SATHEE: Gravitation Question 187

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) $[\frac{2 r_{1} r_{2}}{r_{1} + r_{2}}]$

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 $[= \frac{b^{2}}{a}]$ $[= \frac{a^{2} (1 - e^{2})}{a} = \frac{(r_{1} r_{2})}{(r_{1} + r_{2}) / 2} = \frac{2 r_{1} r_{2}}{r_{1} + r_{2}}]$

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Gravitation Question 187

Question: The largest and the shortest distance of the earth from the sun are [r1] and [r2] , 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:

Answer:

Solution:

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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]