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// Chapter 11 example 13
//------------------------------------------------------------------------------
clc;
clear;
// Given data
apogee = 35000; // farthest point in kms
perigee = 500; // closest point in kms
r = 6360; // radius of earth in kms
G = 6.67*10^-11 // gravitational constant
M = 5.98*10^24; // mass of earth in kgs
// calculations
//funcprot(0)
apogee_dist = apogee + r // apogee distance in kms
perigee_dist= perigee+r ; // perigee distance in kms
a = (apogee_dist + perigee_dist)/2; // semi-major axis of elliptical orbit
T = (2*%pi)*sqrt((a*10^3)^3/(G*M)); // orbital time period
hr = T/3600 // conv. from sec to hrs and min
t = modulo(T,3600) // conv. from sec to hrs and min
mi = t/60 // conv. from sec to hrs and min
u = G*M
Vapogee = sqrt(u*((2/(apogee_dist*10^3)) - (1/(a*10^3)))); // velocity at apogee point
Vperigee = sqrt((G*M)*((2/(perigee_dist*10^3)-(1/(a*10^3))))) // velocity at perigee point
// Output
mprintf('Orbital Time Period = %d Hrs %d min \n Velocity at apogee = %3.3f Km/s\n Velocity at perigee = %3.3f Km/s',hr,mi,Vapogee/1000,Vperigee/1000)
mprintf('\n Note: Calculation mistake in textbook in finding velocity at apogee point')
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