Circular Motion #14

Classical Mechanics Level 4

According to Newton's law of universal gravitation, the force between two point masses \(m_{1}, m_{2}\) with separation \( r \) is given by

\[ F = \frac{ G m_{1} m_{2} }{ r^{2} } \]

Here, \( G \) is the universal gravitational constant and has the value \( 6.674 \times 10^{−11} \text{N m}^{2} \text{ kg}^{-2} \). Use this information to solve the following problem:

A satellite orbits Earth in a circular orbit with radius of orbit \( \approx 42,000 \text{ km} \). Find the time taken (in hours) by the satellite to complete one revolution.

Assumptions and details

  • Mass of Earth is \( 6 \times 10^{ 24 } \text{ kg} \)
  • Assume Earth and satellite to be point masses.
  • Ignore gravitational effects due to any other celestial body, like the Sun, Moon, other planets, etc.

This problem is part of the set - Circular Motion Practice


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