An arti cial satellite is moving in a circular orbit of radius 36,000 km. Calculate its speed if ittakes 24 hours to revolve around the earth
Question
An arti�cial satellite is moving in a circular orbit of radius 36,000 km. Calculate its speed if ittakes 24 hours to revolve around the earth
Solution
To calculate the speed of the satellite, we need to use the formula for speed which is distance/time.
Step 1: Calculate the distance The distance the satellite travels is the circumference of its circular orbit. The formula for the circumference of a circle is 2πr, where r is the radius. Here, the radius is 36,000 km. So, the distance is 2π * 36,000 km = 226,195 km.
Step 2: Convert time to the same unit The time it takes for the satellite to revolve around the earth is given as 24 hours. We need to convert this time into the same unit as the distance, which is in kilometers. There are 60 minutes in an hour and 60 seconds in a minute, so 24 hours is 24 * 60 * 60 = 86,400 seconds.
Step 3: Calculate the speed Now we can calculate the speed by dividing the distance by the time. So, the speed is 226,195 km / 86,400 seconds = 2.62 km/s.
So, the speed of the satellite is approximately 2.62 km/s.
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