Question

define the period of the satellite and prove that the square of the period of the satellite directional proportional of the cube of the radius of satellite​

Answer 1

◆【Solution】◆

♀ Time Period

When a body describing in a circular path with constant speed than the time take to cover the whole length of the circle is known as Time Period of the body describing the circle.

Let w be the rate of change of angle

than time period can be written as....

◆【w = 2π/T】◆

Let M be the mass of the satellite.

R be the radius of the circular path.

T be the period of the Satellite.

m be the .mass of planet.

• A body showing uniform circular motion have force acting radially outwards whose magnitude can be written as....

F = Mw²R

where w be the angular velocity of the body

• Acc to gravitation law ever pair of body with some mass separated by a distance r exert force on each other whose magnitude can be written as....

F = GMm/r²

In the case of satellite these force balance each other that's why it can move with uniform speed in uniform circular motion.

Mw²R = GMm/R²

w² = Gm/R³. (w = 2π/T)

(2π/T)² = Gm/R³

T² = (2π/Gm)R³

◆【T² α R³】◆

2π/Gm is constant hence T² is directly proportional to R³

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