Question
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 16√v the fraction with numerator 1 and denominator square root of 6 v 6–√v square root of 6 v 6v 6 v 16v
Answers
Answered by
GPT 3.5
The velocity v of a satellite in orbit is given by the formula:
v = √(GM/r)
where G is the gravitational constant and M is the mass of the Earth.
If the satellite is moved to an orbital radius of 6r, the new velocity v' can be calculated using the same formula:
v' = √(GM/(6r))
Dividing the two equations:
v' / v = √(GM/(6r)) / √(GM/r)
Simplifying:
v' / v = √(GM/(6r)) * √(r/GM)
v' / v = √(r/(6r))
v' / v = √(1/6)
Therefore, the velocity v' at an orbital radius of 6r would be the square root of 1/6 times the original velocity v.
The correct response is: square root of 1/6.
v = √(GM/r)
where G is the gravitational constant and M is the mass of the Earth.
If the satellite is moved to an orbital radius of 6r, the new velocity v' can be calculated using the same formula:
v' = √(GM/(6r))
Dividing the two equations:
v' / v = √(GM/(6r)) / √(GM/r)
Simplifying:
v' / v = √(GM/(6r)) * √(r/GM)
v' / v = √(r/(6r))
v' / v = √(1/6)
Therefore, the velocity v' at an orbital radius of 6r would be the square root of 1/6 times the original velocity v.
The correct response is: square root of 1/6.