The velocity of the satellite if it is moved to an orbital radius of 4r is v/2
<h3>Which represents the velocity if the satellite is moved to an orbital radius of 4r?</h3>
Let F = gravitational force on satellite = GMm/r² where
- G = universal gravitational constant,
- M = mass of earth,
- m = mass of satellite and
- r = radius of orbit.
Also, let F' = centripetal force on satellite = mv²/r where
- m = mass of satellite,
- v = velocity of satellite and
- r = radius of orbit
Now, at the orbit of the satellite, the gravitational force equals the centripetal force
So, F = F'
GMm/r² = mv²/r
<h3>The velocity of the satellite</h3>
So, making v subject of the formula, we have the velocity of satellite is
v = √(GM/r)
Since G and M are constant, we see that v ∝ 1/√r
Now, given that satellite orbiting Earth at an orbital radius r has a velocity v. We need to find its velocity at an orbit of R = 4r
Let
- v = velocity of satellite at orbit r,
- r = radius of orbit r,
- v' = velocity of satellite at orbit R = 4r and
- R = radius of orbit T = 4r
Since v ∝ 1/√r, we have that
v//v = √(r/R)
So, v' = [√(r/R)]v
Substituting R = 4r into the equation, we have
v' = [√(r/R)]v
v' = [√(r/4r)]v
v' = [√(1/4)]v
v' = [1/2]v
v' = v/2
So, the velocity of the satellite is v/2
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