## Gravitation and Keplers Laws

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# Gravitation and Keplers Laws

Physics Homework Help

Every object around you is attracted to you. In fact, every object in the galaxy is attracted to every other object in the galaxy. Newton postulated and Cavendish confirmed that all objects with mass are attracted to all other objects with mass by a force that is proportional to their masses and inversely proportional to the square of the distance between the objects’ centers. This relationship became Newton’s Law of Universal Gravitation. In this simulation, you will look at two massive objects and their gravitational force between them to observe G, the constant of universal gravity that Cavendish investigated.

1. Take some time and familiarize yourself with the simulation. Notice how forces change as mass changes and as distance changes.

2. Fill out the chart below for the two objects at various distances.

3. Rearranging the equation for Force, you can CALCULATE the value of G using the values given below for m1, m2, and d, and the value for the Force that you obtain in the simulation. Record the force between the two object and then solve (calculate G) for the universal gravitation constant, G and compare it to values published in books, online, or your text book. The numbers you calculate for G will vary slightly from row to row. Remember significant digits! 15 pts

Mass Object 1 Mass Object 2 Distance Force Gravitation Constant,G

 50.00 kg 25.00 kg 3.0m 50.00 kg 25.00 kg 4.0m 50.00 kg 25.00 kg 5.0m 50.00 kg 25.00 kg 6.0m 50.00 kg 25.00 kg 9.0m

What do you notice about the force that acts on each object? 3 pts

Average value of G: _________________2 pts Units of G: _______________2 pts

Published value of G: ________________2 pts Source: _______________2 pts

How did your average value of G compare to the published value for G that you found? 3 pts

Conclusion Questions and Calculations: Bold and Underline the correct answer to each question.

1. Gravitational force is always attractive / repulsive. (circle) 2 pts

2. Newton’s 3rd Law tells us that if a gravitational force exists between two objects, one very massive and one less massive, then the force on the less massive object will be greater than / equal to / less than the force on the more massive object. 2 pts

3. The distance between masses is measured from their edges between them / from their centers / from the edge of one to the center of the other. 2 pts

4. As the distance between masses decreases, force increases / decreases. 2 pts

5. Doubling the mass of both masses would result in a change of force between the masses of 4x / 2x / no change / ½x / ¼x. 2 pts

6. Reducing the distance between two masses to half while doubling the mass of one of the masses would result in a change of force between the masses of 8x / 4x / no change / ½x / ¼x. 2 pts

7. What is the gravitational force between two students, Dylan and Sarah, if Dylan has a mass of 75 kg, Sarah has a mass of 54 kg, and their centers are separated by a distance of .45 m? 2 pts ________________ N

8. What is the gravitational force between two students, John and Mike, if John has a mass of 81 kg, Mike has a mass of 93 kg, and their centers are separated by a distance of .62 m? 2 pts ________________ N

9. Imagine a 4820 kg satellite in a geosynchronous orbit. If an 85 kg piece of space junk floats by at a distance of 3.5 m, what force will the space junk feel? 2 pts ________________ N

10. With what acceleration will the space junk move toward the satellite? 2 pts ______________ m/s2

11. With what acceleration will the satellite move (if any)? 2 pts ______________ m/s2

12. The gravitational force on the moon by the earth. 2 pts ________________ N

13. The gravitational force on the earth by the moon. 2 pts ________________ N

Show your calculation for 12 and 13 here.

The lab is continued on the next page.

1) Run the Simulation, Keep all the default settings, but select the Earth and Satellite option. Turn on all of the options in the “Show” menu, then run and play with the simulation for a while. Which is experiencing a greater gravitational force: The satellite or the earth? 3 pt

2) Pause the Simulation. Hit “Reset”. (not “Reset All”). Alter the mass of the Satellite. Does the mass of the satellite have any impact on its Orbit? Explain. 3 pts

3) Pause the Simulation. Hit “Reset.” Click and drag the “v” at the end of the red velocity in order to decrease the satellite’s velocity.

a. What happens when you hit play? Why? 3 pts

b. Why doesn’t this happen to satellites normally? 3 pts

4) Pause the Simulation. Hit “Reset.” Click and drag to increase the satellite’s velocity. What happens when you hit play? Why? 3 pts

5) Pause the Simulation. Hit “Reset.” Click and drag the satellite itself to move it further away from earth. What happens when you hit play? Why? 3 pts

6) Try to create another stable orbit that is further or closer to earth. What other very important variable would you need to alter with this new orbit? 3 pts

7) Just for fun. Click and drag earth to create a very small velocity for earth. Can the satellite still orbit a moving planet? 3 pts

8) Pause the Simulation. Hit “Reset.” On the top left tabs, change your view so that you are to scale. In the Show menu, you can now also turn on the “Tape Measure”. Run the simulation, with the path shown.

How far out is the satellite? 3 pts

How long does it take for the satellite to orbit earth? 3 pts

9) Switch modes, so that you are now looking at just the earth and the moon.

How far is the moon? 3 pts

How long does it take for the moon to orbit the earth? 3 pts

10) Again Switch modes, so that you are now looking at just the earth and the sun.

How far is the earth from the sun? 3 pts

How long does it take for the earth to orbit the sun? 3 pts

11)

According to Kepler’s third law, the time it takes for one complete orbit is proportional to the mean distance between the centers of two bodies. T2 ≈ r3. When a constant is included, the equation is . Use the adjustable mass controls on the simulation of just the earth and sun to determine what mass the “m” in Kepler’s equation must refer to. Is it the mass of the orbiting object or the mass of the central object?12) Kepler actually proposed three laws.

Kepler’s Laws of Planetary Motion

First Law: Each planet travels in an elliptical orbit around the sun, and the sun is at one of the focal points.

Second Law: An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals.

Third Law: The square of a planet’s orbital period ( T2 ) is proportional to the cube of the average distance ( r3 ) between the planet and the sun, or T2 r3 .

An Illustration of Keplers 1st and 2nd Laws is Shown here: A1=A2. In this case you can see that when a planet is closer to the sun then it must cover more distance in the same time. It must move faster.

Reset all. Select the Earth and Sun. Choose to show only the path and velocities. Manipulate the Simulation until you achieve an elliptical orbit. The speed of the earth increases slightly as it orbits closer to the sun but decreases slightly when it is further from the sun. (hint: move the sun itself.) Do a print screen. Then paste it below into this document. 8 pts