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Lecture 9 ASTR 111 – Section 002

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Ptolmey Copernicus Brahe Kepler Galileo (Galilei) Newton

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**Outline Exam Results Finish Chapter 4 Kepler’s Laws Review**

Newton’s Laws

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This is a picture of Jupiter taken through a 12” telescope at the GMU observatory. I have zoomed in so that you can see three moons. These are the “Galelian” moons (actually there are four of them, but the fourth one is too dim to see). Now, if you watched over the course of the night, you would see these moons move. The one on the right would pass behind Jupiter and the ones on the left in front. The natural thing for you to do would be to estimate the time it took for the moon to return to its original spot. A convenient spot is when the moon goes behind Jupiter.

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Exam Results

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If the moon's orbit was in the ecliptic plane instead of being tilted, there would be a lunar and solar eclipse every month. How many times per year would a lunar eclipse occur during the first quarter moon? 1. once per month. 2. Once per year times per year. 4. Never.

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On the day that someone on Earth says it is a new moon, what will a person on the moon say when they look at Earth? Assume that on this day there is not an eclipse.

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**Kepler proposed elliptical paths for the planets about the Sun**

Using data collected by Brahe, Kepler deduced three laws of planetary motion: the orbits are ellipses a planet’s speed varies as it moves around its elliptical orbit the orbital period of a planet is related to the size of its orbit

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**Kepler proposed elliptical paths for the planets about the Sun**

Using data collected by Brahe, Kepler deduced three laws of planetary motion: the orbits are ellipses a planet’s speed varies as it moves around its elliptical orbit the orbital period of a planet is related to the size of its orbit

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**Lingering questions Kepler’s laws are not so “clean” Need to explain**

Why orbits of planets are elliptical Why distance from Sun is related to orbital period Why planet velocity changes during orbit Also want a recipe that gives good predictions of when eclipses will occur, where the planets will be in the future.

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**Lingering questions Kepler’s laws are not so “clean” Need to explain**

Why orbits of planets are elliptical Why distance from Sun is related to orbital period Why planet velocity changes during orbit Why people on the south pole don’t fall into space … Also want a recipe that gives good predictions of when eclipses will occur, where the planets will be in the future.

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Isaac Newton Isaac developed three principles, called the laws of motion, that apply to the motions of objects on Earth as well as in space

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Isaac Newton Isaac was a little nutty – See short biography “Newton” by James Gleick

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**Newt’s “Principles” (Laws of Motion)**

The law of inertia: a body remains at rest, or moves in a straight line at a constant speed, unless acted upon by a net outside force F = m x a: the force on an object is directly proportional to its mass and acceleration, provided the mass does not change The principle of action and reaction: whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body

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Group Question An object at rest tends to stay at rest. An object in motion tends to stay in motion. What is wrong with this statement? Why don’t we observe “objects in motion tending to stay in motion” more often?

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Group Question An object at rest tends to stay at rest. An object in motion tends to stay in motion What is wrong with this statement? Need to add unless acted on by an external force. Why don’t we observe “objects in motion tending to stay in motion” more often?

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**Newton’s Law of Universal Gravitation**

A number (T.B.D.) Mass m2 Mass m1

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**Mass and Weight are not the same**

Mass refers to how much stuff is in an object (atoms, molecules, etc). Weight refers to how much that stuff will push down on a scale. This depends on what planet you are on.

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**Newton’s Law of Universal Gravitation**

Mass m1 A spring Weight is a number that tells you about how much this spring will compress. If your mass is m2, your weight depends on m1 and r. r Mass m2

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**How to get Weight = mass x gravity**

Mass of Earth m/s2 Radius of Earth

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What about Bob Beamon?

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The law of universal gravitation accounts for planets not falling into the Sun nor the Moon crashing into the Earth

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v v m2 m2 (You will need to take my word on this equation)

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Now suppose Earth provides “pull” instead of string and arm v v m1 m2 m2

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**(Force that can be provided)**

(Force needed to keep it in orbit)

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**Is this right? G = 6.7 x 10-11 N.m2/kg2 m1 = 2 x 1030 kg Mars**

Orbital velocity = 24 km/s Distance from Sun = 228 x 109 km Earth Orbital velocity = 30 km/s Distance from Sun = 150 x 109 km

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**Compare Kepler’s 3rd law relates orbital speed and radius**

Newton’s law of gravitation was used to derive a relationship between orbital speed and radius Both will give the same answer. Which is “better”?

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**To get something in orbit, you need a special horizontal velocity**

The law of universal gravitation accounts for planets not falling into the Sun nor the Moon crashing into the Earth Paths A, B, and C do not have enough horizontal velocity to escape Earth’s surface whereas Paths D, E, and F do. Path E is where the horizontal velocity is exactly what is needed so its orbit matches the circular curve of the Earth

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Question How far would you have to go from Earth to be completely beyond the pull of gravity? Suppose the Earth was 2x its current radius (with the same mass). How would your mass change? How would your weight change?

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**How far would you have to go from Earth to be completely beyond the pull of gravity? r = infinity**

Suppose the Earth was 2x its current radius (with the same mass). How would your mass change? How would your weight change? mass unchanged. r increases to 2r so weight goes down by 1/22=1/4

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Given that Earth is much larger and more massive than the Moon, how does the strength of the gravitational force that the Moon exerts on Earth compare to the gravitational force that Earth exerts on the Moon? Explain your reasoning. Consider the following debate between two students about their answer to the previous question. Do you agree or disagree with either or both students? Explain. Student 1: I thought that whenever one object exerts a force on the second object, the second object also exerts a force that is equal in strength, but in the other direction. So even if Earth is bigger and more massive than the Moon, they still pull on each other with a gravitational force of the same strength, just in different directions. Student 2: I disagree. I said that Earth exerts the stronger force because it is way bigger than the Moon. Because its mass is bigger, the gravitational force Earth exerts has to be bigger too. I think that you are confusing Newton’s third law with the law of gravity..

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How would the strength of the force between the Moon and Earth change if the mass of the Moon were somehow made two times greater than its actual mass?

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Given that Earth is much larger and more massive than the Moon, how does the strength of the gravitational force that the Moon exerts on Earth compare to the gravitational force that Earth exerts on the Moon? Explain your reasoning. Same. Netwon’s third law.

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Consider the following debate between two students about their answer to the previous question. Do you agree or disagree with either or both students? Explain. Student 1: I thought that whenever one object exerts a force on the second object, the second object also exerts a force that is equal in strength, but in the other direction. So even if Earth is bigger and more massive than the Moon, they still pull on each other with a gravitational force of the same strength, just in different directions. Student 2: I disagree. I said that Earth exerts the stronger force because it is way bigger than the Moon. Because its mass is bigger, the gravitational force Earth exerts has to be bigger too. I think that you are confusing Newton’s third law with the law of gravity.

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m1 m2

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How would the strength of the force between the Moon and Earth change if the mass of the Moon were somehow made two times greater than its actual mass? Two times greater

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Earth Mars In the picture, a spaceprobe traveling from Earth to Mars is shown at the halfway point between the two (not to scale). On the diagram, clearly label the location where the spaceprobe would be when the gravitational force by Earth on the spacecraft is strongest. Explain. On the diagram, clearly label the location where the spaceprobe would be when the gravitational force by Mars on the spacecraft is strongest. Explain your reasoning. When the spacecraft is at the halfway point, how does the strength and direction of the gravitational force on the spaceprobe by Earth compare with the strength and direction of the gravitational force on the spaceprobe by Mars. Explain your reasoning.

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Earth Mars On the diagram, clearly label the location where the spaceprobe would be when the gravitational force by Earth on the spacecraft is strongest. Explain. m1 and m2 don’t change. Force increases when r decreases.

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Earth Mars On the diagram, clearly label the location where the spaceprobe would be when the gravitational force by Mars on the spacecraft is strongest. Explain. m1 and m2 don’t change. Force increases when r decreases.

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Earth Mars FMars FEarth When the spacecraft is at the halfway point, how does the strength and direction of the gravitational force on the spaceprobe by Earth compare with the strength and direction of the gravitational force on the spaceprobe by Mars. r is same, mship is same. Only thing left is mEarth vs. mMars

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Earth Mars If the spaceprobe had lost all ability to control its motion and was sitting at rest at the midpoint between Earth and Mars, would the spacecraft stay at the midpoint or would it start to move. If you think it stays at the midpoint, explain why it would not move. If you think it would move, then (a) Describe the direction it would move; (b) describe if it would speed up or slow down; (c) describe how the net (or total) force on the spaceprobe would change during this motion; and (d) identify when/where the spaceprobe would experience the greatest acceleration.

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Earth Mars Where would the spaceprobe experience the strongest net (or total) gravitational force exerted on it by Earth and Mars? Explain your reasoning.

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Earth Mars Imagine that you need to completely stop the motion of the spaceprobe and have it remain at rest while you perform a shutdown and restart procedure. You have decided that the best place to carry out this procedure would be at the postion where the net (or total) gravitational force on the spaceprobe by Mars and Earth would be zero. On the diagram, label the location where you would perform this procedure. (Make your best guess; there is no need to perform any calculations here.) Explain the reasoning behind your choice. Your weight on Earth is simply the gravitational force that Earth exerts on you. Would your weight be more, less, or the same on the Mars. Explain your reasoning.

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Earth Sun 5 1 2 3 4

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Orbital Mechanics

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Tides

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