Essay On Satellite Motion

1266 Words6 Pages
Satellite Motion Radial and angular motion We will be concerned here with the orbiting motion of a satellite, such as a planet around the sun, or the moon around the earth. We neglect the effects of all other bodies. We will assume that the satellite's mass (m) is much smaller than that (M) of the body it moves around. Both bodies actually orbit around the CM of the system, but M moves only a small amount because the CM is so close to it. We ignore this motion as an approximation, and take the center of M to be the origin of our coordinate system. Because gravity (a central and conservative force) is the only force doing work: The total mechanical energy E of the system is conserved. The gravitational force acts along the line between the…show more content…
We will now prove the other two laws. Proof of the 1st law requires an extensive use of calculus, so we will not give it here. Shown is an elliptical orbit and the position of the satellite at two times differing by dt . The satellite moves a distance ds along the orbit, while the line connecting the bodies turns through angle d. The area swept out by the line is that of the narrow triangle Since ds r dwe have The rate at which area is swept out is Since L is a constant, we have shown that the rate at which area is swept out is constant. This is Kepler's 2nd law, which we see is a simple consequence of conservation of angular momentum. If we integrate this rate over the time for a complete revolution (the period T) we obtain the total area of the ellipse. Thus Area LT 2m The area of an ellipse is ab. Substituting from the formulas given above relating E and L to a and b, we find after some algebra: Kepler’s 3rd law a3 T2 GM 42 This shows that the ratio a3 /T2 is the same for all objects orbiting a given mass M. This is Kepler's 3rd law. r d ds By measuring a and T one can use this relation to determine the mass M. It is in
Show More
Related

  • The Importance Of Television

    1006 Words  | 5 Pages

    Television as an invention has clearly transformed both the professional and private lives of the citizens of the developed world. It has been a profound and played a significant role on social lives in varies ways which provide people with a plenty of different capabilities and improving some early ones from the 1940s until the 2000s. (Lule & Jack, 2016) When John Logie Baird from Scotland invented the TV in 1925, he could not have imagined how the TV has changed people’s way of life or where it

    Read More

  • Natural Disasters: Natural Hazards, Earthquakes, Volcanoes

    1522 Words  | 7 Pages

    then trying to control the damage. This essay will discuss two natural hazards; earthquakes, volcanoes. It will then go into detail about the risk management processes for each hazard along with some case studies. Earthquakes are a natural disaster that occur frequently. However only some are at a magnitude that cause huge

    Read More

More about Essay On Satellite Motion

Open Document