Circular Orbit Speed Calculation for Satellite: 42250 Km Radius in 24 Hours

Question:

An artificial satellite is moving in a circular orbit of radius 42250 Km.Calculate its speed if it takes 24 hours to revolve around the earth.

Solution:

Circular orbit speed calculation:

$${Speed =\frac{Distance \ travelled}{Time \ taken}}$$

Speed of the artificial satellite=$${\frac{Distance \ travelled \ by \ the \ satellite}{Time \ taken \ by \ the \ satellite}}$$

Distance travelled in one revolution

The distance travelled by the artificial satellite in one revolution =Cicumference of the circle

$${2 \pi r = (2) (\frac{22}{7}) (42250) \ Km}$$

$${=2,65,571 \ Km}$$

Time taken in one revolution

Time taken by the satellite to complete one revolution

$${=24 \ Hours }$$

Speed of the artificial satellite

$${Speed =\frac{Distance \ travelled}{Time \ taken}}$$

$${=\frac{2,65,571}{24} \ \frac{Km}{hr}}$$

$${=11,065 \ \frac{Km}{hr}}$$

Converting this value into ms^-1

$${11,065 (\frac{5}{18}) \ \frac{m}{s}}$$

$${=3074 \ \frac{m}{s}}$$

The speed of the artificial satellite around the earth is 3074 ms^-1