What linear speed must an earth satellite have to be in a circular orbit at an altitude of 180 km?

Question:

What linear speed must an earth satellite have to be in a circular orbit at an altitude of 180 km?

Orbital velocity

The orbital velocity is the minimum amount of energy required for the satellite to keep the satellite in its orbit. The orbital speed of the earth is near equals to the value of

{eq}29.7\;{\rm{km/s}} {/eq}.

Answer and Explanation:


_Given data_

  • Altitude of a circular orbit is {eq}d = 180\;{\rm{km}} {/eq}


The radius of the earth is {eq}R = 6378.1\;{\rm{km}} {/eq}

The mass of earth is {eq}M = 5.98 \times {10^{24}}\;{\rm{kg}} {/eq}


The expression for radius of earth satellite is,

{eq}\begin{align*} r &= R + d\\ &= 6378.1\;{\rm{km}} + 180\;{\rm{km}}\\ &= 6558{\rm{.1}}\;{\rm{km}} \end{align*} {/eq}


The expression for orbital speed of satellite is,

{eq}{v^2} = \dfrac{{GM}}{r} {/eq}


Here, the universal gas constant is G.


Substitute the value in above expression we get,

{eq}\begin{align*} {v^2} &= \dfrac{{6.67 \times {{10}^{ - 11}} \times 5.98 \times {{10}^{24}}}}{{6558.1}}\\ v &= 246617.11\ \ {\rm{km/s}} \end{align*} {/eq}


Learn more about this topic:

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How Orbits Are Influenced by Gravity & Energy

from Basics of Astronomy

Chapter 25 / Lesson 6
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