#importing modules
import math
from __future__ import division
#Variable declaration
m1=m2=0.5; #mass(kg)
r2=0.1; #distance(m)
r1=float("inf"); #distance(m)
G=6.67*10**-11; #gravitational constant
#Calculation
delta_U=G*m1*m2*((1/r2)-(1/r1)); #gravitational energy(J)
#Result
print "gravitational energy is",delta_U*10**10,"*10**-10 J"
#importing modules
import math
from __future__ import division
#Variable declaration
m1=1; #mass(kg)
m2=2; #mass(kg)
m3=3; #mass(kg)
a=0.5; #side(m)
G=6.67*10**-11; #gravitational constant
#Calculation
delta_U=-G*((m1*m2)+(m2*m3)+(m3*m1))/a; #net energy(J)
#Result
print "net energy is",round(delta_U*10**11,2),"*10**-11 J"
print "answer given in the book is wrong"
#importing modules
import math
from __future__ import division
#Variable declaration
r=4*10**8; #distance(m)
M1=6*10**24; #mass of earth(kg)
M2=7.5*10**22; #mass of moon(kg)
#Calculation
x=r/(1+math.sqrt(M2/M1)); #distance where potential becomes zero(m)
#Result
print "distance where potential becomes zero is",round(x/10**8,1),"*10**8 m"
#importing modules
import math
from __future__ import division
#Variable declaration
g=9.8; #acceleration due to gravity(m/s**2)
R=6.4*10**3; #radius(km)
#Calculation
v=math.sqrt(3*g*R/2); #initial velocity(km/s)
#Result
print "initial velocity is",round(v,1),"km/s"
print "answer given in the book is wrong"
#importing modules
import math
from __future__ import division
#Variable declaration
m=10**-26; #mass(kg)
R=0.5*10**-10; #radius(m)
G=6.67*10**-11; #gravitational constant
#Calculation
V=math.sqrt(G*m/(4*R)); #velocity of particle(m/s)
#Result
print "velocity of particle is",round(V*10**14,2),"*10**-14 m/s"
#importing modules
import math
from __future__ import division
#Variable declaration
m=1; #mass(kg)
r=0.1; #radius(m)
G=6.67*10**-11; #gravitational constant
#Calculation
F=G*m/r**2; #force(N/kg)
U=F*r; #gravitational potential(J/kg)
#Result
print "gravitational potential is",U*10**10,"*10**-10 J/kg"
#importing modules
import math
from __future__ import division
#Variable declaration
rmax=1.2*10**12; #semi minor axis(m)
rmin=0.06*10**12; #semi major axis(m)
#Calculation
e=(rmax-rmin)/(rmax+rmin); #eccentricity of orbit
#Result
print "eccentricity of orbit is",round(e,1)
#importing modules
import math
from __future__ import division
#Variable declaration
Vmin=21; #minimum velocity(km/sec)
rmax=4*10**10; #apogee position(m)
rmin=1.6*10**9; #perigee position(m)
#Calculation
Vmax=Vmin*rmax/rmin; #maximum velocity(km/sec)
#Result
print "maximum velocity is",int(Vmax),"km/sec"
#importing modules
import math
from __future__ import division
#Variable declaration
e=0.05; #eccentricity of orbit
Vmin=36; #minimum velocity(km/sec)
rmin=2.5*10**10; #perigee position(m)
#Calculation
rmax=rmin*((1+e)/(1-e)); #apogee position(m)
Vmax=Vmin*rmin/rmax; #velocity at apogee point(km/s)
#Result
print "apogee position is",round(rmax/10**10,2),"*10**10 m"
print "velocity at apogee point is",round(Vmax,2),"km/s"
#importing modules
import math
from __future__ import division
#Variable declaration
Vmin=23; #minimum velocity(km/sec)
Vmax=25; #velocity at apogee point(km/s)
#Calculation
e=(Vmax-Vmin)/(Vmax+Vmin); #eccentricity of orbit
#Result
print "eccentricity of orbit is",round(e,4)
#importing modules
import math
from __future__ import division
#Variable declaration
r=3.8*10**8; #radius(m)
T=27*24*3600; #time period(sec)
G=6.67*10**-11; #gravitational constant
#Calculation
M=4*math.pi**2*r**3/(G*T**2); #mass of earth(kg)
#Result
print "mass of earth is",round(M/10**24,3),"*10**24 kg"
#importing modules
import math
from __future__ import division
#Variable declaration
T1=225; #time period of venus(days)
T2=365; #time period of earth(days)
#Calculation
a1bya2=(T1/T2)**(2/3); #ratio of semi major axis
#Result
print "ratio of semi major axis is",round(a1bya2,3)
#importing modules
import math
from __future__ import division
#Variable declaration
a2=1; #assume
a1=1.25*a2; #axis of planet
T2=365; #time period of earth(days)
#Calculation
T1=T2*math.sqrt((a1/a2)**3); #time period of planet(days)
#Result
print "time period of planet is",int(T1),"days"
#importing modules
import math
from __future__ import division
#Variable declaration
r1=1; #assume
r2=1-(40/100); #radius of earth
T1=24; #time period of earth(hours)
#Calculation
T2=T1-(T1*((r2/r1)**2)); #change in time period(hours)
#Result
print "change in time period is",T2,"hours"
#importing modules
import math
from __future__ import division
#Variable declaration
R=1; #assume
a1=R/2;
a=R;
T=365; #time period of earth(days)
#Calculation
T1=T*math.sqrt((a1/a)**3)/2; #time interval to reach sun(days)
#Result
print "time interval to reach sun is",round(T1,1),"days"
#importing modules
import math
from __future__ import division
#Variable declaration
R=1.5*10**11; #radius(m)
T=86400*365; #time period(sec)
G=6.67*10**-11; #gravitational constant
#Calculation
M=4*math.pi**2*R**3/(G*T**2); #mass of sun(kg)
#Result
print "mass of sun is",int(M/10**30),"*10**30 kg"