Suppose there existed a planet that went arou | vedclass

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

Question

(C) Time taken by the Earth to complete one revolution around the Sun,$T_{e} = 1 	ext{ year}$.Orbital radius of the Earth,$R_{e} = 1 	ext{ AU}$.Give

Vedclass · Accepted Answer

Lesser by a factor of $0.63$

Vedclass · Answer

(C) Time taken by the Earth to complete one revolution around the Sun,$T_{e} = 1 	ext{ year}$.Orbital radius of the Earth,$R_{e} = 1 	ext{ AU}$.Given that the planet goes around the Sun twice as fast as the Earth,its orbital period $T_{p}$ is half that of the Earth:$T_{p} = \frac{1}{2} T_{e} = 0.5 	ext{ year}$.According to Kepler's third law of planetary motion,the square of the orbital period is proportional to the cube of the semi-major axis (orbital radius):$\left(\frac{R_{p}}{R_{e}}ight)^{3} = \left(\frac{T_{p}}{T_{e}}ight)^{2}$.Substituting the values:$\frac{R_{p}}{R_{e}} = \left(\frac{T_{p}}{T_{e}}ight)^{2/3} = \left(\frac{0.5}{1}ight)^{2/3} = (0.5)^{0.666} \approx 0.63$.Thus,the orbital size of the planet is lesser by a factor of $0.63$ compared to that of the Earth.

Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?

Similar Questions

The time period of a satellite of the Earth is $5$ hours. If the separation between the Earth and the satellite is increased to four times the previous value,the new time period will become ......... $hours$.

$A$ planet $(P_1)$ is moving around a star of mass $2M$ in an orbit of radius $R$. Another planet $(P_2)$ is moving around another star of mass $4M$ in an orbit of radius $2R$. The ratio of the time periods of revolution of $P_2$ and $P_1$ is . . . . . . .

The eccentricity of Earth's orbit is $0.0167$. The ratio of its maximum speed in its orbit to its minimum speed is

If $J$ is the angular momentum of a planet revolving around the Sun,what is the areal velocity of the planet?

The period of a satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius $4R$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module