The largest and the shortest distance of the earth from are r1 and r2. It’s the distance from the sun when it is perpendicular to the major axis of the orbit drawn from the sun.

Option 1) 

\left ( \frac{r1+r2 }{4}\right )

Option 2) 

\left ( \frac{r1+r2 }{r1-r2}\right )

Option 3) 

\left ( \frac{2r1r2}{r1+r2} \right )

Option 4) 

\left ( \frac{r1+r2}{3} \right )

Answers (1)

As we learnt in 

Velocity of planet in terms of Eccentricity -

V_{a}=\sqrt{\frac{GM}{a}\left ( \frac{1-e}{1+e} \right )}

V_{p}=\sqrt{\frac{GM}{a}\left ( \frac{1+e}{1-e} \right )}

V_{A}= Velocity of the planet at apogee

V_{p}= Velocity of perigee

- wherein

Eccentricity (e) = \frac{c}{a}

r_{p}=a-c

r_{a}=a+c

 

The position of a particle moving in an elliptical orbit is represented as

r=\frac{l}{1+e \cos \Theta }

l is perpendicular distance of particle from focus and e is eccentricity of ellipse

r_{1}=\frac{l}{1-e}\ \: \: and\ \: \: \: r_{2}=\frac{l}{1+e}

\Rightarrow 1-e=\frac{l}{r_{1}}\ \: \: and\ \: \: 1+e = \frac{l}{r_{2}}

\Rightarrow 2=l\left ( \frac{1}{r_{1}} + \frac{1}{r_{2}}\right )\Rightarrow l=\frac{2r_{1}r_{2}}{r_{1}+r_{2}}

Most Viewed Questions

Preparation Products

Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Test Series JEE Main 2024

Chapter/Subject/Full Mock Tests for JEE Main, Personalized Performance Report, Weakness Sheet, Complete Answer Key,.

₹ 7999/- ₹ 4999/-
Buy Now
JEE Foundation + Knockout JEE Main 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports,.

₹ 3999/-
Buy Now
Knockout VITEEE 2023

An exhaustive program for the complete preparation of Physics Chemistry Mathematics English and Aptitude of VITEEE, Adaptive Time Table, Chapterwise Questions, Concepts Flashcards for Quick and Effective Revision, Unlimited Chapter wise Subject wise and Full mock test for enhancing Speed & Accuracy,.

₹ 2999/- ₹ 1999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions