An earth satellite X is revolving around the | vedclass

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

Question

(A) The time period of a communication satellite is $T_c = 24 \, hrs$.According to Kepler's third law of planetary motion,the square of the time perio

Vedclass · Accepted Answer

$3 \, hrs$

Vedclass · Answer

(A) The time period of a communication satellite is $T_c = 24 \, hrs$.According to Kepler's third law of planetary motion,the square of the time period is directly proportional to the cube of the orbital radius,i.e.,$T^2 \propto r^3$.Let $r_c$ be the radius of the communication satellite's orbit and $r_x$ be the radius of satellite $X$'s orbit. Given $r_x = \frac{1}{4} r_c$,or $\frac{r_c}{r_x} = 4$.Using the ratio form of Kepler's law: $\frac{T_c}{T_x} = \left( \frac{r_c}{r_x} \right)^{3/2}$.Substituting the values: $\frac{24}{T_x} = (4)^{3/2}$.Since $(4)^{3/2} = (2^2)^{3/2} = 2^3 = 8$,we have $\frac{24}{T_x} = 8$.Therefore,$T_x = \frac{24}{8} = 3 \, hrs$.

An earth satellite $X$ is revolving around the earth in an orbit whose radius is one-fourth of the radius of the orbit of a communication satellite. The time period of revolution of $X$ is ..........

Similar Questions

The distance of Venus from the sun is $0.72\, AU$. The orbital period of Venus is ............ days.

The orbit of a planet around a star is:

Describe the Nicolaus Copernicus model for planetary motion.

In planetary motion,the areal velocity of the position vector of a planet depends on the angular velocity $\omega$ and the distance of the planet from the sun $r$. The correct relation for areal velocity is:

$A$ body revolves around the sun $27$ times faster than the earth. What is the ratio of their orbital radii?

Vedclass Test Series

Exam Paper Generator

Online Exam Module