A satellite orbiting Earth at an orbital radius r has a velocity v. What would the velocity be if the satellite is moved to an orbital radius of 6r?(1 point) Responses 16v 1 sixth v 6–√v square root of 6 v 16√v the fraction with numerator 1 and denominator square root of 6 v 6v
The velocity of a satellite in orbit is determined by the balance between the gravitational force pulling it towards the Earth and the centrifugal force pulling it away from the Earth due to its orbital motion.
The equation for the velocity of a satellite in orbit can be given as:
v = sqrt(G*M/r)
Where:
v = velocity of satellite
G = gravitational constant
M = mass of the Earth
r = orbital radius
If the satellite is moved to an orbital radius of 6r, we can substitute 6r for r in the equation:
v' = sqrt(G*M/(6r))
Simplifying the equation, we can cancel out the factor of 6:
v' = sqrt(G*M/r) * 1/sqrt(6)
This can be written as the fraction:
v' = (1/sqrt(6))*v
So, the velocity of the satellite at an orbital radius of 6r would be the fraction with numerator 1 and denominator square root of 6 times the original velocity, or (1/sqrt(6))v.