The Solar System
The Solar System
10th Edition
ISBN: 9781337672252
Author: The Solar System
Publisher: Cengage
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Chapter 4, Problem 3P
To determine

The duration of one retrograde cycle and fraction of retrograde cycle to mars’s orbital period.

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On the evening of an autumnal equinox day Siddhant noticed that Mars was exactly along the north-south meridian in his sky at the exact moment when the sun was setting. In other words, the Sun and Mars subtended an angle of exactly 90° as measured from the Earth. If the orbital radius of Mars is 1.52 au, What will be the approximate rise time of the mars on the next autumnal equinox day?
one trajectory that can be used to send spacecraft from earth to mars is an elliptical orbit that has the sun at one focus, its perihelion at earth, and it's aphelion at mars. the spacecraft is launched from earth and coasts along this ellipse until it reaches mars, when a rocket is fired to either put the spacecraft into orbit around mars or cause it to land on mars. (a) find the semimajor axis of the ellipse (in au). (hint: draw a picture showing the sun and the orbits of earth, mars, and the spacecraft. treat the orbits of earth and mars as circles.) [enter your answer in units of au]
A)At what altitude would a geostationary sattelite need to be above the surface of Mars? Assume the mass of Mars is 6.39 x 1023 kg, the length of a martian solar day is 24 hours 39minutes 35seconds, the length of the sidereal day is 24hours 37minutes 22seconds, and the equatorial radius is 3396 km. The answer can be calculated using Newton's verison of Kepler's third law.

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Kepler's Three Laws Explained; Author: PhysicsHigh;https://www.youtube.com/watch?v=kyR6EO_RMKE;License: Standard YouTube License, CC-BY