Today’s topic: Gravity…

Reminder: midterm on Wed Oct 8. I will do a review session second half of today’s class Midterm will cover everything through last week. Remember to bring you star wheel for the midterm!

Next Wed Oct 15: Kitt Peak trip. Leave at 4 pm, return about 10 pm; TOCC van will continue to Sells. Let me know if you have transportation questions, problems!

Last week: how stars form… gravity was mentioned a lot

Gravity pulls inward, gas pressure pushes outward

•  Gravity is responsible for the different sizes of stars

Calculation of forces new positions

Mathematical calculations show how different masses interact

but how does gravity affect our daily life? What is the “law of gravity”?

First, a few questions:

Besides the force of gravity, which of the following hold us to Earth’s surface? a. Air pressure from Earth’s atmosphere. b. Forces from Earth’s spinning motion. c. Magnetism from Earth’s magnetic field. d. More than one of the above factors. e. No other significant factors; only gravity.

Which of the following would make you weigh half as much as you do right now?

a. Take away half of Earth’s atmosphere. b. Take away half of Earth’s mass. c. Take away half of Earth’s magnetic field. d. Make Earth spin half as fast. e. Move Earth twice as far from the Sun.

An astronaut standing on the Moon’s surface has a pen in his hand and releases it. What happens to the pen?

a. It falls to the surface at a slower rate than it would on Earth.

b.  It falls to the surface at a faster rate than it would on Earth.

c.  It doesn’t fall : floats where it is.

d.  It doesn’t fall and slowly drifts away.

Why do things fall to the ground?

Why does it do more damage to drop something from a greater height than a smaller height?

If you drop a heavy object, and a lighter object, does the heavier object fall faster than the lighter object?

Sir Isaac Newton, 1642-1727

From observations of falling objects, Newton proposed a force between any two objects described by the law of gravity. The force between two bodies is directed along a line joining them:

• The force increases directly with the mass of either body

• It decreases with the square of the distance between the two bodies

Why does an apple fall? What holds you to the surface of the earth? (your weight) What keeps the moon in orbit around the earth?

This force is what makes us weigh what we do.

Let’s represent gravity as an equation

G is a constant number, depending on the units you are using

Examples:

1. Suppose mass Mb doubles. What happens to the force?

2. Suppose distance, r, doubles. What happens to the force?

(which is larger? 1/2, 1/3, 1/4 )

Do the astronauts in the space station feel gravity?

What is the diameter of the Earth?

How far above the Earth does the space shuttle orbit?

Do the astronauts in space station feel gravity? Let’s explore this.

The space shuttle, and the astronauts inside, are falling around the earth!

…And the moon is falling around the earth

And the earth-moon system is…

How far from a body (earth, sun, etc) does gravity exist?

Suppose an astronaut lands on the moon. What happens to the force between the astronaut and the moon- what we call his weight?

A calculation shows that the astronaut’s weight (the force pulling him down) is only 0.17 what it was on earth.

Bodies in orbit follow a relation (an equation) between their masses, their period (“year”) and the distance between them.

If you know two of these quantities, you can find the third: let P = period, R= distance between two bodies, and M be the

mass of each: P2 (Ma + Mb) = R3

Another effect of law of gravity:

P is period of moon around earth

R is distance to moon

Then we can find the mass of earth-moon system!

- We watch the stars revolve around each other to get their period, P: - We measure the angle between them, (and if we know the distance) –Then we can calculate the mass of the two stars from P2 (Ma + Mb) = R3

Another example: From APOD, last week, Albireo, a double star We can find the masses of the two stars:

And a final example, using this equation: P2 (Ma + Mb) = R3

We can calculate how fast the sun is moving around the Milky Way galaxy: its galactic period, P

We can calculate the distance to the center of our galaxy , R

…and then we can solve for the mass of our galaxy: how many stars in the galaxy !

So, try these again:

Besides the force of gravity, which of the following hold us to Earth’s surface? a. Air pressure from Earth’s atmosphere. b. Forces from Earth’s spinning motion. c. Magnetism from Earth’s magnetic field. d. More than one of the above factors. e. No other significant factors; only gravity.

Which of the following would make you weigh half as much as you do right now?

a. Take away half of Earth’s atmosphere. b. Take away half of Earth’s mass. c. Take away half of Earth’s magnetic field. d. Make Earth spin half as fast. e. Move Earth twice as far from the Sun.