# Newton s Law of Universal Gravitation describes the attractive gravitational force that exists between any two bodies with the following equation:

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1 Newton s Laws & Gravitation Newton s Law of Universal Gravitation describes the attractive gravitational force that exists between any two bodies with the following equation: F G = GMm 2 r G is the gravitational constant (which for this activity you can assign a value of 1). M and m are the masses of the two objects attracting one another, and r is the distance from the center of one object to the center of the other object. 1. 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. 2. Consider the following debate between two students about their answer to the previous question. Student 1: I thought that whenever one object exerts a force on a second object, the second object also exerts a force that is equal in strength, but in the other direction. So even though 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 you are confusing Newton s 3 rd law with the law of gravity. Do you agree or disagree with either or both of the students? Why? CAPER TEAM DRAFT EDITION, 2005 LECTURE-TUTORIALS FOR INTRODUCTORY ASTRONOMY 1

2 Newton s Laws & Gravitation 3. How would the force between the Moon and Earth change if the mass of the Moon were somehow made two times greater? II. Force Distance Relationship In the picture below, the Earth-Moon system is shown (not to scale) along with six possible positions (A-H) for a spacecraft traveling from Earth to the Moon. Note that position D is exactly half-way between Earth and the Moon. Earth A B C D E F G H Moon 4. At which lettered position (A-H) is the gravitational force by Earth on the spacecraft the strongest? Explain your reasoning. 5. At which lettered position (A-H) is the gravitational force by the Moon on the spacecraft the strongest? Explain your reasoning. 6. When the spacecraft is at point D, how does the strength and direction of the gravitational force on the spacecraft by Earth compare with the strength and direction of the gravitational force on the spacecraft by the Moon? Explain your reasoning. CAPER TEAM DRAFT EDITION, 2005 LECTURE-TUTORIALS FOR INTRODUCTORY ASTRONOMY 2

3 Newton s Laws & Gravitation 7. At which of the position(s) (A-H) would the gravitational force on the spacecraft by the Moon be stronger than the gravitational force on the spacecraft by Earth? Make your best guess, there is no need to perform any calculations? Explain your reasoning. 8. Imagine that you needed to do some repairs to your spacecraft. You have decided that the best place to carry out your repairs would be at the position where the net (or total) gravitational force on the spacecraft by the Moon and Earth would be zero. Which of the positions would be the best possible one to stop at to make your repairs? Make your best guess, there is no need to perform any calculations? Explain the reasoning behind your choice. 9. 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 Moon? Why? CAPER TEAM DRAFT EDITION, 2005 LECTURE-TUTORIALS FOR INTRODUCTORY ASTRONOMY 3

4 Astronomy Ranking Task: Exercise #1 Description: The figure below shows several objects (A D) of different masses located on the surface of the earth. A B C D A. Ranking Instructions: Rank (from greatest to least) the strength of the gravitational force exerted by Earth on each of the objects (A D). Ranking Order: Greatest Least Or, the gravitational force exerted on each object is the same. (indicate with a check mark) B. Ranking Instructions: Rank (from greatest to least) the strength of the gravitational force exerted by each of the objects A D on Earth. Ranking Order: Greatest Least Or, the gravitational force exerted by each object is the same. (indicate with a check mark)

5 Astronomy Ranking Task: Exercise #2 Description: The figures below (A E) each show two rocky asteroids with masses (m), expressed in arbitrary units, separated by a distance (d), also expressed in arbitrary units. A B C D D E m = 20

6 A. Ranking Instructions: Rank (from greatest to least) the strength of the gravitational force exerted on the asteroid located on the left side of each pair. Ranking Order: Greatest Least Or, the strength of the gravitational force exerted in each case is the same. (indicate with a check mark) B. Ranking Instructions: Rank (from greatest to least) the strength of the gravitational force exerted on the asteroid located on the right side of each pair. Ranking Order: Greatest Least Or, the strength of the gravitational force exerted in each case is the same. (indicate with a check mark)

7 Exercise #3 Astronomy Ranking Task: Description: In the picture below, the Earth-Moon system is shown (not to scale) along with five possible positions (A - E) for a spacecraft traveling from Earth to the Moon. Note that position C is exactly half-way between Earth and the Moon.. Moon A B C D E Earth A. Ranking Instructions: Rank (from greatest to least) the strength of the gravitational force at positions A - E exerted by the Moon on the spacecraft. Ranking Order: Greatest Least Or, the gravitational force exerted at each position is the same. (indicate with a check mark) B. Ranking Instructions: Rank (from greatest to least) the strength of the net (or total) gravitational forces at positions A - E exerted by both the Earth and the Moon on the spacecraft. Ranking Order: Greatest Least Or, the gravitational force exerted at each position is the same. (indicate with a check mark)

8 Exercise #4 Astronomy Ranking Task: Description: The figures below (A D) each show two rocky asteroids with masses (m), expressed in arbitrary units, separated by a distance (d), also expressed in arbitrary units. A B C D m = 20

9 A. Ranking Instructions: Rank (from greatest to least) the strength of the gravitational force exerted on the asteroid located on the left side of each pair. Ranking Order: Greatest Least Or, the strength of the gravitational force exerted in each case is the same. (indicate with a check mark) B. Ranking Instructions: Using Newton s Second Law, rank the acceleration (from greatest to least) that the asteroids located on the left side of each pair would experience due to the gravitational force exerted on it. Ranking Order: Greatest Least Or, the accelerations for each asteroid is the same. (indicate with a check mark)

10 Exercise #5 Astronomy Ranking Task: Description: The figures below (A D) each show a large central asteroid along with two other asteroids located to the right and left of the central asteroid. The masses (m) of the asteroids are expressed in arbitrary units, and the distance (d) from the center asteroid is also expressed in arbitrary units. A d = 3 d = 3 B d = 3 d = 3 C d = 2 d = 3 D d = 3 d = 3

11 Ranking Instructions: Rank (from greatest to least) the strength of the net (or total) gravitational force exerted on the center asteroid by its two neighboring asteroids. Ranking Order: Greatest Least Or, gravitational forces are all the same strength. (indicate with a check mark)

12 Astronomy Ranking Task: Exercise #6 Description: The table below shows the masses and distances (expressed in arbitrary units) between four different pairs of stars (Cases A D). Case Mass of star #1 Distance between star #1 and star #2 Mass of star #2 A B C D Ranking Instructions: Rank (from greatest to least) the strength of the gravitational force exerted between the pairs of stars in cases A - D. Ranking Order: Greatest Least Or, the strength of the gravitational force exerted between each pair of stars is the same. (indicate with a check mark)

13 Exercise #7 Astronomy Ranking Task: Description: The figure below shows two identical asteroids located very near one another but moving in an orbit that keeps them from colliding. D C A B Ranking Instructions: Rank (from greatest to least) the net (or total) gravitational force that would be exerted on an astronaut if he/she were standing on the asteroids at the various locations (A D). Ranking Order: Greatest Least Or, the net force exerted on the astronaut would be the same at each location. (indicate with a check mark)

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