Understanding the Period of Revolution
To calculate the period of revolution of a polar satellite orbiting close to the Earth's surface, we can use the formula derived from Newton's law of gravitation and circular motion principles.
Key Variables
- R = Radius of the Earth = 6400 km = 6.4 x 10^6 m
- g = Acceleration due to gravity = 9.8 m/s²
Steps to Calculate the Period
1. Centripetal Force and Gravitational Force
For a satellite in a low orbit, the gravitational force provides the necessary centripetal force. Thus, we have:
- Gravitational Force (F) = g * m
- Centripetal Force (F_c) = (m * v²) / R
Where m is the mass of the satellite and v is its orbital velocity.
2. Equating Forces
Setting the gravitational force equal to the centripetal force:
- g * m = (m * v²) / R
- This simplifies to: v² = g * R
3. Finding the Velocity
Hence, the orbital velocity v can be calculated as:
- v = √(g * R)
4. Calculating the Period (T)
The period T is related to the velocity and the circumference of the orbit:
- T = 2πR / v
- Substituting v gives: T = 2πR / √(g * R)
5. Final Calculation
Plugging in the values:
- T = 2π * (6.4 x 10^6) / √(9.8 * 6.4 x 10^6)
- Evaluating this will yield the period.
Conclusion
The calculated period will provide the time it takes for the satellite to complete one revolution around the Earth, essential for understanding satellite dynamics in orbit. The value will be approximately 5060 seconds or roughly 84 minutes, indicating that a polar satellite orbits the Earth in a relatively short duration.