You want to move a spacecraft that is in 300 km circular orbit around Venus into another circular orbit around Venus of 600 km. Explain how you would accomplish this. Solve for the velocities that need to be applied.

The final velocity will be half of the initial velocity of the spacecraft.

Explanation:

Angular momentum is conserved for the circular force motion and central force motion.

Considering

L = MVR = Constant

Where

M = Mass of the object

V = Velocity of the object

r = radius of circle

We know that

V =

So,

=

As per the given data

= Initial Radius = 300 km

= Final Radius = 600 km

= Initial Velocity =

= Final Velocity =

Placing values in the formula

=

=

=

Hence, The final velocity will half of the initial velocity of the spacecraft.

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.