If the distance between the earth and the sun | vedclass

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

Question

(B) According to Kepler's third law,the square of the orbital period $(T)$ is proportional to the cube of the semi-major axis $(r)$,i.e.,$T^2 \propto

Vedclass · Accepted Answer

$129$

Vedclass · Answer

(B) According to Kepler's third law,the square of the orbital period $(T)$ is proportional to the cube of the semi-major axis $(r)$,i.e.,$T^2 \propto r^3$.Let $T_1 = 365$ days and $r_1$ be the present distance.Given $r_2 = \frac{1}{2} r_1$.Then,$\left( \frac{T_2}{T_1} ight)^2 = \left( \frac{r_2}{r_1} ight)^3 = \left( \frac{1}{2} ight)^3 = \frac{1}{8}$.Taking the square root on both sides,$\frac{T_2}{T_1} = \sqrt{\frac{1}{8}} = \frac{1}{2\sqrt{2}}$.Therefore,$T_2 = \frac{T_1}{2\sqrt{2}} = \frac{365}{2 	imes 1.414} \approx \frac{365}{2.828} \approx 129$ days.

If the distance between the earth and the sun becomes half its present value,the number of days in a year would have been

Similar Questions

State and prove Kepler's second law (Law of Areas) of planetary motion.

$A$ planet moving around the Sun sweeps out an area $A_{1}$ in $2$ days,$A_{2}$ in $3$ days,and $A_{3}$ in $6$ days. Then,the relation between $A_{1}, A_{2}$,and $A_{3}$ is

Choose the incorrect statement from the following.

Assume that the earth moves around the sun in a circular orbit of radius $R$ and there exists a planet which also moves around the sun in a circular orbit with an angular speed twice as large as that of the earth. The radius of the orbit of the planet is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module