The Relationship Between Orbital Velocity and Radius
The orbital velocity of a satellite is determined by the following equation:
* v = √(GM/r)
Where:
* v is the orbital velocity
* G is the gravitational constant
* M is the mass of the central body (e.g., Earth)
* r is the orbital radius (distance from the center of the central body to the satellite)
The Effect of Doubling the Radius
If you double the radius (r), you're essentially taking the square root of half the original value. This means the orbital velocity will decrease.
Specifically:
* The orbital velocity will decrease by a factor of √2 (approximately 1.414).
In simpler terms:
If the satellite was initially orbiting at a velocity of 'x', doubling the radius would make it orbit at approximately 'x/1.414'.
Example:
Let's say a satellite has an orbital velocity of 8 km/s. If you double the radius, the new orbital velocity would be approximately:
* 8 km/s / 1.414 ≈ 5.66 km/s
Key Takeaway:
Increasing the orbital radius of a satellite reduces its orbital velocity. This makes intuitive sense, as the satellite has to travel a longer distance to complete one orbit, but the force of gravity is weaker at a greater distance.
