Consider a planet moving around a star in an | vedclass

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

Question

(A) The area $A$ of an ellipse with semi-major axis $a$ and semi-minor axis $b$ is given by $A = \pi ab$.For an elliptical orbit,the semi-minor axis $

Vedclass · Accepted Answer

$T^{4/3}$

Vedclass · Answer

(A) The area $A$ of an ellipse with semi-major axis $a$ and semi-minor axis $b$ is given by $A = \pi ab$.For an elliptical orbit,the semi-minor axis $b$ is related to the semi-major axis $a$ and eccentricity $e$ by $b = a\sqrt{1-e^2}$.Thus,$A = \pi a^2 \sqrt{1-e^2}$.Since $e$ is a constant for a given orbit,$A \propto a^2$.According to Kepler's $III$ law of planetary motion,the square of the time period $T$ is proportional to the cube of the semi-major axis $a$:$T^2 \propto a^3$$a \propto T^{2/3}$Substituting this into the area relation:$A \propto (T^{2/3})^2$$A \propto T^{4/3}$Therefore,the area of the elliptical orbit is proportional to $T^{4/3}$.

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

Describe the Nicolaus Copernicus model for planetary motion.

$Assertion$ : For the planets orbiting around the sun,angular speed,linear speed and $K.E.$ change with time,but angular momentum remains constant.
$Reason$ : No torque is acting on the rotating planet. So its angular momentum is constant.

$A$ planet is revolving around the sun in an elliptical path as shown. The orbital velocity of the planet will be minimum at:

$A$ satellite orbits the Earth in a circular orbit of radius $R$. Another satellite orbits in an orbit of radius $1.02 R$. What is the percentage increase in the time period of the second satellite compared to the first (in $\%$)?

The average distance of the Earth from the Sun is $L_{1}$. If one year of the Earth is $D$ days, then one year of another planet whose average distance from the Sun is $L_{2}$ will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module