The time period of a geostationary satellite | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to Kepler's Third Law of planetary motion,the square of the time period $(T)$ is proportional to the cube of the orbital radius $(r)$: $

Vedclass · Accepted Answer

$6 \sqrt{2} \; h$

Vedclass · Answer

(A) According to Kepler's Third Law of planetary motion,the square of the time period $(T)$ is proportional to the cube of the orbital radius $(r)$: $T^2 \propto r^3$ or $T \propto r^{3/2}$.The orbital radius $r$ is the distance from the center of the Earth,given by $r = R_{E} + h$,where $h$ is the height above the surface.For the first satellite: $r_1 = R_{E} + 6 R_{E} = 7 R_{E}$ and $T_1 = 24 \; h$.For the second satellite: $r_2 = R_{E} + 2.5 R_{E} = 3.5 R_{E}$.Using the ratio: $\frac{T_2}{T_1} = \left( \frac{r_2}{r_1} ight)^{3/2} = \left( \frac{3.5 R_{E}}{7 R_{E}} ight)^{3/2} = \left( \frac{1}{2} ight)^{3/2} = \frac{1}{2 \sqrt{2}}$.Therefore,$T_2 = T_1 	imes \frac{1}{2 \sqrt{2}} = \frac{24}{2 \sqrt{2}} = \frac{12}{\sqrt{2}} = 6 \sqrt{2} \; h$.

The time period of a geostationary satellite is $24 \; h$,at a height $6 R_{E}$ ($R_{E}$ is the radius of the Earth) from the surface of the Earth. The time period of another satellite whose height is $2.5 R_{E}$ from the surface will be:

Similar Questions

$A$ planet orbits the sun in an elliptical path as shown in the figure. Let $v_P$ and $v_A$ be the speed of the planet when at perihelion and aphelion respectively. Which of the following relations is correct?

What is the direction of areal velocity of the earth around the sun?

The time period of a satellite of the Earth is $5$ hours. If the separation between the Earth and the satellite is increased to four times the previous value,the new time period will become ......... $hours$.

If the earth is at one-fourth of its present distance from the sun,the duration of the year will be

$A$ Saturn year is $29.5$ times the Earth year. How far is Saturn from the Sun if the Earth is $1.50 \times 10^{8} \; km$ away from the Sun?

Vedclass Test Series

Exam Paper Generator

Online Exam Module