Chapter 13Gravity

The Universal GravityThe gravitational attraction of two objects of m1 and m2 is given by (magnitude only):

The Sun and the Earth

How small are we?

ExampleFind the gravitational force between two people of mass m=70kg, r =0.5m away from each other.

Example

What is the gravitational force on a 1kg mass on the surface of the Earth?

Weight = Fgravity

Weight on the Moon Find the weight of a 1kg mass on the moon.

g changes with distance

ExampleIf your weight on Earth is WE. What will your weight on the surface of a mysterious Planet X given RX = 20 RE and MX = 300 ME.

Orbital Motion

Calculate the Period of the Moon

rEM RE

SatelliteFind the period and tangential velocity of a satellite of mass m at distance r from the center of the Earth.

Alternative Method (using v)

Alternative Method (Continued)

Conservation of (Total) EnergyTotal energy is always conserved. We will be dealing with only two kinds of energy, kinetic energy and potential energy.

Gravitational Potential Energy

What about PEG = mgh?

PEG = mgh is only true near the planet’s surface. Far away the gravitational field gets weak and PEG = mgh is no longer true.

How to derive mgh

Alternatively

Conservation of energyA rocket is launched vertically upward at v0= 2.1km/s. How high can it go?

What is the initial KE and PE?

If it reaches radial distance r, what is the final KE and PE?

Conservation of EnergyHere is the basic equation we will use over and over again:

Conservation of energy

Conservation of EnergyHow fast must the launch speed be for the rocket to reach a height above the earth equal to RE.

Shoot highHow fast must the launch speed be for the rocket to reach a height above the earth equal to RE.

Escape VelocityWhat must v0 be to launch it to infinity?

What you have learned

• Universal gravity• Gravitation potential energy• Orbital motion• Escape velocity

Physics jokes- A seminar on time travel will be given two weeks ago.

- Entropy isn't what it used to be.

- Two atoms were walking across a road when one of them said, "I think I lost an electron!" "Really!" the other replied, "Are you sure?" "Yes, I 'm absolutely positive."