Kepler's Third Law
Kepler's Third Law of Planetary Motion states the relationship between the orbital period (time it takes to complete one orbit) and the average distance from the Sun:
* T² ∝ r³
Where:
* T = orbital period
* r = average distance from the Sun
Understanding the Relationship
This law tells us that the square of the orbital period is proportional to the cube of the average distance from the Sun.
* If the distance increases, the orbital period will also increase.
Speed Calculation
To relate this to orbital speed, consider the following:
* Orbital speed = (2 * π * r) / T
* Where:
* π (pi) is a mathematical constant (approximately 3.14)
* r is the average distance from the Sun
* T is the orbital period
How the Speed Changes
1. Distance increases by 4 times: Let's say the original distance is 'r', the new distance is '4r'.
2. Orbital period changes: From Kepler's Third Law, if the distance increases by 4 times (4³ = 64), the orbital period will increase by the square root of 64, which is 8 times.
3. Speed decreases:
* The new orbital speed will be (2 * π * 4r) / (8T)
* This simplifies to (1/2) * (2 * π * r) / T
* Therefore, the orbital speed is reduced by half when the distance from the Sun increases by 4 times.
Conclusion
If the distance from the Sun is increased by 4 times, the orbital speed of an object around the Sun will decrease by half.
