The time period of an artificial satellite in | vedclass

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

Question

(B) 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 $R$,i.e.,$

Vedclass · Accepted Answer

its radius of orbit is $4 \, R$ and orbital velocity is $\frac{v_0}{2}$

Vedclass · Answer

(B) 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 $R$,i.e.,$T^2 \propto R^3$.Given $T_1 = 2 \, days$,$R_1 = R$,$T_2 = 16 \, days$,and $R_2 = ?$.Using the ratio: $\frac{T_2^2}{T_1^2} = \frac{R_2^3}{R_1^3} \Rightarrow \frac{16^2}{2^2} = \left(\frac{R_2}{R}\right)^3$.$\frac{256}{4} = 64 = \left(\frac{R_2}{R}\right)^3$.Taking the cube root on both sides: $\frac{R_2}{R} = 4$,so $R_2 = 4R$.For orbital velocity $v = \sqrt{\frac{GM}{R}}$,we have $v \propto \frac{1}{\sqrt{R}}$.Therefore,$\frac{v_2}{v_1} = \sqrt{\frac{R_1}{R_2}} = \sqrt{\frac{R}{4R}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$.Thus,$v_2 = \frac{v_1}{2} = \frac{v_0}{2}$.

The time period of an artificial satellite in a circular orbit of radius $R$ is $2 \, days$ and its orbital velocity is $v_0$. If the time period of another satellite in a circular orbit is $16 \, days$,then:

Similar Questions

$A$ $10\; kg$ satellite circles Earth once every $2\; hours$ in an orbit having a radius of $8000\; km$. Assuming that Bohr's angular momentum postulate applies to satellites just as it does to an electron in the hydrogen atom, find the quantum number of the orbit of the satellite.

Two heavenly bodies $S_1$ and $S_2$,not far from each other,are seen to revolve in orbits:

The orbital speed of a satellite revolving around a planet in a circular orbit is $v_0$. If its speed is increased by $10 \%$,then ..........

Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in a circular orbit of radius $R$ around the sun will be proportional to

Satellites which give high value data for remote sensing,meteorology and environmental studies are

Vedclass Test Series

Exam Paper Generator

Online Exam Module