Concept explainers
A satellite orbits the Earth at a height of 200 km in a circle of radius 6570 km. Find the linear speed of the satellite and the time taken to complete one revolution. Assume the Earth’s mass is 6.0 × 1024 kg. [Hint: The gravitational force provides the
The speed of the satellite and the time taken by the satellite which is rotating in a circular orbit at an altitude of
Answer to Problem 47SP
Solution:
Explanation of Solution
Given data:
The altitude of satellite from Earth’s surface is
The radius of the Earth is
The mass of the Earth is
Formula used:
The expression for gravitational force on the satellite is written as,
Here,
The centrifugal force, which is equal in magnitude of centripetal force but opposite in the direction that is in outwards direction, on the satellite is expressed as,
Here,
Explanation:
Consider the expression for gravitational force on the satellite.
Understand that standard value of
Consider the expression for centrifugal force on satellite.
Substitute
Understand that for the continuous rotation of the satellite in the orbit, the gravitational forceon the satellite must be balanced by the centrifugal force on the satellite
Substitute
Further solve as,
The speed of the satellite is
Consider the distance covered by the satellite in one revolution
Here,
Substitute
Consider the formula for speed of the satellite
Substitute
The time taken by the satellite for one revolution is
Conclusion:
The speed of the satellite is
The time taken by the satellite for one revolution is
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Chapter 9 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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