Lecture 8
Summer 2006
Gravity and Orbital Motion
Key Concepts:
- What are the Newton's Laws of Motion?
- How are "mass" and "weight" different?
- What is momentum and angular momentum? What does conservation
of angular momentum mean?
- What causes the ocean tides?
- What is escape velocity? How fast should a spaceship
travel in order to leave the Earth or the Moon?
A body remains at rest or in uniform motion in
a straight line unless it is made to change that state by forces acting
on it.
- Inertia = tendency of an object to remain at rest or in motion
- Mass = a measure of the amount of material in an object;
a measure of inertia
Newton's Second Law of Motion
A net force is need to change the velocity
of an object.
- Velocity = a measure of motion; a rate of change in position and direction
- Acceleration = a rate of change in velocity
Law of Gravity
Every mass exerts a force of attraction on every other mass. The strength of the force is proportional to the masses divided by the square of their separation.
Newton's Third Law of Motion
When two bodies interact, they create equal and
opposite forces on each other.
Conservation of Momentum and Angular Momentum
- Momentum = (mass) x (velocity)
- Angular Momentum = (mass) x (velocity) x (radius)
Tides
- Ocean level rises falls twice a day.
- Earth stretched by the gravitational forces of the Moon.
- The Sun also exerts a tidal force on the Earth.
- Spring tides: The Sun and the Moon aligned
- Neap tides: The Sun and the Moon aligned perpendicularly
- Tidal Friction: Earth rotates against the stretch
- The Earth tidal bulge leads the Moon in rotation, and the Earth is slowed down by the Moon (a day is 1 second shorter in 50,000 yrs).
- In turn, the Moon is sped up and spirals outwards (conservation of angular momentum)
Escape Velocity
- When you throw a ball straight up, the harder you throw, the
higher it goes.
- If thrown hard enough (at high enough velocity), the ball will
"escape" Earth.
Question: The mass of the Moon is only about 1/100th of the Earth.
It has a radius about a quarter that of the Earth.
How much larger or small is the escape velocity from the Moon compared
with the escape velocity from the Earth?
Reading assignment for next lecture: Chapter 8 (p.197-p.223)