HW23 Kepler\'s Laws for Satellites Resources a previous | 1 of 4 | next » Kepler
ID: 1770898 • Letter: H
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HW23 Kepler's Laws for Satellites Resources a previous | 1 of 4 | next » Kepler's Laws for Satellites Part A This applet shows satellites orbiting a central body from various starting distances. The mass of the central body is much greater than the masses of the satellites. You should think of this applet as data obtained in an experiment (e.g. a set of videos made by compiling data of observations of satellites) Determine the orbital period Tp of the purple (innermost) satellite when it has an initial speed of 2.0 velocity units. For this problem, the units are chosen for convenience. Read the time in the box under the "reset" button; the small box beside the slider gives the time in steps of 0.1 the unit of time. Note that simply watching one orbit and seeing how long it takes will not give you three significant figures. Try to think of a technique that will Express your answer to three significant figures. Hints Tp= 3.16 time units Submit My Answers Give Up Correct Part B Determine the period T of revolution for the red satellite if its initial speed is 1.5 velocity units. Express your answer to three significant figures. Hints T, = 107 time units Submit My Answers Give Up Correct Part C Find the length of the major axis 2ap of the orbit of the purple satellite with initial speed 2.0 and the length of the major axis 2a, of the orbit of the red satellite with initial speed 1.5. Recall that the semi-major axis of an ellipse is usually denoted ; hence we use the notation 2ap for the major axis of the purple satellite's orbit. Give the length of the major axis for the purple satellite followed by the length for that of the red satellite separated by a comma. Express your answers to two significant figures.Explanation / Answer
Part D)
The periods of the planets are proportional to the 3/2 powers of the semi-major axis lengths of their orbits.
In other words, if you have an orbit of period T , then the length a of the semi-major axis will be related to the period by T = k (a)3/2 , where k is a constant of proportionality. If you set up this relation for two different orbits, then you can divide the equations to eliminate the unknown constant k.
ar/ap = 2.25
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