00:01
Hi, in this question we are given with a satellite.
00:03
So, it is unnamed.
00:04
So, first we have to find the so first we have to find the eccentricity.
00:09
So, eccentricity is given by the formula it is rp minus ra divided by so magnitude of rp minus ra divided by rp plus ra where r is the so rp is the radius of the perigee and ra is the radius of the apogee.
00:25
So, substituting the given values we have e is equal to magnitude of 7000 minus 70000 divided by 7000 plus 70000.
00:35
So, magnitude is taken so we can omit the neglect sign we have this is answer is 9 by 11.
00:42
Then we have to calculate so this is the first answer.
00:46
The second part we have to calculate the semi major axis.
00:50
So, semi major axis of the orbit is given by the formula it is rp divided rp plus ra divided by 2 where rp is the radius of the perigee and ra is the radius of the apogee.
01:02
So, on substituting the values we have 7000 plus 70000 divided by 2 which is equal to 38500 kilo meters.
01:11
Then we have to calculate the period of the orbit.
01:14
So, it is given by the formula t is equal to 2 pi divided by root mu into a power 3 by 2 where a is the semi major axis and mu is the so mu value has the value of 3 9.
01:28
So, mu is 398600 so kilometer cube per second square.
01:35
So, then a is the semi major axis on substituting the values we have this answer is 20 .88 r.
01:43
Then so here we get answer in second so it should be divided by 3600 to get this answer.
01:49
Then in the fourth part we have to calculate the specific energy so which is given by the formula minus mu divided by 2a.
01:57
So, we have the value of mu here and a value is semi major axis on substituting all of these values we have the answer for the energy is minus 5 .1766 kilometer square per second square.
02:10
In the next part of the question we have we have to consider the true anomaly theta.
02:18
So, we have to consider the expression for the distance to the focus r in the eccentricity which is in terms of eccentricity which is a into 1 minus e square divided by 1 plus 1 plus a into cos theta.
02:31
So, substituting for theta we have theta is equal to cos inverse of 1 minus e square.
02:38
So, a into 1 minus e square divided by r minus 1 by e.
02:43
So, on substituting all of this value so we have the eccentricity value and we have a value r value is so we have to substitute for r value.
02:52
So, first let us have the so let us substitute the values so a is 38500 into 1 minus 9 by 11 whole square divided by r value is it is 1000...