Understanding Critical Velocity
Critical velocity is the minimum velocity an object needs to be in orbit around a celestial body. It depends on the gravitational force of the body and the distance from the center of the body.
The Formula
The formula for critical velocity (also known as orbital velocity) is:
* v = √(GM/r)
Where:
* v = critical velocity
* G = gravitational constant
* M = mass of the Earth
* r = radius of the Earth
The Effect of Doubling the Radius
If the radius (r) is doubled, the formula becomes:
* v = √(GM/(2r))
Notice that the critical velocity is now inversely proportional to the square root of the radius.
Conclusion
When the radius of the Earth is doubled, the critical velocity will be reduced by a factor of √2 (approximately 1.414).
In simpler terms: If you double the distance from the center of the Earth, an object needs to move about 1.414 times slower to stay in orbit.
