In [1]:

```
from math import pi
#Variable declaration
Ta = 0.24 #Antenna temperature (K)
ang = 0.005 #Subtended angle (degrees)
hpbw = 0.116 #Antenna half power beamwidth (degrees)
#Calculations
Ts = Ta*(hpbw**2)/(pi*(ang**2/4))
#Result
print "The averate temperature of the surface is", round(Ts), "K"
```

In [2]:

```
from math import pi, sqrt
#Variable declaration
eff_aper = 500 #Antenna effective aperture (m^2)
wave_lt = 20e-2 #Wavelength (m)
Tsky = 10.0 #sky temperature (K)
Tgnd = 300.0 #Ground temperature (K)
beam_eff = 0.7 #Beam efficiency (unitless)
aper_eff = 0.5 #Aperture efficiency (unitless)
#Calculations
phy_aper = aper_eff/eff_aper #Physical aperture (m^2)
diam = 2*sqrt(phy_aper/pi) #Antenna diameter (m)
diam_l = diam/wave_lt #Antenna diameter (lambda)
ta_sky = Tsky*beam_eff #Sky contribution to antenna temp. (K)
ta_side = 0.5*Tsky*(1-beam_eff) #Side-lobe contribution to antenna temp. (K)
ta_back = 0.5*Tgnd*(1-beam_eff) #Back-lobe contribution to antenna temp. (K)
Ta = ta_sky + ta_side + ta_back
#Result
print "The total antenna temperature is", Ta, "K"
```

In [3]:

```
#Variable declaration
Tn = 50.0 #Noise temperature (K)
Tphy = 300.0 #Physical temperature (K)
Eff = 0.99 #Efficiency (unitless)
Tn_stg = 80.0 #Noise temperature of first 3 stages (K)
gain_db = 13.0 #Gain (dB)
Tphy_tr = 300 #Transmission line physical temperature (K)
Eff_tr = 0.9 #Transmission line efficiency (unitless)
#Calculations
gain = 10**(gain_db/10)
T_r = Tn_stg + Tn_stg/(gain) + Tn_stg/(gain**2)
#Receiver noise temperature (K)
Tsys = Tn + Tphy*(1/Eff - 1) + Tphy_tr*(1/Eff_tr - 1) + (1/Eff_tr)*T_r
#System temperature (K)
#Result
print "The system temperature is", round(Tsys), "K"
```

In [7]:

```
from math import sqrt
#Variable declaration
phy_aper = 2208 #Physical aperture (m^2)
f = 1415e6 #Frequency (Hz)
aper_eff = 0.54 #Aperture efficiency (unitless)
Tsys = 50 #System temperature (K)
bw = 100e6 #RF Bandwidth (Hz)
t_const = 10 #Output time constant (s)
sys_const = 2.2 #System constant (unitless)
k = 1.38e-23 #Boltzmann's constant (J/K)
#Calculations
Tmin = sys_const*Tsys/(sqrt(bw*t_const)) #Minimum detectable temperature(K)
eff_aper = aper_eff*phy_aper #Effective aperture (m^2)
Smin = 2*k*Tmin/eff_aper #Minimum detectable flux density (W/m^2/Hz)
#Result
print "The minimum detectable flux density is %.1e W/m^2/Hz" % Smin
```

In [8]:

```
from math import pi, log10
#Variable declaration
k = 1.38e-23 #Boltzmann's constant (J/K)
trans_pow = 5 #Transponder power (W)
r = 36000e3 #Distance (m)
wave_lt = 7.5e-2 #Wavelength (m)
ant_gain = 30 #Antenna gain (dB)
earth_ant = 38 #Earth station antenna gain (dB)
Tsys = 100 #Earth station receiver system temperature (K)
bw = 30e6 #Bandwidth (Hz)
#Calculations
s_n = wave_lt**2/(16*(pi**2)*(r**2)*k*Tsys*bw)
s_n = 10*log10(s_n) #Signal to Noise ratio (dB)
trans_pow_db = 10*log10(trans_pow) #Transponder power (dB)
erp = ant_gain + trans_pow_db #Effective radiated power (dB)
s_n_downlink = erp + earth_ant + s_n #Signal to Noise ratio downlink(dB)
#Result
print "The earth station S/N ratio is", round(s_n_downlink,1), "dB"
```

In [9]:

```
from math import exp
#Variable declaration
tf = 0.693 #Absorption co-efficient (unitless)
Te = 305 #Earth temperature (K)
Ta = 300 #Satellite antenna temperature (K)
#Calculations
Tf = (Ta - Te*exp(-tf))/(1-exp(-tf))
#Result
print "The forest temperature is", round(Tf), "K"
```

In [14]:

```
#Variable declaration
f = 10e9 #Frequency (Hz)
wind_speed = 350 #Wind speed (km/h)
c = 3e8 #Speed of light (m/s)
vr = 1e3 #Differential velocity (m/h)
#Calculations
wave_lt = c/f #Wavelength (m)
freq_shift = 2*(wind_speed*1000/3600)/wave_lt
#Doppler Frequency shift (Hz)
T = 1/(2*freq_shift) #Pulse repetition interval (s)
prf = 1/T #Pulse repetition frequency (Hz)
fmin = 2*(vr/3600)/wave_lt #Frequency resolution (Hz)
N = 1/(round(fmin,1)*T) #Number of pulses
#Result
print "The minimum pulse repetition frequency is", round(prf,-3), "Hz"
print "The number of pulses to be sampled is", round(N)
```