The Great Attractor

NODE 01

Mystery of Falling

• Objects fall to Earth.
• The Moon doesn't fall into Earth.
• How does the same idea explain both?

NODE 02

Universal Gravitation

• F = Gm₁m₂ / r².
• Inverse-square relationship.
• Universal, attractive nature.

NODE 03

Gravitational Constant

G

• Universal constant.
• G ≠ g.
• Crucial distinction for beginners.

NODE 04

Gravity Near Earth

• W = mg.
• g ≈ 9.8 m/s².
• Gravitational acceleration and weight.

NODE 05

Deriving g

F = GMm/R²F = mgg = GM/R²

• Connecting Universal Law to local g.
• g depends on Earth's mass and radius.

NODE 06

Mass vs Weight

• Mass: Inertial property (constant).
• Weight: Gravitational force (varies with g).

NODE 07

Variation of g

• g decreases with altitude.
• g decreases with depth.
• g varies with latitude.

NODE 08

Gravitational Field

• Force experienced per unit mass.
• g⃗ = F⃗/m.
• Source mass vs Test mass.

NODE 09

Field Lines

• Radial field directed toward mass.
• Field density indicates strength.
• Prepares for electric fields.

NODE 10

Superposition

• g⃗total = g⃗₁ + g⃗₂ + ...
• Resultant field using vector addition.
• Symmetry and cancellation points.

NODE 11

Grav Potential

V = U/mV = -GM/r

• Scalar quantity. Reference at infinity.
• Negative value. Bridge between force & energy.

NODE 12

Grav Potential Energy

U = -Gm₁m₂/r

• Energy of two masses.
• Bringing masses together vs separating them.
• Connects to mgh near Earth's surface.

NODE 13

Escape Velocity

• Minimum ideal speed to escape gravity.
• vₑ = √(2GM/R).
• Independent of projectile's mass.

NODE 14

Orbital Velocity

• Circular orbit speed: vₒ = √(GM/r).
• Near Earth: vₒ = √(gR).
• vₑ = √2 vₒ.

NODE 15

Why Orbits Exist

• Satellite continuously falls toward Earth...
• ...while simultaneously moving sideways.
• Result: Continuous free fall around Earth.

NODE 16

Circular Orbits

• Gravitational force provides centripetal force.
• GMm/r² = mv²/r.
• Unites Realms 04, 05, and 07.

NODE 17

Orbital Period

T = 2πr/vT² = 4π²r³/GM

• Time for one circular orbit.
• The mathematical doorway to Kepler's third law.

NODE 18

Kepler's First Law

• Planets move in elliptical orbits.
• Sun at one focus.
• Circular orbit is a special simplified case.

NODE 19

Kepler's Second Law

• Equal areas swept in equal times.
• Faster near perihelion, slower near aphelion.
• Conservation of angular momentum (Realm 05).

NODE 20

Kepler's Third Law

• Square of period proportional to cube of semi-major axis.
• T² ∝ a³ (or r³ for circular orbits).

NODE 21

Orbital Energy

• Kinetic (K), Potential (U), Total (E).
• Total energy E = -GMm/2r (negative = bound orbit).

NODE 22

Geo-Stationary

• Equatorial orbit, matches Earth's rotation.
• Appears stationary from surface.
• Comms, weather, broadcasting.

NODE 23

Polar Orbits

• Near-polar inclination.
• Earth observation, mapping, remote sensing.
• Global coverage as Earth rotates beneath.

NODE 24

Sat Classification

📡🛰️🌍

• Natural (Moon) vs Artificial.
• Comms, Nav, Weather, Sci, Military.

NODE 25

Satellite Launch

• Reaching altitude + reaching orbital speed.
• Circularization, gravity losses.

NODE 26

Multiple Orbits

• LEO, MEO, GEO, HEO.
• Orbital radius changes speed, period, and energy.

NODE 27

Weightlessness

↓

• Apparent weightlessness.
• Person + spacecraft are in continuous free fall.
• Not outside of gravity.

NODE 28

Tides

• Differential gravitational force (Moon/Sun).
• Tidal bulges, spring tides, neap tides.

NODE 29

Solar System

• Sun, planets, moons, asteroids.
• Why inner planets orbit faster.

NODE 30

Beyond Earth

• Surface gravity of other planets.
• Binary systems, galaxy-scale gravity.

NODE 31

Gravity & Light

• Gravity affects trajectories of light.
• Massive bodies bend spacetime.
• Preview of General Relativity.

NODE 32

Gravitational Assist

• Exchange of orbital energy/momentum with planets.
• Slingshot trajectory modification.

NODE 33

Darker Gravity

• Black holes, event horizons.
• Extreme gravity, gravitational waves.

NODE 34

Gravity Lab

• Measure g with a pendulum.
• Study free fall, verify inverse-square behavior.

NODE 35

Solving Engine

• What creates field? Where is object?
• Force vs Field? Surface vs Orbit?
• Use F, g, or Energy method.

NODE 36

Misconceptions

• "No gravity in space" → False.
• "Heavier objects fall faster in vacuum" → False.
• "Geostationary = stationary in space" → False.

NODE 37

The Master Map

MASS → FORCE → FIELDPOTENTIAL → ENERGYORBIT → ESCAPE → COSMOS

• The complete chain of gravitation.
• From a falling apple to planetary systems.