A satellite revolving around a planet in a st | vedclass

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

Question

(D) The time period of a satellite is given by $T = 2\pi \sqrt{\frac{r^3}{GM}}$.From this,we have $T \propto \sqrt{\frac{r^3}{M}}$,which implies $\fra

Vedclass · Accepted Answer

$1.05 	imes 10^4 	ext{ km}$

Vedclass · Answer

(D) The time period of a satellite is given by $T = 2\pi \sqrt{\frac{r^3}{GM}}$.From this,we have $T \propto \sqrt{\frac{r^3}{M}}$,which implies $\frac{T_1}{T_2} = \left(\frac{r_1}{r_2}ight)^{3/2} \left(\frac{M_2}{M_1}ight)^{1/2}$.Here,$T_1 = 6 	ext{ hours}$,$T_2 = 24 	ext{ hours}$ (for Earth's geostationary orbit).$M_1 = \frac{M_e}{4}$ and $M_2 = M_e$.$r_2 = 4.2 	imes 10^4 	ext{ km}$.Substituting the values: $\frac{6}{24} = \left(\frac{r_1}{4.2 	imes 10^4}ight)^{3/2} \left(\frac{M_e}{M_e/4}ight)^{1/2}$.$\frac{1}{4} = \left(\frac{r_1}{4.2 	imes 10^4}ight)^{3/2} 	imes (4)^{1/2}$.$\frac{1}{4} = \left(\frac{r_1}{4.2 	imes 10^4}ight)^{3/2} 	imes 2$.$\frac{1}{8} = \left(\frac{r_1}{4.2 	imes 10^4}ight)^{3/2}$.Taking the power of $2/3$ on both sides: $\left(\frac{1}{8}ight)^{2/3} = \frac{r_1}{4.2 	imes 10^4}$.$\frac{1}{4} = \frac{r_1}{4.2 	imes 10^4}$.$r_1 = \frac{4.2 	imes 10^4}{4} = 1.05 	imes 10^4 	ext{ km}$.

$A$ 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 $4.2 \times 10^4 \text{ km}$)

Similar Questions

The periodic time of a satellite revolving above Earth's surface at a height equal to $R$ (where $R$ is the radius of the Earth) is given by (where $g$ is the acceleration due to gravity at Earth's surface):

Two satellites are revolving around the Earth with orbital velocities $v_1$ and $v_2$ at radii $r_1$ and $r_2$ respectively,where $r_1 > r_2$. Then:

The orbit of a geo-stationary satellite is circular. The time period of the satellite depends on:
$(i)$ mass of the satellite
(ii) mass of the earth
(iii) radius of the orbit
(iv) height of the satellite from the surface of the earth
Which of the following is correct?

Choose the correct statement from the following: The radius of the orbit of a geostationary satellite depends upon

Vedclass Test Series

Exam Paper Generator

Online Exam Module