Question

Two satellites 1 and 2 orbiting with the time periods T1 and T2 respectively lie on the same line . After what minimum time again the satellites will remain on the same line? Assume that the two satellites should lie in same side of the center of their concentric circular path​

Answer 1

Answer:

Let the satellites 1 and 2 described angle θ

1

and θ

2

at the center of earth during a time t respectively .Suppose 2 is ahead of 1 by an angle θ hence we can write

θ−θ

2

−θ

1

They will be again lie on same line after a minimum time T say.for this θ=2π.This gives θ

2

−θ

1

=2πDividing T in both sides we have

T

′

θ

2

−

T

′

θ

1

=

T

′

2π

Substituting

T

′

θ

2

=ω

2

and

T

′

θ

1

=ω

1

,we have

T

′

2π

=ω

2

−ω

1

where ω

2

=

T

2

2π

and ω

1

=

T

1

2π

Then

T

′

1

=

T

2

1

−

T

1

1

This gives T

′

=

T

1

−T

2

T

1

T

2