What is the angular velocity of the satellite in radians per minute? How far does…

What is the angular velocity of the satellite in radians per minute? How far does the satellite travel in 1 hour?

I can’t give a numeric answer without the satellite’s orbital period or its orbital radius/altitude — please provide the orbital period $T$ (in minutes) or the orbital radius $r$ (in km or m).

Explanation

  • Angular speed for a circular orbit (in radians per minute) is

$$\omega=\frac{2\pi}{T}$$
where $T$ is the orbital period in minutes.

  • Distance traveled in time $t$ (e.g., $t=60\text{ min}$ for 1 hour) along a circular orbit of radius $r$ is

$$s=r\theta=r\omega t=r\left(\frac{2\pi}{T}\right)t.$$
Equivalently, the fraction of an orbit covered in $t$ minutes is $t/T$, so
$$s=\frac{t}{T}\cdot 2\pi r.$$

Example (typical low Earth orbit): if $T=90\text{ min}$ and altitude $\approx400\text{ km}$, then $r\approx6371+400=6771\text{ km}$.

  1. $\omega=\dfrac{2\pi}{90}\approx0.0698\ \text{rad/min}.$
  2. In one hour ($t=60\text{ min}$), fraction of orbit $=60/90=2/3$, so

$$s=\frac{60}{90}\cdot2\pi\cdot6771\text{ km}\approx2.836\times10^4\text{ km}.$$

If you give me the actual $T$ or $r$ (or altitude), I’ll compute the exact $\omega$ and the distance for 1 hour.

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