HW-Lab_02.sagews

#################  Lecture Question 1  ####################
Re = 6378.1366;     #Radius of Earth in km
a = 6828.;          #Given semi-major axis in km
Xd = 0.81;
Xe = 0.57;
Pe = 1150;
Pd = 1150;
P = (1.6586690213e-4)*a^(3/2); #P in minutes (from equation C-19 of SME)
print 'The period is: ', P, 'minutes';

MAX_Te = P*arcsin(Re/a)/(RealField(30)(pi));  #From equation C-37 (a little confused on units here)
print 'The maximum eclipse is: ', MAX_Te, 'minutes';

Td = P - MAX_Te;
print 'Td: ', Td, 'minutes';

Psa = ((Pe*MAX_Te/Xe) + (Pd*Td/Xd))/(Td);
print 'Psa: ', Psa;

The period is: 93.5836548213360 minutes The maximum eclipse is: 35.918249 minutes Td: 57.665406 minutes Psa: 2676.4275

#################  Lecture Question 2  ####################
Id = 0.72;
theta = 23.5*2*RealField(30)(pi)/360;
efficiency = 0.247;
Po = efficiency*1353;
print 'Po: ', Po;

Pbol = Po*Id*cos(theta);
print 'Pbol: ', Pbol, 'watts/m^2'

Po: 334.191000000000 Pbol: 220.66072 watts/m^2

#################  Lecture Question 3  ####################
Peol = Pbol*(1-.0375)^4;
print 'Peol: ', Peol, 'watts/m^2';

Peol: 189.37733 watts/m^2

#################  Lecture Question 4  ####################
Asa = Psa/Peol;
print 'Asa: ', Asa;

Asa: 14.132777

#################  Lecture Question 5  ####################
Num_Cycles = 4*(3.156e+7)/60/P;   #Sidereal year in minutes divided by period
print 'The number of cycles in 4 years: ', Num_Cycles;

The number of cycles in 4 years: 22482.5585623560

#################  Lecture Question 6  ####################
Capacity = Pe*(MAX_Te/60)/(0.3*0.85);
print 'Capacity: ', Capacity;

Capacity: 2699.7377

#################  Lecture Question 7  ####################
pii = RealField(30)(pi);
c=3e8;  #Speed of light
Gains = [10, 20, 30, 40, 50, 75];
G=10.;
eta=0.55;
freq = 450e6;    #Frequency given
lamda=c/freq;

for j in range(6): #Using 16-9 and 16-11
    print 'Size for a gain of', Gains[j], 'is', sqrt((1/eta)*10^(Gains[j]/10.))*c/(pii*freq), 'meters, with a beam width of', 21/((freq/(1e9))*sqrt((1/eta)*10^(Gains[j]/10.))*c/(pii*freq));

Size for a gain of 10 is 0.90485194 meters, with a beam width of 51.573815 Size for a gain of 20 is 2.8613931 meters, with a beam width of 16.309072 Size for a gain of 30 is 9.0485194 meters, with a beam width of 5.1573815 Size for a gain of 40 is 28.613931 meters, with a beam width of 1.6309072 Size for a gain of 50 is 90.485194 meters, with a beam width of 0.51573815 Size for a gain of 75 is 1609.0796 meters, with a beam width of 0.029002087