Chapter 4: Satellite Hardware

Example 4.1, page no-122

In [2]:
#Variable Declaration
I=250     #specific impulse of a propellant
g=9.807   # acceleration due to gravity


#Calculation
v=I*g


#Result
print("Ejection velocity of the propellant mass is, v= %.2f m/s"%v)

Ejection velocity of the propellant mass is, v= 2451.75 m/s

Example 4.2, page no-122

In [3]:
import math

#Variable Declaration
m=4330.0      #initial mass of the satellite
i=290.0       #specific impulse of a propellant
del_v=-100    #velocity increment
g=9.807       #acceleration due to gravity


#Calculation
m1=m*(1-math.exp(del_v/(g*i)))


#Result
print("Mass of propellant necessary to be burnt is, m= %.0fkg"%math.ceil(m1))

Mass of propellant necessary to be burnt is, m= 150kg

Example 4.3, page no-123

In [4]:
#Variable Declaration
m=2950.0      #initial mass of the satellite
F=450.0       #required thrust
T=10.0        #thrust for time period
i=300.0       #specific impulse of a propellant
g=9.807       #acceleration due to gravity


#Calculation
mi=F*T/(i*g)


#Result
print("Mass of propellant that would be consumed is, m=%.2fkg"%mi)

Mass of propellant that would be consumed is, m=1.53kg

Example 4.5, page no-134

In [5]:
import math

#Variable Declaration
p=2000.0       # electrical energy to be generated from solar panel in Watt
fi=1250.0      # solar flux falling normally to the solar cell in worst case
s=4*10**-4     # Area of each solar cell
e=0.15         # conversion efficiency of solar cell includingthe losses
theta=10.0     # angle made by rays of sun with normal 


#Calculation
n=p/(fi*s*e)
n1=math.ceil(n)*math.pi
n2=math.ceil(n1)/math.cos(math.pi*(theta)/180.0)


#Result
print("Required no of solar cells, n = %.0f cells"%math.ceil(n1))
print("\n No of cells when sunrays are making an angle of 10° are %.0f"%math.ceil(n2))

Required no of solar cells, n = 83777 cells

 No of cells when sunrays are making an angle of 10° are 85070

Example 4.6, page no-134

In [6]:
#Variable Declaration
p=3600.0     #Power required
t=1.2        #worst case eclipse period
c=90.0       #capacity of each cell in Ah
v=1.3        #voltage of each cell in V
d=0.8        # Depth of discharge
e=0.95       #Discharge efficiency
E_sp=60.0    #specific energy specification of the battery


#Calculation
energy=p*t
n=energy/(c*v*d*e)
E_b=energy/(d*e)
m=E_b/E_sp


#Result
print("No of cells, n= %.0f cells\n Energy required to be stored in the battery system is %.1f Wh\n Mass of battery system = %.2f kg"%(n,E_b,m))

No of cells, n= 49 cells
 Energy required to be stored in the battery system is 5684.2 Wh
 Mass of battery system = 94.74 kg

Example 4.7, page no-153

In [9]:
import math
#Variable Declaration
theta=0.5         #azimuth beam width=Elevation beam width
f=6.0*10**9       #operating frequency 6 Ghz
c=3.0*10**8       #speed of light in cm/s


#Calculation
theta_r=theta*math.pi/180.0
theta_r=math.ceil(theta_r*10**5)/10**5
A=4*math.pi/(theta_r**2)
A=math.ceil(A*100)/100
A_dB=10*math.log10(A)
lam=c/f
Ag=(A*lam**2)/(4*math.pi)


#Result
print("Gain in dB = %.2f dB \nAntenna gain expressed in terms of\nantenna aperture(A) is given by G = %.2f m^2"%(A_dB,Ag))

Gain in dB = 52.17 dB 
Antenna gain expressed in terms of
antenna aperture(A) is given by G = 32.80 m^2

Example 4.8, page no-153

In [10]:
#Variable Declaration
la=0.5      #length efficiency in azimuth direction
le=0.7      #length efficiency in elevation direction 
A=10        #Actual projected area of an antenna


#Calculation
Ae=la*le
Aee=Ae*A

#Result
print("Aperture efficiency = %.2f \n Effective Aperture = %.1f m^2"%(Ae,Aee))

Aperture efficiency = 0.35 
 Effective Aperture = 3.5 m^2

Example 4.9, page no-154

In [11]:
import math
#Variable Declaration
p=100        #Antenna power in W
pd=10        #Power Density in mW/m^2
d=1000       #distance in m
p2=10000     #New antenna power


#Calculation
directivity=10*math.log10(p2/p)


#Result
print("Directivity (in dB)= %d dB"%directivity)

Directivity (in dB)= 20 dB

Example 4.10, page no-154

In [12]:
#Variable Declaration
beam_w=0.4   #antenna's 3dB beam width
Ae=5         #Effective Aperture of Antenna


#Result
print("The null-to-null beam width of a paraboloid reflector is twice its 3dB beam width. \n Therefore, Null-to-null beam width = %.1f°"%(2*beam_w))

The null-to-null beam width of a paraboloid reflector is twice its 3dB beam width. 
 Therefore, Null-to-null beam width = 0.8°

Example 4.11, page no-154

In [13]:
import math
#Variable Declaration
d=20.0        #received signal strenth in dB
loss=3.0      #incident polarization is circular and antenna is circularly polarized
theta=60.0    #received wave making angle with horizontal


#Calculation
total=d+loss
los=d*math.log10(1/math.cos(math.pi*theta/180.0))


#Result
print("(a)\n When received polarization is same as antenna \n polarization,thepolarization loss is zero.\n Therefore, received sinal strenth = %ddB"%total)
print("\n\n(b)\n When the incident wave is vertically polarized,\n the angle between incident polarization and antenna polarization is 90°\n Hence, Polarization loss = infinity\n received signal strength = 0")
print("\n\n(c)\n When incident wave is left-hand circularly polarized\n and antenna polarization is linear,\n then there is polarization loss of %ddB and\n received signal strength is %ddB"%(loss,d))
print("\n\n(d)\n Polarization loss = %ddB \n Received signal strength = %ddB"%(los,math.ceil(total-los)))

(a)
 When received polarization is same as antenna 
 polarization,thepolarization loss is zero.
 Therefore, received sinal strenth = 23dB


(b)
 When the incident wave is vertically polarized,
 the angle between incident polarization and antenna polarization is 90°
 Hence, Polarization loss = infinity
 received signal strength = 0


(c)
 When incident wave is left-hand circularly polarized
 and antenna polarization is linear,
 then there is polarization loss of 3dB and
 received signal strength is 20dB


(d)
 Polarization loss = 6dB 
 Received signal strength = 17dB

Example 4.12, page no-155

In [14]:
import math
#Variable Declaration
Ea=1              #effective aperture
f=11.95*10**9     #downlink operating frequency
c=3*10**8         #speed of light

Ae=math.floor((math.pi*1000*Ea**2)/4)/1000
lamda=math.floor(c*1000/f)/1000
ag=math.floor(100*4*math.pi*Ae/lamda**2)/100
adb=math.floor(100*10*math.log10(ag))/100
width=70*lamda/Ea
print("Operating wavelength = %.3fm\n Antenna Gain = %.2f\n Antenna Gain in dB = %.2fdB\n 3dB beam width = %.2f°"%(lamda,ag,adb,width))

Operating wavelength = 0.025m
 Antenna Gain = 15783.36
 Antenna Gain in dB = 41.98dB
 3dB beam width = 1.75°

Example 4.13, page no-155

In [15]:
import math
#Variable Declaration
f=2.0          # reflector focal length
d=2.0          # reflector diameter
l=90.0/100.0   # 90% of the angle


#Calculation
theta=4*180.0*(math.atan(1/(4*f/d)))/math.pi
theta=4*180.0*math.atan(0.25007)/math.pi    # this value gives exact answer as in book
dbw=l*theta

#Result
print("The angle subtended by the focal point feed\n at the edges of the reflector is, theeta = %.2f°\n\n 3dB beam width = %.2f°\n null-to-null beam width = % .2f°"%(theta,dbw,math.floor(200.0*dbw)/100.0))

The angle subtended by the focal point feed
 at the edges of the reflector is, theeta = 56.16°

 3dB beam width = 50.54°
 null-to-null beam width =  101.08°

Example 4.14, page no-155

In [16]:
import math

#Variable Declaration
c=3*10**8     #speed of light 
f=2.5*10**9   #operating frequency
s=0.1         #inter element spacing
theta =10     #10° right towards array axis

#Calculation
l=c/f
fi=(360*s/l)*math.ceil(10000*math.sin(math.pi*theta/180.0))/10000
fi=math.ceil(10*fi)/10

#Result
print("The phase angle for elements 1,2,3,4 and 5 \n are respecively 0°,%.1f°,%.1f°,%.1f° and %.1f°"%(fi,2*fi,3*fi,4*fi))

The phase angle for elements 1,2,3,4 and 5 
 are respecively 0°,52.2°,104.4°,156.6° and 208.8°

Example 4.15, page no-156

In [17]:
import math

#Variable Declaration
p=10000        #power fed to the antenna in W
ag=60          #Antenna gain
loss=2         #Power lossin feed system


#Calculation
adb=10*math.log10(p)
EIRP=adb+ag-loss


#Result
print("Earth station EIRP = %ddB"%EIRP)

Earth station EIRP = 98dB