OrbitsTides

The UniversalLaw of Gravitation

Announcements

Test #1 is next Wednesday:Do not leave today without the Study Guide/Crossword puzzle.

Monday will be review – bring clickers and calculators!

Next week: Lab does not meet because you will be doing Moon observations.

Today’s Handout…

The Universal Law of Gravitation

1. All masses attract all other masses through a force called gravity.

The Universal Law of Gravitation

1. All masses attract all other masses through a force called gravity.

2. The strength of the gravitational force is directly proportional to the product of the two masses.

The Universal Law of Gravitation

1. All masses attract all other masses through a force called gravity.

2. The strength of the gravitational force is directly proportional to the product of the two masses.

3. The strength of the gravitational force goes down with the square of the distance between their centers.

The Universal Law of Gravitation

2

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If the Moon were to be moved to twice its current distance from Earth, what would happen to the force of gravity Earth exerts on the Moon?

A) It would be 4 times stronger

B) It would be 2 times stronger

C) It wouldn’t change

D) It would be 2 times weaker

E) It would be 4 times weaker

Example 1: What gravitational force does the Earth exert on the Moon?

2

311

skg

m 1067.6

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221

d

MMGFg

2

311

skg

m 1067.6

G

221

d

MMGFg

Example 1: What gravitational force does the Earth exert on the Moon?

2

311

skg

m 1067.6

G

221

d

MMGFg

Example 1: What gravitational force does the Earth exert on the Moon?

Example 2: What gravitational force does the Moon exert on the Earth?

Example 2: What gravitational force does the Moon exert on the Earth?

Newton’s Third Law of Motion

When object 1 exerts a force on object 2, object 2 exerts the SAME force on object 1, but in the opposite direction

Sometimes called “Action – Reaction”

Possible “orbits”

Newton’s Law of Gravity and Laws of Motion lead to a variety of possible orbital

shapes

“Conic Sections”

Newton’s laws lead directly to, or “explain”, ALL ofKepler’s Laws of Planetary Motion

Is it possible for a large man to teeter-totter with a small child?

A) No. They have to have the same weight to balance.

B) Yes, but only if they are the same distance from the balance point.

C) Yes, but only if the child is closer to the balance point.

D) Yes, but only if the man is closer to the balance point.

E) No. Newton’s laws make it clear that they can’t possibly balance.

Is it possible for a large man to teeter-totter with a small child?

A) No. They have to have the same weight to balance.

B) Yes, but only if they are the same distance from the balance point.

C) Yes, but only if the child is closer to the balance point.

D) Yes, but only if the man is closer to the balance point.

E) No. Newton’s laws make it clear that they can’t possibly balance.

Objects orbit their common center of mass

Two stars of equal mass

A large star and a small star

A star and a large planet

Center of Mass

The Earth and Moon both move in circles around their common center of mass.

Objects orbit their common center of mass

Newton derived a version of Kepler’s 3rd Law that involves the masses of the two bodies.

This will allow us to determine the masses of planets, stars, black holes, etc., by observing objects orbiting them!

Orbital Energy

Low kinetic energyHigh potential energy

High kinetic energyLow potential energy

Total energy remains the same throughout the orbit

Orbital Energy

Higher orbits have higher total energy

To change orbits, the energy of the satellite must be changed

Adding energy raises the satellite to a higher orbit

Orbital Energy

“Escape velocity”

Of course, you can add so much energy that the

satellite never comes back!

R

GMv

2e

Example 3: What is the escape velocity from the surface of the Earth?

R

GMv

2e

Example 4: What is the escape velocity for Earth, starting from the orbital distance of the Moon?

R

GMv

2e

Tides

The gravity of the Moon causes “tidal bulges” on Earth.

Both the solid Earth and the oceans bulge, but the ocean bulge is most obvious.

The ocean bulge, along with the rotation of the Earth, cause two high tides every day.

The Sun also creates tidal bulges on Earth, though not as extreme.

Spring tides

Sun and Moon align, so their tidal bulges add, creating more extreme tides

New Moon and Full Moon

Neap tides

Sun and Moon are at right angles, so their tidal bulges cancel each other a bit,

creating less extreme tides

1st and 3rd quarters

The tidal bulge is actually a little east of the Moon, due to drag and the Earth’s rotation.

The tidal bulge is actually a little east of the Moon, due to drag and the Earth’s rotation.

The Moon’s gravity acts on the “Center of Gravity” of the Earth.This is a “backwards” pull, slowing the Earth’s rotation.

The Earth pulls forward on the Moon (Newton’s 3rd Law), speeding it up, and causing it to drift away from Earth a few centimeters each year.

Center of gravity

Moon’s pull on Earth’s Center of gravity

How many low tides does a coastal city experience every day?

A) 1

B) 2

C) 3

D) 4

Why do all objects on earth fall with the same acceleration?

Why do all objects on earth fall with the same acceleration?

Combining these two we find …

m

Fa g 2d

MmGFg

Why do all objects on earth fall with the same acceleration?

Combining these two we find …

m

Fa g 2d

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2d

GMa

Example 5: Calculate the acceleration due to gravity on the surface of the Earth.

2d

GMa

Example 6: Calculate the acceleration due to gravity on the surface of Europa, a moon of Jupiter.

2d

GMa

If everything falls with the same acceleration, why does a piece of paper fall more slowly than a rock?

A) Because its lighter, and lighter things fall more slowly

B) Because the paper has more air resistance

C) Because rocks exert more gravitational force on the Earth

D) Because of electrostatic repulsion between the Earth and the paper