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.

To find the speed of the artificial satellite moving in a circular orbit around the Earth, we can use the formula relating the circumference of the orbit to the time taken for one revolution.

The formula for the circumference of a circle is 2 x π x radius

Given:
– Radius of the orbit r = 42250 km
– Time taken for one revolution T = 24 hours

Calculations:
The circumference of the circular orbit:
Circumference = 2 x π x radius = 2 x π x 42250 km

The speed of the satellite is given by the formula:
Speed = Circumference / Time taken for one revolution

First, let’s convert the time from hours to seconds because the speed is usually measured in distance per unit time in seconds.

Given: 1 hour = 3600 seconds
Time taken for one revolution in seconds = 24 hours 3600 seconds/hour = 86400 seconds

Now, calculate the speed:
Speed = (2 x π x 42250 km) / (86400 seconds)
Speed ≈ (2 x 3.1416 x 42250 km) / (86400 seconds)
Speed ≈ 265258 km) / (86400 seconds)
Speed ≈ 3.07 km/s

Therefore, the speed of the artificial satellite moving in a circular orbit of radius 42250 km, taking 24 hours to revolve around the Earth, is approximately 3.07 kilometers per second.