Consider a planet moving around a star in an | vedclass

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

Question

(a)

Area of ellipse

$A=\pi r_1 r_2$

$\because r_1=a-a e=a(1-e)$

$	ext { and } r_2=a+a e=a(1+e)$

$A=\pi\{a(1-e)\}\{a(1+e)\}$

$=\pi a

Vedclass · Accepted Answer

$T^{4 / 3}$

Vedclass · Answer

(a)

Area of ellipse

$A=\pi r_1 r_2$

$\because r_1=a-a e=a(1-e)$

$	ext { and } r_2=a+a e=a(1+e)$

$A=\pi\{a(1-e)\}\{a(1+e)\}$

$=\pi a^2(1-e)(1+e)$

$=\pi a^2\left(1^2-e^2ight)$

$\because e^2 \ll a^2 	ext { then }$

$A=\pi a^2$

$	ext { So, } a \propto A^{1 / 2}$

$	ext { According to Keplar's $III$ law }$

$T^2 \propto a^3$

$T^2 \propto\left[(A)^{1 / 2}ight]^3$

$T^2 \propto A^{3 / 2}$

$A \propto\left(T^2ight)^{2 / 3}$

$A \propto T^{4 / 3}$

Consider a planet moving around a star in an elliptical orbit with period $T$. The area of the elliptical orbit is proportional to ...........

Similar Questions

If the earth is at one-fourth of its present distance from the sun, the duration of the year will be

If the angular momentum of a planet of mass $m$, moving a round the Sun in a circular orbit its $L$, about the center of the Sun, its areal velocity is

The earth revolves round the sun in one year. If the distance between them becomes double, the new period of revolution will be

The motion of planets in the solar system is an example of the conservation of

Which of the following quantities does not depend upon the orbital radius of the satellite