Calculation Examples; Geosynchronous Orbits - Sharp EL-5230 Operation Manual

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
2
4π
2
3
T = ——
r
GM
where T = period of orbit
G = Gravitational constant (6.6742 × 10
M = Mass of the Earth (5.976 × 10
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.
Press b 0 23 [ 56 [ 4.09
1.
[ I 6.
• Determining the value of T.
Press x T to store the result as global
2.
variable T.
Press @ J 1 1 4.
3.
• Select the scientific display format with
four significant digits.
• Use the solver function to solve the
equation for r.
Press j ; T A ; =
4.
( 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.
110
–11 3 –1
m kg s
24
kg)
23∂56∂4.09∂Ωse
c
AnsÒT
TŒ=(4πŒ)©(GM)˚
R„_
TŒ=(4πŒ)©(GM)˚
R„
G=z
–2
)
86164.09
86164.09
8.616
0.000
0.000