import math
#Given that
t1 = 1 # time period of satellite s1 in hours
t2 = 8 # time period of satellite s2 in hour
r1 = 1.2e4 # radius of orbit of satellite s1 in km
print "Standard formula r2/r1 = (t2/t1)**(2/3)"
r2 = r1 * (t2/t1)**(2/3) # calculation of radius of orbit of satellite s2 in km
v1 = 2 * pi * r1 / t1 # calculation of speed of satellite s1 in km/h
v2 = 2 * pi * r2 / t2 # calculation of speed of satellite s2 in km/h
del_v = v2 - v1 # calculation of relative speed of satellites in km/h
print " Relative speed of satellite s2 wrt satellite s1 is ",del_v," km/h."
import math
#Given that
h = 2620 # distance of satellite from surface of Earth in km
R_e = 6400 # radius of Earth in km
M_e = 6e24 # mass of Earth in kg
G = 6.67e-11 # universal gravitational constant
print "Standard formula used \t v_o = math.sqrt(G*M_e/r) "
print " \t T = 2 * pi * r / v_o "
r = R_e + h
v_o = math.sqrt(G * M_e / (r * 1e3))
T = 2 * pi * r*1000 / (v_o*3600)
print " Orbital velocity of satellite is ",round(v_o / 1000,4)," km/s period of revolution is ",round(T,4)," h."
import math
#Given that
h = 3e5 # distance of satellite from surface of Earth in m
R_e = 6.38e6 # radius of Earth in km
M_e = 6e24 # mass of Earth in kg
g = 9.8 # gravitational acceleration in m/s2
print "Standard formula used v_o = math.sqrt(G*M_e/r) "
print "Standard formula used T = 2 * pi * r / v_o "
r = R_e + h # calculation of effective distance between Earth and satellite
G = g * R_e**2 / M_e # calculation of gravitational constant
v_o = math.sqrt(G * M_e / r) / 1000 # calculation of orbital velocity of satellite
T = 2 * pi * r / (v_o * 1000) / 3.6e3 # calculation of period of revolution of satellite
print " Orbital velocity of satellite is ",round(v_o,4)," km/s period of revolution is ",round(T,4)," h."
import math
#Given that
t = 27.3 # period of lunar orbit around Earth in days
r = 3.9e5 # distance of satellite from Earth in km
G = 6.67e-11 # universal gravitational constant
print "Standard formula used T = 2 * pi * math.sqrt ((r**3)/G*M_e) "
T = t * 24 * 60 * 60 # calculation of time in seconds
M_e = 4 * pi**2 * (r * 1000)**3 / (G * T**2) # calculation of mass of Earth
print " Estimated mass of Earth is ",M_e," kg."
import math
#Given that
t = 1 # period of Earth's revolution around Sun in years
r = 1.5e8 # distance between Sun and Earth in km
G = 6.67e-11 # Universal gravitational constant
print "Standard formula used T = 2 * pi * math.sqrt ((r**3)/G*M_e) "
T = t * 24 * 60 * 60 *356 # calculation of time period in seconds
M_s = 4 * pi**2 * (r * 1000)**3 / (G * T**2) # calculation of mass of Sun
print " Estimated mass of Sun is ",M_s," kg."
import math
#Given that
R_e = 6.4e6 # radius of Earth in km
M_e = 6e24 # mass of Earth in kg
G = 6.67e-11 # universal gravitational constant
u = 6e3 # initial speed of rocket in m/s
print "Standard formula used U_f - U_i = 1/2 * m *(u**2 - v**2) "
h = ((R_e * 1e3)**2 * u**2) / (2 * G * M_e - R_e * u**2) / 1000 # calculation of Height reached by rocket before returning to Earth
print " Height reached by rocket before returning is ",h," km."
import math
#Given that
R_e = 6.4e6 # radius of Earth in km
M_e = 6e24 # mass of Earth in kg
G = 6.67e-11 # universal gravitational constant
print "Standard formula used U_f - U_i = 1/2 * m *(u**2 - v**2) "
h = 10 * R_e
v = math.sqrt (2 *h * G * M_e / (R_e * h)) # calculation of velocity required by mass to reach given height
print " Velocity required by mass is ",round(v,4)," m/s."
import math
#Given that
r1 = 1e12 # distance of first planet from Sun in m
r2 = 1e13 #distance of first planet from Sun in m
print "Standard formula used T**2 = k* r**3"
print " Standers formula used v = 2 * pi * r / T"
r_ratio = r1 / r2 # r_ratio is ratio of distances from Sun
T_ratio = r_ratio**(3/2) #calculation of Ratio of time period
v_ratio = r_ratio / T_ratio # calculation of ratio of speed
print " Ratio of time period is ",T_ratio," and ratio of speed is ",v_ratio," ."
import math
#Given that
r1 = 1.5e8 # distance of Earth from Sun in km
t1 = 1 # let
print " Standard formula used T**2 = k* r**3"
t2 = 29.5 * t1 # calculation of time period of Saturn
r2 = r1 * (t2 / t1) ** (2/3) #calculation of distance of stern from Sun
print " Distance of Saturn from Sun is ",r2," km ."
import math
#Given that
r_peri = 360 # distance of perigee of satellite from Earth surface in km
r_apo = 2500 # distance of apogee of satellite from Earth surface in km
R_e = 6400 # radius of Earth in km
v_p = 30000 # speed of satellite at apogee position in km/h
print " Standard formula used v * r = k "
r_p = r_peri + R_e # calculation of distance of perigee
r_a = r_apo + R_e # calculation of distance of apogee
v_a = v_p * r_p / r_a # calculation of speed at apogee
print " Speed at perigee is ",v_p," km/h and at apogee is ",v_a," km/h ."
import math
#Given that
h = 600 # distance of satellite from surface of Earth in km
R_e = 6400 # radius of Earth in km
m_s = 100 # mass of satellite in kg
g = 10 # gravitational acceleration in m/s2
v_y = 2500 # upward velocity of launched satellite
print " Standard formula used 1/2 *(m_s * v **2 / r) = g * R_E**2 * m /R_e**2 "
r = R_e + h # calculation of effective height of satellite
v = math.sqrt (g * (R_e * 1e3)**2 / (r * 1e3)) # calculation of orbital velocity of satellite
P_x = m_s * v # calculation of momentum in x direction
P_y = m_s * v_y # calculation of momentum in y direction
U = math.sqrt(P_x**2 + P_y**2 ) # calculation of magnitude of impulse required
theta1 = (180 / pi) * math.atan (P_y / P_x ) # calculation of direction of impulse required
print " Magnitude and direction of impulse required are respectively ",round(U,4),"kgm/s and ",round(theta1,4)," degree."
import math
#Given that
b_e = 13.6 # Binding energy of electron to proton in eV
c= 3e8 # speed of light in m/s
print " Standard formula used E = m*c**2"
del_m = b_e * (1.6e-19) / c**2 * 1000
print " Loss in mass during formation of 1 atom of hydrogen is ",del_m," g."
import math
#Given that
M_p = 1.6725e-24 # mass of proton in g
M_n = 1.6748e-24 # mass of neutron in g
M_d = 3.3433e-24 # mass of deuteron in g
c= 3e8 # speed of light in m/s
print " Standard formula used E = m*c**2"
del_m = M_p + M_n - M_d # calculation of Loss in mass during formation of 1 atom of hydrogen
b_e = (del_m / 1000) * c**2 / (1.6e-19 * 1e6) # calculation of Binding energy of deuteron
print " Binding energy of deuteron is ",b_e," MeV."