Lecture 5 F 2. Applications of Newton Laws
1. Understanding Orbits
- An object's speed in one direction is not affected by forces in other directions.
- Suppose I drop a bullet at the same instant that I fire another out a gun horizontally.
Q: Which hits the ground first?
- Bullet's horizontal motion is not affected by vertical pull of gravity: it takes the
same time to reach the ground.
- Now imagine that I fire a bullet horizontally SO fast that it moves
far over the horizon before an unfired bullet would fall to ground.
- If the Earth's curved surface is falling away from the bullet as fast as
the bullet is falling, THEN THE BULLET IS IN ORBIT!
- Since such an orbiting bullet is still falling,
so we know it is still affected by the Earth's gravity.
OR
- The circular path of the bullet also tells us a force is on the bullet: its
direction keeps changing, so it is accelerating, meaning a force -- gravity
-- is acting on it.
- So astronauts are not really in zero gravity -- they just feel no gravity, because
they're in free fall.
- (homework problem #8, p.56, is meant to show you that gravity in Earth's orbit is not
zero!)
2. Conservation Angular Momentum
- a rotating object's angular momentum is given by:
(mass)x(velocity)x(radial distance from rotation axis)
- Newton showed angular momentum is constant, or "conserved" as physicists say
- so if any one quantity above gets smaller, another must get bigger -- EXAMPLE:
- if an orbiting planet gets closer to the Sun, its radius decreases
- but constant angular momentum means something must increase
-- mass or velocity?
- but planets don't change mass...
- so velocity must increase!
- Who's law predicted such behavior by planets?
- Which law was it?
3. Newton's Laws explain Kepler's Laws -- FYI
- K's 1st = N's (1/R2) formula for gravity means orbits are ellipses
- K's 2nd = angular momentum conservation = N's 1st
- K's 3rd = N's 2nd & formula for gravity