A satellite is launched into a circular orbit of radius r around the earth. A second satellite is launched into an orbit of radius 1.01 r . The period of the second satellite is larger than that of first one by approximately

Question

A satellite is launched into a circular orbit of radius r around the earth. A second satellite is launched into an orbit of radius 1.01 r . The period of the second satellite is larger than that of first one by approximately (A)  0.5 %  (B)  1.0 %  (C)  1.5 %  (D)  3.0 %

Tardigrade Admin · Accepted Answer

Period of a satellite T propto r3 / 2 Hence, (Δ T/T)=(3/2) (Δ r/r) As (Δ r/r)=(1.01 r-r/r) =0.01=0.01 × 100 %=1 % Hence, (Δ T/T)=(3/2) × 1 %=1.5 %

Q. A satellite is launched into a circular orbit of radius $r$ around the earth. A second satellite is launched into an orbit of radius $1.01 r$ . The period of the second satellite is larger than that of first one by approximately

$0.5%$

$1.0%$

$1.5%$

$3.0%$

Period of a satellite $T \propto r^{3/2}$
Hence, $\frac{Δ T}{T} = \frac{3}{2} \frac{Δ r}{r}$
As $\frac{Δ r}{r} = \frac{1.01 r - r}{r}$
$= 0.01 = 0.01 \times 100% = 1%$
Hence, $\frac{Δ T}{T} = \frac{3}{2} \times 1% = 1.5%$

Q. A satellite is launched into a circular orbit of radius r around the earth. A second satellite is launched into an orbit of radius 1.01r . The period of the second satellite is larger than that of first one by approximately

0.5%

1.0%

1.5%

3.0%