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

The time period of a satellite is 7 hours. The radius is increased to 3 times its previous value. Find the new time period.

$$T^2 \propto r^3$$, so:

$$\frac{T_2^2}{T_1^2} = \frac{r_2^3}{r_1^3} = \left(\frac{r_2}{r_1}\right)^3 = 3^3 = 27$$

$$T_2 = T_1\sqrt{27} = 7 \times 3\sqrt{3} = 21\sqrt{3} \approx 21 \times 1.732 \approx 36.37 \text{ hours}$$

The approximate new time period is 36 hours.

Hence, the correct answer is Option A: 36 hours.