Question

Two satellites S1 and S2 revolve around a planet in coplaner circular orbits.Their periods of revolution are 1hr and 8 hrs respectively.if the radius of the orbit of S1 is 104 km,what is the radius of the orbit of S2?​

Answer 1

Explanation:

According to Kepler's law T2×r3

(T1​T2​​)2=(r1​r2​​)3

r2​=r1​(T1​T2​​)2/3

r2​=(104)(18​)2/3

r2​=4×104km

∴V1​=T1​2πr1​​=12π(104)​=2π×104Km/hr

Similarly,

V2​=T2​2πr2​​=82π(4×104)​=π×104Km/hr

(a) Speed of S2​ relative to S1​=(V2​−V1​)

=π×104(1−2)=−π×104Km/hr

(b) Angular speed of S2​ as observed by astronaut in S1​

Wr​=r2​−r1​V1​−V2​​

      =4×104−104π×104Km/hr​

      =3π​ rad/hr