Calculating the Speed of an Artificial Satellite

To calculate the speed of an artificial satellite, we need to consider its orbital motion and the time it takes to complete one full revolution around the Earth.

Given Information:
- Radius of the circular orbit: 2250 km
- Time taken for one revolution: 24 hours

Step 1: Converting Time to Seconds
To ensure consistency in units, we need to convert the time taken for one revolution from hours to seconds. Since 1 hour consists of 60 minutes and 1 minute consists of 60 seconds, we can calculate the total time taken in seconds using the following conversion:

24 hours x 60 minutes/hour x 60 seconds/minute = 86,400 seconds

Therefore, the time taken for one revolution is 86,400 seconds.

Step 2: Calculating the Circumference of the Orbit
To calculate the speed of the satellite, we need to determine the distance it covers during one revolution. Since the satellite is moving in a circular orbit, the distance covered in one revolution is equal to the circumference of the orbit.

The formula for the circumference of a circle is given by:

Circumference = 2πr

Where:
- π (pi) is a mathematical constant approximately equal to 3.14159
- r is the radius of the orbit

Using the given radius of 2250 km, we can calculate the circumference as follows:

Circumference = 2 x 3.14159 x 2250 km = 14,137.16 km

Step 3: Calculating the Speed
The speed of the satellite can be determined by dividing the distance covered in one revolution by the time taken for that revolution.

Speed = Distance/Time

Using the values we calculated earlier:

Speed = 14,137.16 km / 86,400 seconds

To simplify the calculation, we can convert the speed from km/second to km/hour by multiplying by the conversion factor:

Speed = (14,137.16 km / 86,400 seconds) x (3600 seconds / 1 hour) = 2317.08 km/hour

Therefore, the speed of the artificial satellite is approximately 2317.08 km/hour.

Summary:
The artificial satellite is moving at a speed of approximately 2317.08 km/hour in its circular orbit with a radius of 2250 km. It takes 24 hours (or 86,400 seconds) to complete one full revolution around the Earth.