Question

A satellite is launched into circular orbit of radius R around the earth while a second satellite is launched into an orbit of Radius 1.02 R. The percentage change in the time periods of the two satellite is

• A. 0.7
• B. 1
• C. 1.5
• D. 3

Answer 1

The correct option is D 3

From kepler's law $T^2\propto r^3$

By applying small approximation method,

$⟹2(\frac{\Delta T}{T}\times 100)=3(\frac{\Delta r}{r}\times 100)$

$⟹2(\frac{\Delta T}{T}\times 100)=3(\frac{1.02R-R}{R}\times 100)$

$⟹2(\frac{\Delta T}{T}\times 100)=3\times 0.02\times 100$

$⟹2(\frac{\Delta T}{T}\times 100)=3\times 2$

$⟹\frac{\Delta T}{T}\times 100=$ Percentage difference in the time period $=3$