LEO (~400 km): ~7700 m/s orbital speed, ~90 min period.
Geostationary (~36,000 km): ~3000 m/s orbital speed, 24-hour period.
Changing Speed in Circular Orbits
For a STABLE ORBIT at a given radius, there is only ONE correct speed.
IF SPEED INCREASES (same radius):
Object moves too fast for the gravity at that radius to maintain circular orbit.
Object spirals OUT to a larger orbit (higher altitude).
IF SPEED DECREASES (same radius):
Gravity exceeds the centripetal force needed for that (slower) speed.
Object spirals IN to a smaller orbit (lower altitude).
CONSEQUENCES FOR SATELLITES:
A satellite slows due to atmospheric drag → orbit decays → re-enters.
Satellite needs to fire engines periodically to maintain orbit (compensate for drag).
TRANSFER ORBITS:
To move from low orbit to high orbit: fire engines to INCREASE speed → transition to higher orbit.
To move from high orbit to low orbit: fire engines to DECREASE speed → fall to lower orbit.
Counter-intuitive: firing engines forward → end up in higher, SLOWER orbit.
GEOSTATIONARY ORBIT:
Specific radius where orbital period = 24 hours (Earth's rotation period).
Satellite appears stationary above equator.
Only one geostationary orbit altitude exists: ~35,786 km.
Escape Velocity and Black Holes
ESCAPE VELOCITY: the minimum speed needed to leave a body's gravitational field.
For Earth: ~11.2 km/s.
BLACK HOLES:
Extremely dense objects where escape velocity exceeds the speed of light.
Light cannot escape → perfectly black.
Formed when very massive stars collapse in supernova.
Schwarzschild radius: the radius within which nothing can escape.
GRAVITATIONAL EFFECTS ON SPACE-TIME:
Massive objects curve space-time → affects path of light.
Gravitational lensing: light from distant galaxies bent around massive objects → multiple images.
TIDES:
Differences in gravitational pull of the Moon on near and far sides of Earth → tidal bulges.
Sun also contributes — spring and neap tides.
KEPLER'S LAWS (context):
Planets move in ellipses.
A planet sweeps equal areas in equal times (moves faster near the Sun).
Orbital period² ∝ (orbital radius)³.
⚠️ Common Mistake
In circular motion at constant speed, the object is ACCELERATING (velocity direction changes). The centripetal force is always directed towards the CENTRE — it's provided by gravity for orbital motion. To move to a HIGHER orbit, a satellite must increase speed — but the final speed in the higher orbit is actually lower (paradoxically).
📌 Key Note
Gravity = centripetal force for orbits. Lower orbit: stronger gravity, faster speed, shorter period. Geostationary: 36,000 km, 24 hrs, appears stationary. If speed↑ at same radius → spiral out to larger orbit. If speed↓ → fall to smaller orbit. LEO satellites decay due to atmospheric drag → re-enter.
🎯 Matching Activity — Orbital Mechanics
Match each orbital scenario to the correct outcome. — drag the symbols on the right to match the component names on the left.
Satellite at correct orbital speed
Drop here
Satellite speed increases at same radius
Drop here
Atmospheric drag slows LEO satellite
Drop here
Geostationary orbit
Drop here
~36,000 km altitude, 24-hour period — appears stationary above equator
Stable circular orbit — gravity exactly provides centripetal force
Spirals outward to higher orbit — centripetal force required exceeds gravity
Orbit decays — satellite spirals inward and re-enters atmosphere
⭐ Higher Tier Only
HT only — explain qualitatively how gravity provides centripetal force for circular orbits. Explain why orbital speed must change if orbital radius changes for a stable orbit. Describe what happens when a satellite's speed changes.