Question

The time period of an artificial satellite in a circular or bit of radius R is 2 days and its orbital velocity isIf time period of another satellite in a circular orbit is 16 days then

• A. Its radius of orbit is 4R and orbital velocity is
• B. Its radius of orbit is 4R and orbital velocity $\frac { \mathrm { v } _ { \mathrm { o } } } { 2 }$ is
• C. Its radius of orbit is 2R and orbital velocity is
• D. Its radius of orbit is 2R and orbital velocity is

Answer 1

Answer: (B)

Its radius of orbit is 4R and orbital velocity $\frac { \mathrm { v } _ { \mathrm { o } } } { 2 }$ is

Answer 2

According to Kepler’s third law

$\therefore \frac { \mathrm { T } _ { 1 } } { \mathrm {~T} _ { 2 } } = \left( \frac { \mathrm { R } _ { 1 } } { \mathrm { R } _ { 2 } } \right) ^ { 3 / 2 }$

Or $\mathrm { R } _ { 2 } = \left( \mathrm { R } _ { 1 } \right) \left( \frac { \mathrm { T } _ { 2 } } { \mathrm {~T} _ { 1 } } \right) ^ { 2 / 3 } = \left( \mathrm { R } _ { 1 } \right) \left( \frac { 16 } { 2 } \right) ^ { 2 / 3 }$

(given ) ….(i)

Orbital velocity,

(using (i))

Or