Question:
question about satellite?
2009-10-26 21:51:38 UTC
Robert is calculating the orbit for a weather satellite so that it will circle the Earth with an orbital period T. Find the radius of this orbit in terms of T. How high above Earth's surface will the satellite orbit? How fast will the satellite move in its orbit? Calculate the altitude and speed of a weather satellite that circles the Earth every 150 minutes.
Three answers:
Vansig
2009-10-28 20:11:31 UTC
Orbits are elliptical, and so the speed and height of the orbit changes continuously. Therefore, we will use the length of the semi-major axis according to Kepler's laws. As a special case, if the orbit is circular, then the speed and height are constant, and the semi-major axis is the radius.



if T is the period, then

( T / 2pi )^2 = a^3 / (GM),



where a is the length of the semi-major axis, G is the gravitational constant, and M is the mass of earth.



for a circular orbit of 150 minutes,



(150x60 / 2pi)^2 = a^3 / ( 6.674e-11 x 5.97e24 )



a^3 = (((150 × 60) / (2 × pi))^2) × 6.67400e-11 × 5.97e24

= 8.17496337e20



a = e^(ln(8.17496337e20) / 3) = 9 350 365.88 m



in other words, the radius is about 9350 km.



the satellite travels 2 pi of these in 150 minutes;

speed = (9 350 365.88 x 2 x pi) / (150 x 60) = 6 527.78683



so 6527.8 m/s
?
2016-12-18 18:34:13 UTC
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ant hed
2009-10-26 21:59:19 UTC
I hope you do not graduate, because if you do and you are invovled in such future calculations we can be sure for the Satillite to be lost in space - or worse - crash into earth. One can only hope it will be your house that it crashes on.



Do us all a favor and go flip burgers.


This content was originally posted on Y! Answers, a Q&A website that shut down in 2021.
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