Orbits Tides The Universal Law 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

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?

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 of Kepler’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 3 rd 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 energy High potential energy High kinetic energy Low 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!

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

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

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 1 st and 3 rd quarters

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 3 rd 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?

Combining these two we find …

Why do all objects on earth fall with the same acceleration? Combining these two we find …

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

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

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