Gravity


Isaac Newton: the law of gravity
 Mathematically, F = G x M1x M2 / d 2

Revisiting Kepler's Laws, with physics and gravity:

1. Kepler: orbits are ellipses. Newton: solving laws of motion combined with force of gravity gives rise to mathematical solutions for orbits:
 2. Kepler: equal areas in equal time. Newton: Conservation of angular momentum means the speed on an orbit changes.
 3. Kepler: P2 = a3 . Newton: Planets nearer the Sun move faster because the force of gravity is stronger. Also, a more general solution exists for any object orbiting another:


Think: Why is this important?




When do I use Kepler's version and when do I use Newton's?
  • Kepler's version ONLY works when
    • you are talking about things orbiting the Sun.
    • you are measuring P in years and a in AU.
  • Newton's version works ALWAYS, but make sure units match the units of the gravitational constant G.



Gravity and Tides


The force of the moon's gravity changes across the Earth. Why?

This causes a stretching of the Earth along a line towards the Moon, like this:
"side view" 

(courtesy Gettysburgh College)

As the Earth rotates, any piece of the Earth passes "through" the tidal bulges twice a day -- two tides a day.

Think:
The Sun also exerts a tidal stretching on the Earth (but less than the Moon does -- why?).
Spring tide: Moon and Sun stretch Earth in same direction --  extreme tides
Neap tide: Moon and Sun stretch Earth in opposite directions -- very weak tides
  • When do we get spring tides? When do we get neap tides?

Tidal Friction


The Earth's rotation tries to make its tidal bulges lead the Moon on its orbit.
"top view"

(courtesy Gettysburgh College)


This has two important effects:
  • The Earth is being pulled slightly "back" from its sense of rotation . So the Earth's rotation slows (by ~ 1 second every 50,000 years).
  • The Moon is being pulled slightly "forward" on its orbit. So it is harder for the Earth to hold it in place, and it moves further away from the Earth (by ~ 3-4 cm/yr).
How does this jibe with the idea of "conservation of angular momentum"?

And how the heck to we know all this? See "Journey into Deep Time" by Edward Greding.


What happens if we wait long enough?



Synchronous Rotation

Eventually the Earth's rotation will slow until the bulges no longer lead the Moon -- the Earth will rotate in exactly the same time it takes for the Moon to orbit. When this happens (billions of years from now), the Earth's day will be 47 current days long. We would then say the Earth is "tidally locked" to the Moon.

Orbits and Orbital Energy


Think of a satellite on an elliptical orbit around the Earth.


Orbits cannot change spontaneously. To change orbits, we must change orbital energy. How can we do that

Escape velocity: the velocity needed to escape the gravitational pull of an object.