Question

The time period of a satellite in a circular orbit of
radius R is T. The period of another satellite in a
circular orbit of radius 4R is
​

Answer 1

Given

For a satellite revolving arround an orbit of radius R, Time period = T

Let Another satellite is in radius R' = 4 R

and Time period be T'

We know,

$(Time \ period)^{2} \ is \ directly \ proportional \ to \ ( Radius \ of \ orbit)^3$

or vice versa i.e. cube of radius of orbit is directly proportional to square of time period

square

For

First satellite

$R^3$ ∝ $T^2$  .... eqn (i)

For second satellite

$(R')^3$ ∝ $(T')^2$   .... eqn (ii)

Diving (i) and (ii) eqn

We get

$\frac{R^{3} }{(R')^3} = \frac{T^2}{(T')^2}$

Using values of R' = 4R

Eqn will become:

$(\frac{R}{4R} )^3 = (\frac{T}{T'} )^2$

$(T')^2 = (\frac{4R}{R} )^3T^2\\= (4)^3 T^2 \\= 64 T^2$

Which implies

T' = 8 T