Question

The time period of a satellite revolving around the earth in a given orbit is 7 hours. If the radius of the orbit is increased to three times its previous value, then the approximate new time period of the satellite will be ______.

विकल्प

• 40 hours

• 36 hours

• 30 hours

• 25 hours

Answer 1

The time period of a satellite revolving around the earth in a given orbit is 7 hours. If the radius of the orbit is increased to three times its previous value, then the approximate new time period of the satellite will be 36 hours.

Explanation:

By Kepler's III law of motion, we have:

`T^2 ∝ R^3`

`(T_1/T_2)^2 = (R_1/R_2)^3`

Hence, `T_2^2 = (R_2/R_1)^3 xx T_1^2`

= `((3R)/R)^3 xx (7)^2`

= 27 × 49

= 1323

T = `sqrt(1323) = 36.37` hours

= 36 hours