MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Kepler's Law

A planet revo...

Question

A planet revolves around the sun in an elliptical orbit. If $v_{p}$ and $v_{a}$ are the velocities of the planet at the perigee and apogee respectively, then the eccentricity of elliptical orbit is given by :

A

\frac{v_{p}}{v_{a}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

\frac{v_{a} - v_{p}}{v_{a} + v_{p}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

\frac{v_{p} + v_{a}}{v_{p} - v_{a}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\frac{v_{p} - v_{a}}{v_{p} + v_{a}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B $\frac{v_{p} - v_{a}}{v_{p} + v_{a}}$
As $\frac{v_{p}}{v_{a}} = \frac{a (1 + e)}{a (1 - e)}$
where a is semi-major axis of the ellipse
$v_{p} (1 - e) = v_{a} (1 + e)$ or $v_{p} - {e v}_{p} = v_{a} + {e v}_{a}$

$e (v_{a} + v_{p}) = v_{p} - v_{a}$ or $e = \frac{v_{p} - v_{a}}{v_{a} + v_{p}}$

Suggest Corrections

thumbs-up

2

Similar questions

Q. A planet orbits the sun in a n elliptical path as shown in the figure. Let

v_{P}

v_{A}

be speed of the planet when at perihelion and aphelion respectively. Which of the the following relations is correct.?

Q. A planet is revolving round the sun. Its distance from the sun at Apogee is

r_{A}

and that at Perigee is

r_{P}

. The masses of planet and sun are

m

M

v_{A}

is the velocity of planet at Apogee and

v_{P}

is at Perigee respectively and

T

is the time period of revolution of planet round the sun, then identify the wrong answer.

Q. Let the speed of the planet at the perihelion P in Figure. be

v_{P}

and the Sun-planet distance SP be

r_{P}

r_{P}, v_{P}

to the corresponding qualities at the aphelion

(r_{A}, v_{A})

. Will the planet take equal times to traverse BAC and CPB?

Q. The speed of the planet at the perihelion P in the figure is

v_{P}

and the sun-planet distance SP is

r_{P}

r_{P}, v_{P}

) to the corresponding quantities (

r_{A}, v_{A}

) at the aphelion A. Will the planet take equal time to traverse BAC and CPB?

Q. A planet orbits in an elliptical path of eccentricity

e

around a massive star considered fixed at one of the foci. The point in space where it is closest to the star is denoted by

P

and the point where it is farthest is denoted by

A

v_{P}

v_{A}

be the respective speeds at

P

A

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Kepler's Law

PHYSICS

Watch in App

explore_more_icon

Explore more

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon