Which of the following statements is correct | vedclass

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

Question

(D) geostationary satellite orbits the Earth in the equatorial plane with a time period of $24 	ext{ hours}$.To calculate its height $h$,we use the f

Vedclass · Accepted Answer

Its height above the earth's surface is about six times the radius of the earth.

Vedclass · Answer

(D) geostationary satellite orbits the Earth in the equatorial plane with a time period of $24 	ext{ hours}$.To calculate its height $h$,we use the formula for the orbital radius $r = R_e + h$,where $R_e$ is the radius of the Earth.Using Kepler's Third Law,$T^2 = \frac{4\pi^2 r^3}{GM}$,where $M$ is the mass of the Earth.Substituting $T = 86400 	ext{ s}$,$G = 6.67 	imes 10^{-11} 	ext{ Nm}^2/	ext{kg}^2$,and $M = 5.97 	imes 10^{24} 	ext{ kg}$,we find $r \approx 42,200 	ext{ km}$.Since $R_e \approx 6,400 	ext{ km}$,the height $h = r - R_e \approx 42,200 - 6,400 = 35,800 	ext{ km}$.This height is approximately $5.6$ to $6$ times the radius of the Earth $(6 	imes 6,400 = 38,400 	ext{ km})$.Therefore,statement $(d)$ is the correct description.

Which of the following statements is correct in respect of a geostationary satellite?

Similar Questions

Two satellites $A$ and $B$ go round a planet in circular orbits having radii $4R$ and $R$,respectively. If the speed of satellite $A$ is $3v$,then the speed of satellite $B$ is:

Given the radius of Earth $R$ and the length of a day $T$,the height of a geostationary satellite is: [$G$ = Gravitational Constant,$M$ = Mass of Earth]

The correct formula for the height $h$ of a satellite from the Earth's surface is:

$A$ satellite revolving around a planet in a stationary orbit has a time period of $6 \text{ hours}$. The mass of the planet is one-fourth the mass of the Earth. What is the radius of the orbit of the satellite? (Given: Radius of the geostationary orbit for Earth is $4.2 \times 10^4 \text{ km}$)

Two satellites $A$ and $B$ go round a planet in circular orbits having radii $4 R$ and $R$ respectively. If the speed of $A$ is $3 v$,the speed of $B$ will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module