Question:
The longest and the shortest distance of our planet from sun is and $R_1$ and $R_2$. Distance from sun when it is normal to major axis of orbit is .
The longest and the shortest distance of our planet from sun is and $R_1$ and $R_2$. Distance from sun when it is normal to major axis of orbit is .
Updated On: Jun 7, 2022
- $\frac{R_1+R_2}{2}$
- $\sqrt{\frac{R^2_1+R^2_2}{2}}$
- $\frac{R_1R_2}{R_1+R_2}$
- $\frac{2R_1R_2}{R_1+R_2}$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
$r_1 = (1 +e) a ;r_2 = (1 - e) a$
$ a = \frac{r_1+r_2}{2} ; r_1r_2 = (1 - e^2)a^2$
= $\frac{b^2}{a}$
$= \frac{a^2(1 - e^2)}{a} = \frac{r_1r_2}{\frac{r_1+r_2}{2}} = \frac{2r_1r_2}{r_1+r_2}$
$ a = \frac{r_1+r_2}{2} ; r_1r_2 = (1 - e^2)a^2$
= $\frac{b^2}{a}$
$= \frac{a^2(1 - e^2)}{a} = \frac{r_1r_2}{\frac{r_1+r_2}{2}} = \frac{2r_1r_2}{r_1+r_2}$
Was this answer helpful?
0
0
Top Questions on Keplers Laws
- Applying the principle of homogeneity of dimensions, determine which one is correct. Where \( T \) is the time period, \( G \) is the gravitational constant, \( M \) is the mass, and \( r \) is the radius of the orbit.
- JEE Main - 2024
- Physics
- Keplers Laws
- Correct formula for height of a satellite from earths surface is :
- JEE Main - 2024
- Physics
- Keplers Laws
If the distance of the earth from Sun is $15 \times 10^6 km$ Then the distance of an imaginary planet from Sun, if its period of revolution is $2.83$ years is :
- JEE Main - 2023
- Physics
- Keplers Laws
- Every planet revolves around the sun in an elliptical orbit:-
A. The force acting on a planet is inversely proportional to square of distance from sun
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun
C. The Centripetal force acting on the planet is directed away from the sun
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit
Choose the correct answer from the options given below:- JEE Main - 2023
- Physics
- Keplers Laws
- The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.
- JEE Main - 2023
- Physics
- Keplers Laws
View More Questions
Questions Asked in JIPMER exam
- Binomial nomenclature was first introduced by
- JIPMER - 2015
- KCET - 2022
- Diversity In The Living World
- A convex lens $'A'$ of focal length $20\, cm$ and a concave lens $'B'$ of focal length $5\, cm$ are kept along the same axis with a distance $'d'$ between them. If a parallel beam of light falling on $'A'$ leaves $'B'$ as a parallel beam, then the distance $'d'$ in cm will be :
- JIPMER - 2021
- Spherical Mirrors
- A bacterial flagellum is composed of
- JIPMER - 2021
- Prokaryotic Cells
- $2,4-DNP $ test can be used to identify :
- JIPMER - 2021
- Chemical Reactions
- How many moles of acidified $K_2Cr_2O_7$ is required to liberate $6$ moles of $I_2$ from an aqueous solution of $I^-$ ?
- JIPMER - 2020
- Mole concept and Molar Masses
View More Questions
Concepts Used:
Keplers Laws
Kepler’s laws of planetary motion are three laws describing the motion of planets around the sun.
Kepler First law – The Law of Orbits
All the planets revolve around the sun in elliptical orbits having the sun at one of the foci.
Kepler’s Second Law – The Law of Equal Areas
It states that the radius vector drawn from the sun to the planet sweeps out equal areas in equal intervals of time.
Kepler’s Third Law – The Law of Periods
It states that the square of the time period of revolution of a planet is directly proportional to the cube of its semi-major axis.
T2 ∝ a3