Sharp EL-5230 User Manual download pdf (Page 112)

110

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

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.

Chapter 8: Application Examples

23∂56∂4.09∂Ωse

86164.09

AnsÒT

8.616

0.000

TŒ=(4πŒ)©(GM)˚

R„

TŒ=(4πŒ)©(GM)˚

R„

G=z 0.000

= ——

where T = period of orbit

G = Gravitational constant (6.6742 × 10

–11

–1

–2

)

M = Mass of the Earth (5.976 × 10

kg)

r = Distance between the satellite and the center of the Earth (radius of orbit)

4π

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Sharp EL-5230 User Manual Page 112

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