Question

11. Two satellites S, and S, are revolving round a
planet in coplanar and concentric circular orbits
of radii R, and R, in the same direction
respectively. Their respective periods of
revolution are 1 hr and 8 hr. The radius of the
orbit of satellite S, is equal to 104 km. Their
relative speed when they are closest, in kmph is.​

Answer 1

Solution :

By kepler's 3rd law,

T2R3= constant ∴T21R31=T32R32 or 1(104)3=64R32

or R2=4×104km

distance travelled in one revolution,

S1=2πR1=2π×104 and S2=2πR2=2π×4×104

v1=S1t1=2π×1041=2π×104kmph and v2=S2t2=2π×4×1048=π×104kmph

∴ relative velocity =v1−v2=2π×104−π×104=π×104kmph.