In a eliptical planetary motion, the velocity of a planet changes continously so as to keep the angular momentum conserved. So can we can that the planet also has a tangential acceleration while orbiting?

If yes then in a 1998 JEE PYQ, (attached), the answer was (a). How????? Please explain

 

Asked by prajwalkambale85 | 17th Feb, 2022, 10:32: AM

Expert Answer:

Let us analyse each of the given options
 
(a) Acceleraion of satellite is always directed towards centre of earth.
 
Satellite moving in elliptical orbit does not have tangential acceleration and has only acceleration towards earth.

If the satellite has any tangential acceleration , then its orbit will not be constnat. Its orbit will change.
 
Change in direction of velocity of the satellite gives acceleration that is directed towards earth as described in the figure given below.

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(b) Angular momentum of statellite changes in direction but its magnitude remains constant.
 
Angular momentum begin mathsize 14px style L with rightwards arrow on top end style is given by 
begin mathsize 14px style L with rightwards arrow on top end style = begin mathsize 14px style r with rightwards arrow on top end style x begin mathsize 14px style p with rightwards arrow on top end style
where begin mathsize 14px style p with rightwards arrow on top end style is linear momentum vector and begin mathsize 14px style r with rightwards arrow on top end style is the position vector of satellite by taking center of earth as origin.
Hence, direction of angular momentum is perpendicular to the plane of orbit that has satellite and earth.
 
Hence, direction of angular momentum will never change if the plane of orbit remains constant.
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(c) Total mechanical energy of S varies linearly with time
 
Total mechanical energy is sum of potential and kinetic enrgy .
 
when satellite is far away from earth it moves slowly and its kinetic energy is less but potential energy is greater.
 
when satellite is near to earth it moves faster and its kinetic energy is more but potential energy is less.
 
Hence sum of kinetic energy and potential energy is always constant.
 
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(d) Linear momentum remains constant in magnitude
 
Linear mmentum is not constant in elliptical orbit .
 
when satellite is far away from earth it moves slowly but when satellite is near to earth it moves faster .

Answered by Thiyagarajan K | 17th Feb, 2022, 03:11: PM

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