Asatellite that goes around the earth once every 24 hours iscalled a geosynchronous satellite. if a geosynchronoussatellite is in an equatorial orbit, its position appearsstationary with respect to a ground station, and it is known as ageostationary satellite
find the radius rof the orbit of a geosynchronous satellite that circles the earth.(note that ris measured from the center of the earth, not the surface.) you mayuse the following constants:
the universal gravitational constant g is 6.67 \times 10^{-11}\; {\rm n \; m^2 / kg^2}.
the mass of the earth is 5.98 \times 10^{24}\; {\rm kg}.
the radius of the earth is 6.38 \times 10^{6}\; {\rm m}.

35870474.30504 m

Explanation:

r = Distance from the surface

T = Time period = 24 h

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

m = Mass of the Earth =  5.98 × 10²⁴ kg

Radius of Earth =

The gravitational force will balance the centripetal force

From Kepler's law we have relation

Distance from the center of the Earth would be

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.