Plz Help me understand this problem!!! A satellite is in an elliptic orbit about
ID: 1897513 • Letter: P
Question
Plz Help me understand this problem!!!
A satellite is in an elliptic orbit about the earth with the center of attraction located at The plane of the orbit is the earth equatorial plane. At a time t1, when the satellite is at point Pi, at the edge of the semi-latus rectum, the radius-vector is measured as r1 = r1Q and the true anomaly theta = theta1. At a. later time 1/2, when the satellite is located at point P2, the radius vector is measured as r2 = - r2P and the true anomaly is theta = theta2 = theta1+ 90 degree. Here P and Q are the unit vectors in the x and y directions, respectively, in the perifocal system of coordinates with its origin at ln this problem, the vectors r1; and r2 and their magnitudes r1 and r2 are known, the times t1 and t2 and the true anomalies theta1 and theta2 are known. The semi-major axis a and the eccentricity e the elliptic orbit are not known. Determine the functions f, g df/dt and dg/dt this orbit, simplifying the expressions as much as possible. Determine the velocity vectors v1anc v2 at P1 and P2 respectively.Explanation / Answer
This is very mathematically evolved question. In perifocal coordinate system equation of ellipse, (r( heta) = a(1-e^2)/(1-e cos heta)) (a) r1 = a(1 - e^2); at theta = 90 r2 = a(1 - e); at theta = 180 gives e = r1/r2 -1 and a = r2 / (2 - r1/r2) f = ae = (r1 - r2)/(2 - r1/r2) g = 1- sqrt(1- e^2) = 1- sqrt((r1/r2)(2- r1/r2)) (b) ( ec{V_2} = - sqrt{ rac{GM_{earth}}{r_2}} Q)