Question

a artificial satellite is moving in a circular orbit of radius 36000km.if it takes 24 hours to complete one orbit around the earth find its linear speed?

Answer 1

An artificial satellite is orbiting at an orbital radius of 36,000 km. It takes 24 hours to complete one orbit.



Now, one orbit consists of $360^{\circ}$, which is equivalent to $2\pi$ radians. 

Also, the satellite takes 24 hours to complete the orbit. So, 24 hours become the time period of the satellite. 

Here, we can calculate the angular velocity of the satellite. 

$\text{Let Angular Velocity } = \omega \\ \\ \\ \implies \omega = \frac{2\pi \, \, radians}{24 \times 60 \times 60 \, \, seconds} \\ \\ \\ \implies \omega = \frac{\pi}{4.32 \times 10^4} \, \, rad / sec$


Now, we have the angular velocity. We also have the radius of the circular orbit:

$r = 36000 \, \, km \\ \\ \implies r=3.6\times 10^4 \, \, km \\ \\ \implies r=3.6 \times 10^7 \,\, m$


Now, we can easily find linear velocity by the following relation:

$v=r\omega \\ \\ \\ \implies v = (3.6 \times 10^7) \times \left( \frac{\pi}{4.32 \times 10^4} \right) \, \, m / s \\ \\ \\ \implies v \approx 2.61799 \times 10^3 m/s \\ \\ \\ \implies \boxed{v \approx 2.62 \times 10^3 \, \, m/s}$


Hope it helps
Purva
Brainly Community