QUESTIONS:
1. Why does the law of INERTIA (Newton's first law) imply that there must be a force of attraction (rather than repulsion) between each planet and the Sun? [consider the result of having a repulsive gravity]
NOTE: For this -- and all other quantitative problems -- DO NOT simply write down a number from the texbook (or other source) as an answer. I want to know if you can calculate that number yourself. Therefore, SHOW your WORK (calculations) on all problems and USE UNITS ON ALL NUMBERS where appropriate. Failure to do so will result in loss of credit.
PROBLEMS:
1. How much less would you weigh on the summit of Mt. Everest (29,000 feet [8.84 km] above sea level), if you weigh 130 lbs. at sea level? The radius of the earth is 6,367 km.
HINT: This problem, like many others, is very easy to calculate. To approach it, consider the following: What relationship (i.e., equation) can you find that relates "weight" with the information given in the problem? It has been presented in class (NEWTON) and is in your text. Throw out the "junk" in the equation that will not change from one condition to the other (sea level vs peak of Everest) and compare the two situations. How do you compare them? Finding a "ratio" would be a good idea. This ratio can then be used to alter the value of your sea level weight...to that of your mountain top weight.
2. Find the mass of Jupiter in Solar units using Kepler's third law (as modified by Newton) and data from Table E-3 using Callisto as the orbiting body. THEN, convert your answer to kilograms (kg). Remember to show all work leading to the answer and proper units. How does your answer compare to the mass of Jupiter given in Table E-2?
3. Given two stars, one being twice as massive as the other. Calculate where their center of mass must lie along a line connecting their centers.
HINT: Draw a picture of the above situation. Label the constituent parts, including a provisional barycenter (center of mass). Set up an equation to describe what you know about the line (L) between the two bodies. Substitute this into the main equation (for center of mass) and solve for d1 or d2. Some other obvious substitutions will also be necessary. In the end, when most terms have cancelled out, you will have a simple equation that looks something like this: d = y/x L, where y/x is a fraction, and L is the total length of the center-center line. For full credit, you must use a mathematical proof to get the answer in the general form illustrated in the last sentence.