Sharp EL-5250, EL-5230 Calculation Examples, 23∂56∂4.09∂Ωse, 86164.09 86164.09 AnsÒT 8.616

Chapter 8: Application Examples

Calculation Examples

Geosynchronous orbits

The orbit of a satellite about the Earth is geosynchronous if the period of the orbit matches the period of the Earth’s rotation. At what distance from the center of the Earth can geosynchronous orbit occur?

The period of an orbit is described by the equation

T	2	4π2	3
		= —— r
		GM
where T =			period of orbit
		G = Gravitational constant (6.6742 ⋅ 10–11m3 kg–1s–2)
		M = Mass of the Earth (5.976 ⋅ 1024 kg)
		r = Distance between the satellite and the center of the Earth (radius of orbit)

The Earth rotates once every 23 hours, 56 minutes and 4.09 seconds. At first, convert this time into seconds.

1.Press b 0 23 [ 56 [ 4.09

[ I 6.

•Determining the value of T.

2.Press x T to store the result as global variable T.

3.Press @ J 1 1 4.

•Select the scientific display format with four significant digits.

•Use the solver function to solve the equation for r.

4.Press j ;T A ; = ( 4 @ s A ) z ( ; G ; M ) k ; R 1.

5.Check the equation on the display and press I 5 to enter the solver function.

23∂56∂4.09∂Ωse

c

86164.09

86164.09 AnsÒT

8.616

0.000 TŒ=(4πŒ)©(GM)˚ R„_

TŒ=(4πŒ)©(GM)˚ R„ G=z 0.000

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