# Chapter 1:Relativity¶

## Example 1.1,Page no:9¶

In :
import math

#Varible declaration
t0= 3600  # time interval on Earth, seconds
t= 3601.0  #time interval for spacecraft as measured from Earth, seconds

#Calculation
c= 2.998 *(10**8)  #speed of light, m/s
v=c*math.sqrt((1-((t0/t)**2)))  #relative velocity of spacecraft, m/s

#Result
print"The speed of the Spacecraft relative to Earth is:%.2g "%v,"m/s"

The speed of the Spacecraft relative to Earth is:7.1e+06  m/s


## Example 1.2,Page no:13¶

In :
#Varible declaration
fg= 5.6*(10**14)  #frequency of green color, Hz
fr= 4.8*(10**14)  #frequency of red color, Hz
c= 3.0*(10**8)  #velocity of light, m/s

#Calculation
v= c*((fg**2 - fr**2)/(fg**2 + fr**2))  #longitudinal speed of observer, m/s
v= v*3.6  #convert to km/h
R= 1.0  #rate at which fine is to be imposed per km/h, $l= 80.0 #speed limit upto which no fine is to be imposed, km/h fine= v-l # fine to be imposed,$

#Result
print"The fine imposed is:",fine,"$\n" print"NOTE:Approx value of v is taken in book as 1.65*10^8,which is very less precise.\nTherefore,chnge in final answer"  The fine imposed is: 165176390.588$

NOTE:Approx value of v is taken in book as 1.65*10^8,which is very less precise.
Therefore,chnge in final answer


## Example 1.3,Page no:14¶

In :
import math

#Varible declaration
v= 6.12*(10**7)  #receding velocity with respect to Earth, m/s
c= 3.0*(10**8)  #velocity of light, m/s
L0= 500.0  #initial wavelength of spectral line, nm

#Calculation
L= L0*math.sqrt(((1+(v/c))/(1-(v/c))))  #final wavelength of spectral light, nm
Ls= L-L0  #shift in wavelength, nm

#Varible declaration
print"Shift in Green spectral line is: ",round(Ls),"nm"

Shift in Green spectral line is:  115.0 nm


## Example 1.4,Page no:19¶

In :
import math

#Varible declaration
StartingAge= 20  #starting age for both Dick and Jane
c= 3*(10**8)  #velocity of light, m/s
v= 0.8*c  #rate of separation of Dick and Jane, m/s
t0= 1  #interval for emission of signals, yr

#Calculation
t1= t0*((1+v/c)/(1-v/c))  #interval for reception of signals on outward journey, yr
t1= t0*(math.sqrt((1+v/c)/(1-v/c)))  #interval for reception of signals on outward journey, yr
t2= t0*(math.sqrt((1-v/c)/(1+v/c)))  #interval for reception of signals on return trip, yr
#Dick's frame of reference
Tout1= 15  #duration of outward trip, yr
Tin1= 15  #duration of return trip, yr
JaneAge= StartingAge+(Tout1/t1)+(Tin1/t2)  #Jane's age according to Dick
#Jane's frame of reference
Tout2= 25  #duration of outward trip, yr
d= 20  #delay in transmission of signal to Jane, caused by distance of the star, yr
Tin2= 5  #duration of return trip
DickAge= StartingAge+((Tout2+d)/t1)+(Tin2/t2)  #Dick's age according to JAne

#Result
print"According to Dick, age of Jane is:",JaneAge,"years"
print"According to Jane, age of Dick is:",DickAge,"years"

According to Dick, age of Jane is: 70.0 years
According to Jane, age of Dick is: 50.0 years


## Example 1.6,Page no:27¶

In :
import math

#Varible declaration
mf= 1  #mass of each entity, kg
c= 3*(10**8)  #velocity of light, m/s
v= 0.6*c  #velocity of fragments relative to original body, m/s

#Calculation
E0= 2*((mf*(c**2))/math.sqrt(1-((v/c)**2)))  #Total energy of fragments
m= E0/(c**2)  #mass of original body, kg

#Result
print"The total mass of the stationary body is: ",m,"kg"

The total mass of the stationary body is:  2.5 kg


## Example 1.7,Page no:28¶

In :
import math

#Varible declaration
r=1.4  # Rate of arrival of Solar Energy at erath, kW per square meter
R=1.5*(10**11)  #Radius of Earth, m

#Calculation
P=r*(4*math.pi*(R**2))  #Total power recieved by Earth, kW
P= P*(10**3)  #W
C= 3*(10**8)  #Velocity of light, m/s
E=P  #Energy lost by Sun, J
m= E/(C**2)  #Mass of Sun lost per second as energy, kg

#Result
print"Mass lost by sun per second, is:%.2g"%m,"kg"

Mass lost by sun per second, is:4.4e+09 kg


## Example 1.8,Page no:32¶

In :
import math

#Varible declaration
c= 3*(10**8)  #Velocity of light, m/s
me= 0.511/(c**2)  #mass of electron, MeV
mp=0  #mass of proton, MeV
p= 2.000/c  #momenta for both particles, MeV

#Calculation
##Using Eq. 1.24 and 1.25, Page 31
Ee=math.sqrt(((me**2)*(c**4))+((p**2)*(c**2)))  #Total energy of electron, MeV
Ep= p*c  #Total energy of proton, MeV

#Result
print"Total energy of Electron is: ",round(Ee,3),"MeV"
print"Total energy of Photon is: ",Ep,"MeV"

Total energy of Electron is:  2.064 MeV
Total energy of Photon is:  2.0 MeV


## Example 1.11,Page no:44¶

In :
#Varible declaration
c=3*(10**8)  #velocity of light, m/s
VaE= 0.90*c  #velocity of spacecraft alpha w.r.t Earth, m/s
VbA= 0.50*c  #velocity of spacecraft beta w.r.t. Alpha, m/s

#Calculation
VbE= (VaE+VbA)/(1+((VaE*VbA)/(c**2)))  #velocity of beta w.r.t Earth, m/s
VbE=VbE/c  #Converting to percent of c

#Result
print"The required velocity of spacecraft Beta w.r.t. Earth  is:",round(VbE,2),"c"

The required velocity of spacecraft Beta w.r.t. Earth  is: 0.97 c