1. 4.4 The Universal Law of Gravitation & 4.5 Orbits, Tides & Gravity

2. Newton’s universal law of gravitation: Every object in the universe exerts a gravitational attraction to all other objects in the universe
The amount of gravitational force depends upon the mass of the objects and the distance between the objects

3. The strength of gravity
The attraction is directly proportional to the product of their masses
The attraction is inversely proportional to the square of the distance between them (1/d2).

4. This means? The greater the mass, the greater the force
The greater the distance, the less the force
Gravity in Space

5. How do gravity and energy together allow us to understand orbits?
More gravitational energy;
Less kinetic energy
Total orbital energy (gravitational + kinetic) stays constant
This means orbits cannot change spontaneously.
The concept of orbital energy is important to understanding orbits.
Less gravitational energy;
More kinetic energy
Total orbital energy stays constant

6. Changing an Orbit
So what can make 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…

7. 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.

8. Tides
Tides are the slow, daily rise and fall of the ocean surface over a large area
They are caused by the gravitational pull of the Moon.
In most places, there are 2 high tides and 2 low tides each day.

10. How does gravity cause tides?
Gravitational pull deceases with distance
Moon’s gravity pulls harder on near side of Earth weaker on the far side
Difference in Moon’s gravitational pull stretches Earth
The oceans rise relative to land at these points.

11. Tides & Phases Spring tide
the highest tide, when the tidal effects of the Sun and Moon reinforce each other
Happens at either new moon or full moon

12. Tides & Phases Neap tide
the smallest tide, when the tidal effects of the Sun and Moon partially cancelled each other
Happens at either first quarter or third quarter

13. Tidal Friction
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.
Optional special topic. You might wish to perform the demonstration shown in the figure…

14. What have we learned? What determines the strength of gravity?
Directly proportional to the product of the masses (M x m)
Inversely proportional to the square of the separation
How do gravity and energy together allow us to understand orbits?
Change in total energy is needed to change orbit
Add enough energy (escape velocity) and object leaves
How does gravity cause tides?
Moon’s gravity stretches Earth and its oceans.