1. Gravity, Tides and Orbits
4.4 & 4.5

2. Newton’s Law of Universal Gravitation
Newton discovered that gravity is universal. Everything pulls on everything else in a way that involves only mass and distance.

3. Newton’s Law of Universal Gravitation
The force of gravity between objects depends on the distance between their centers of mass.

4. Newton’s Law of Universal Gravitation
The law of universal gravitation states that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object.

5. Newton’s Law of Universal Gravitation

6. Gravity and Distance: The Inverse-Square Law

7. How does gravity help us understand orbits ?
In an elliptical orbit, at all points on the orbit—except perihelion and aphelion —some of the gravitational force is parallel to the direction of the planet’s motion.
This part of the force changes the speed and, thus, the KE.
What actually causes the speed to change?

8. Changing an Orbit
Is there anything that can cause an object gain or lose orbital energy?
Friction or atmospheric drag
A gravitational encounter.
Examples worth mentioning:
satellites in low-Earth orbit crashing to Earth due to energy loss to friction with atmosphere
captured moons like Phobos/Deimos or many moons of Jupiter: not easy to capture, and must have happened when an extended atmosphere or gas cloud allowed enough friction for the asteroid to lose significant energy.
Gravitational encounters have affected comets like Halley’s; also used by spacecraft to boost orbits…

9. Escape Velocity
If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit)
Escape velocity from Earth ≈ 11 km/s from sea level (about 40,000 km/hr)
Can use this to discuss how adding velocity can make a spacecraft move to a higher orbit or ultimately to escape on an unbound orbit.

10. Ocean Tides
Newton showed that the ocean tides are caused by differences in the gravitational pull of the moon on opposite sides of Earth.

11. Ocean Tides
The moon’s attraction is stronger on Earth’s oceans closer to the moon, and weaker on the oceans farther from the moon.
(A differential pull)
This difference in pulls across Earth slightly elongates it.
This is simply because the gravitational force is weaker with increased distance

12. Ocean Tides
The two tidal bulges ( 1 meter on average, on opposite sides of Earth) remain fixed with respect to the moon. The Earth spins beneath them, producing two high tides and two low tides each day.
Tidal friction gradually slows Earth rotation (and makes Moon get farther from Earth).
Moon once orbited faster ; tidal friction caused it to “lock” in synchronous rotation.

13. Tidal Range

14. Tides & Phases Spring tide the largest tidal range
the tidal effects of the Sun and Moon reinforce each other
at new moon and full moon

15. Tides & Phases Neap tide the smallest tidal range
The tidal effects of the Sun and Moon partially cancelled each other
At first quarter and third quarter