## Activity Based Physics Thinking Problems in Mechanics: Universal Gravitation

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### Activity Based Physics Thinking Problems in Mechanics: Universal Gravitation

1) Someone once stopped me in the hall and said: "I can prove Newton's theory of gravity is wrong. The sun is 320,000 times as massive as the earth, but only 400 times as far from the moon as the earth is. Therefore the force of the sun's gravity on the moon should be twice as big as the earth's and the moon should go around the sun instead of around the earth. Since it doesn't, Newton's theory of gravity must be wrong!" What's the matter with this reasoning?

2) The next problem uses the computer program ORBITS *.

Run ORBITS and select the scenario SPSTATN (Space Station). This features a space ship in the same circular geosynchronous as a space station. Unfortunately, it is in orbit one-fourth of an orbit behind a space station. You want to rendezvous with the station by matching position and velocity with it.

Try to rendezvous with the station by adding or subtracting velocity (thrust) to your space ship using the + key to control the amount of thrust and the arrow keys on the numeric keypad to control the direction (of Dv). Try a variety of procedures before choosing a final one. When you have decided on a procedure, perform it and write down what you did and the total amount of thrust you used. You can reset the program to the starting values by pressing <esc> and selecting SPSTATN again. (Hint: A rendezvous can be achieved using only 2 thrusts.)

To view how closely you've rendezvoused, when you are satisfied, press<Ctrl><F2> to record your final positions and velocities to the data tables. Return to the data tables by pressing <BACKSPACE>. Press <PrtSc> to print out the exact values of the x and y positions and the x and y velocities of the space ship and space station. Calculate your distance from the space station and the relative velocity between you and the space station using the Pythagorean theorem.

3) The orbiting Hubble telescope was recently repaired by a crew of astronauts from the Space Shuttle Endeavor. The Hubble is in a circular orbit 600 km above the surface of the earth. For half of the Hubble's orbital period it is in sunlight and for half it is in the darkness of the earth's shadow. As a result of the change in fit of the various parts of the Hubble due to heating and cooling of the telescope, the astronauts could only work on certain repairs while the Hubble was in darkness. Estimate how much time the astronauts had to work on these repairs before having to stop "for a sun-break".

 4) On the figure at the right is shown a space ship going in an elliptical orbit around the earth. Take the origin of your coordinate system to be at the center of the earth. (a) On a copy of the figure on your paper, draw vectors representing the position of the space ship when it is at A and B; the velocity of the space ship when it is at A and B the acceleration of the space ship when it is at A and B. Draw your vectors so that each type of vector can be distinguished. Be sure to give a legend that shows how each type is being represented. (b) Have you drawn the velocity vector at A longer, shorter, or the same length as the one at B? Explain why. (c) Have you drawn the acceleration vector at A longer, shorter, or the same length as the one at B? Explain why you have done so.

5) Suppose you are piloting the space ship in the problem above and that the point at A is at a distance of 3 earth radii from the earth's surface, and the point B is at a distance of 1 earth radius from the center. You are at point A and want to change your orbit.

(a) What would happen to the shape of your orbit if you decided to speed up in the direction you are heading by firing your aft rockets briefly?
(b) What would happen to the shape of your orbit if you decided to slow down in the direction you are heading by firing your fore rockets briefly?
(c) If you want to put yourself into a circular orbit passing through the point A, how would you do it? (Be quantitative!)

6) Two schoolmates, Romeo and Juliet, catch each other's eye across a crowded dance floor at a school dance. Estimate the gravitational attraction they exert on each other.

* This software may be obtained from Physics Academic Software

These problems written and collected by E. F. Redish. These problems may be freely used in classrooms. They may be copied and cited in published work if the Activity Based Physics Thinking Problems in Physics site is mentioned and the URL given. Web page edited by K.A. Vick.

To contribute problems to this site, send them to redish@physics.umd.edu.

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Comments and questions may be directed to E. F. Redish