Gravitation Question 187
Question: The largest and the shortest distance of the earth from the sun are $ [r_{1}] $ and $ [r_{2}] $ , its distance from the sun when it is at the perpendicular to the major axis of the orbit drawn from the sun[CBSE PMT 1991]
Options:
A) $ [\frac{r_{1}+r_{2}}{4}] $
B) $ [\frac{r_{1}r_{2}}{r_{1}+r_{2}}] $
C) $ [\frac{2r_{1}r_{2}}{r_{1}+r_{2}}] $
D) $ [\frac{r_{1}+r_{2}}{3}] $
Show Answer
Answer:
Correct Answer: C
Solution:
The earth moves around the sun is elliptical path. so by using the properties of ellipse $ [r_{1}=(1+e),a] $ and $ [r_{2}=(1-e),a] $ $ [\Rightarrow ,a=\frac{r_{1}+r_{2}}{2}] $ and $ [r_{1}r_{2}=(1-e^{2}),a^{2}] $ where a = semi major axis b = semi minor axis e = eccentricity Now required distance = semi latusrectum $ [=\frac{b^{2}}{a}] $ $ [=\frac{a^{2}(1-e^{2})}{a}=\frac{(r_{1}r_{2})}{(r_{1}+r_{2})/2}=\frac{2r_{1}r_{2}}{r_{1}+r_{2}}] $
