• The Sun’s massive gravity pulls Earth inward
• Earth’s forward motion (velocity) prevents it from falling straight into the Sun
• Result: A stable elliptical orbit

This balance is called orbital equilibrium.

Effects of Sun’s Gravity on Earth

1. Earth’s Orbit
   • One revolution ≈ 365.25 days
2. Seasons
   • Caused by Earth’s axial tilt (23.5°) not distance
3. Solar Tides
   • Sun also contributes to ocean tides (less than Moon but still significant)

4. Earth–Moon Gravitational Relationship

Why the Moon Orbits Earth

• Earth’s gravity pulls the Moon
• Moon’s sideways motion keeps it in orbit

Key Effects

1. Tidal Locking

• Moon rotates once on its axis in the same time it orbits Earth
• Result: We always see the same face of the Moon

2. Ocean Tides on Earth

• Moon’s gravity pulls Earth’s oceans
• Creates:
  • High tide on the side facing the Moon
  • High tide on the opposite side (due to inertia)
• Earth rotates → tides move

Moon causes ~70% of tidal effect, Sun causes ~30%

3. Stabilization of Earth’s Axis

• Moon stabilizes Earth’s tilt
• Prevents extreme climate variations
• Important for long-term habitability

5. Sun–Moon Gravitational Relationship

Although the Moon orbits Earth, the Sun’s gravity on the Moon is actually stronger than Earth’s.

So why doesn’t the Moon orbit the Sun independently?

Because:

• The Moon’s motion around Earth is a small wobble added to its path around the Sun
• Technically, the Moon follows a wavy orbit around the Sun always moving forward

6. Combined Effects: Sun + Moon on Earth

1. Spring Tides

• Occur during New Moon & Full Moon
• Sun, Earth and Moon aligned
• Gravitational forces add up
• Result: Very high tides & very low tides

2. Neap Tides

• Occur during First & Third Quarter Moon
• Sun and Moon at right angles
• Forces partially cancel
• Result: Weaker tides

7. Eclipses: A Gravitational Alignment Outcome

Solar Eclipse

• Moon comes between Earth and Sun
• Possible because:
  • Moon’s size and distance perfectly match Sun’s apparent size
• Requires precise gravitational alignment

Lunar Eclipse

• Earth comes between Sun and Moon
• Earth’s shadow falls on the Moon

8. Barycenter: The Hidden Balance Point

Earth and Moon do not orbit each other directly.

They orbit a common center of mass called the barycenter.

• Located inside Earth but not at its center
• Causes Earth to slightly wobble
• Important for detecting exoplanets using similar wobble methods

9. Long-Term Evolution of the System

Moon Is Slowly Moving Away

• Distance increases ~3.8 cm per year
• Due to tidal energy transfer

Earth’s Rotation Is Slowing

• Days are getting longer (very slowly)

Far Future

• Moon may become fully tidally locked with Earth
• Earth–Moon system will be more stable but different

10. Why This Gravitational System Is Important

• Keeps Earth in a stable orbit
• Controls day–night cycle
• Creates tides
• Stabilizes climate
• Enables eclipses
• Makes Earth habitable

Without this precise gravitational balance, life as we know it would not exist.