A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are usefulfor communication and weather observation because the satellite remains above the same point on Earth(provided it orbits in the equatorial plane in the same direction as Earth's rotation). Calculate the radius ofsuch an orbit.

According to Kepler's third law, T2∝r3 Assuming the orbit based on moon's parameters, Moon's orbital…

Answered: A geosynchronous Earth satellite is one…

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter13: Gravitation

Section: Chapter Questions

Problem 46P: A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits...

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A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are useful
for communication and weather observation because the satellite remains above the same point on Earth
(provided it orbits in the equatorial plane in the same direction as Earth's rotation). Calculate the radius of
such an orbit.

Expert Solution

Step 1

According to Kepler's third law,

$T^{2} \propto r^{3}$

Assuming the orbit based on moon's parameters,

Moon's orbital radius is $\begin{array}{rcl} 3 \end{array} \begin{array}{rcl} . \end{array} \begin{array}{rcl} 84 \end{array} \begin{array}{rcl} \times \end{array} \begin{array}{rcl} 10 \end{array} \begin{array}{rcl} \end{array}$ ⁵ km.

Moon's orbital period is $0.07481 year$ .

Orbital period of geosynchronous earth satellite is 1 day.

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