def calculateOrbitalVelocity( measurement1, measurement2 ):
'''
To solve the velocity of a circular orbit, we need Newton's gravitational
constant and two of the following three items:
G = Newton's gravitational constant
m = planetary mass (i.e., mass of the thing being orbited)
r = orbit radius (the distance from the center of mass)
T = orbital period
---- velocity in terms of mass and radius
v = sqrt( G*m/r )
---- velocity in terms of radius and period
v = 2*pi*r/T
---- velocity in terms of mass and period
v = ( 2*pi*cbrt( T^2*G*m/4*pi^2 ) ) / T
'''
validUnitTypes = [
[ 'mass', 'time' ],
[ 'length', 'time' ],
[ 'mass', 'length' ],
]
arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes )
if not arguments:
raise ValueError( '\'orbital_velocity\' requires specific measurement types (see help)' )
if 'mass' in arguments:
mass = arguments[ 'mass' ]
if 'length' in arguments:
bRadius = True
radius = arguments[ 'length' ]
else:
bRadius = False
period = arguments[ 'time' ]
else:
# radius and period
radius = arguments[ 'length' ]
period = arguments[ 'time' ]
velocity = divide( getProduct( [ 2, pi, radius ] ), period )
return velocity.convert( 'meter/second' )
if bRadius:
# mass and radius
velocity = getRoot( divide( multiply( getNewtonsConstant( ), mass ), radius ), 2 )
else:
# mass and period
term = divide( getProduct( [ period, period, getNewtonsConstant( ), mass ] ),
getProduct( [ 4, pi, pi ] ) )
velocity = divide( getProduct( [ 2, pi, getRoot( term, 3 ) ] ), period )
return velocity.convert( 'meter/second' )
def calculateOrbitalMass( measurement1, measurement2 ):
'''
To solve for the planetary mass for an object in a circular orbit, we need
Newton's gravitational constant and two of the following three items:
G = Newton's gravitational constant
T = orbital period
v = orbital velocity
r = orbit radius (the distance from the center of mass)
---- mass in terms of period and velocity
m = v^3*T/2*pi*G
---- mass in terms of period and radius
m = 4*pi^2*r3/G*T^2
---- mass in terms of velocity and radius
m = v^2*r/G
'''
validUnitTypes = [
[ 'time', 'length' ],
[ 'velocity', 'length' ],
[ 'time', 'velocity' ],
]
arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes )
if not arguments:
raise ValueError( '\'orbital_mass\' requires specific measurement types (see help)' )
if 'time' in arguments:
period = arguments[ 'time' ]
if 'length' in arguments:
bRadius = True
radius = arguments[ 'length' ]
else:
bRadius = False
velocity = arguments[ 'velocity' ]
else:
# velocity and radius
radius = arguments[ 'length' ]
velocity = arguments[ 'velocity' ]
mass = divide( getProduct( [ velocity, velocity, radius ] ), getNewtonsConstant( ) )
return mass.convert( 'kilogram' )
if bRadius:
# radius and period
mass = divide( getProduct( [ 4, pi, pi, radius, radius, radius ] ),
getProduct( [ getNewtonsConstant( ), period, period ] ) )
else:
# velocity and period
mass = divide( getProduct( [ velocity, velocity, velocity, period ] ),
getProduct( [ 2, pi, getNewtonsConstant( ) ] ) )
return mass.convert( 'kilogram' )
def calculateOrbitalRadius( measurement1, measurement2 ):
'''
To solve the radius of a circular orbit, we need Newton's gravitational
constant and two of the following three items:
G = Newton's gravitational constant
m = planetary mass (i.e., mass of the thing being orbited)
T = orbital period
v = orbital velocity
---- radius in terms of period and mass
r = cbrt( T^2*G*m/4*pi^2 )
---- radius in terms of velocity and mass
r = G*m/v^2
---- radius in terms of velocity and period
r = v*T/2*pi
'''
validUnitTypes = [
[ 'mass', 'time' ],
[ 'velocity', 'time' ],
[ 'mass', 'velocity' ],
]
arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes )
if not arguments:
raise ValueError( '\'orbital_radius\' requires specific measurement types (see help)' )
if 'mass' in arguments:
mass = arguments[ 'mass' ]
if 'time' in arguments:
bPeriod = True
period = arguments[ 'time' ]
else:
bPeriod = False
velocity = arguments[ 'velocity' ]
else:
# period and velocity
period = arguments[ 'time' ]
velocity = arguments[ 'velocity' ]
radius = divide( multiply( velocity, period ), fmul( 2, pi ) )
return radius.convert( 'meter' )
if bPeriod:
# period and mass
term = divide( getProduct( [ getPower( period, 2 ), getNewtonsConstant( ), mass ] ),
fmul( 4, power( pi, 2 ) ) )
radius = getRoot( term, 3 )
else:
# velocity and mass
radius = divide( multiply( getNewtonsConstant( ), mass ), getPower( velocity, 2 ) )
return radius.convert( 'meter' )
def calculateOrbitalPeriod( measurement1, measurement2 ):
'''
To solve the period of a circular orbit, we need Newton's gravitational
constant and two of the following three items:
G = Newton's gravitational constant
m = planetary mass (i.e., mass of the thing being orbited)
r = orbit radius (the distance from the center of mass)
v = orbital velocity
---- period in terms of radius and mass
T = 2*pi*sqrt( r^3/G*m )
---- period in terms of radius and velocity
T = 2*pi*r/v
---- period in terms of mass and velocity
T = 2*pi*G*m/v^3
'''
validUnitTypes = [
[ 'mass', 'length' ],
[ 'velocity', 'length' ],
[ 'mass', 'velocity' ],
]
arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes )
if not arguments:
raise ValueError( '\'orbital_period\' requires specific measurement types (see help)' )
if 'mass' in arguments:
mass = arguments[ 'mass' ]
if 'length' in arguments:
bRadius = True
radius = arguments[ 'length' ]
else:
bRadius = False
velocity = arguments[ 'velocity' ]
else:
# radius and velocity
radius = arguments[ 'length' ]
velocity = arguments[ 'velocity' ]
period = divide( getProduct( [ 2, pi, radius ] ), velocity )
return period.convert( 'second' )
if bRadius:
# radius and mass
term = divide( getPower( radius, 3 ), multiply( getNewtonsConstant( ), mass ) )
period = getProduct( [ 2, pi, getRoot( term, 2 ) ] )
else:
# velocity and mass
period = divide( getProduct( [ 2, pi, getNewtonsConstant( ), mass ] ),
getPower( velocity, 3 ) )
return period.convert( 'second' )
def calculateSurfaceGravity( measurement1, measurement2 ):
validUnitTypes = [
[ 'mass', 'density' ],
[ 'mass', 'length' ],
[ 'mass', 'volume' ],
[ 'density', 'length' ],
[ 'density', 'volume' ],
]
arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes )
if not arguments:
raise ValueError( '\'surface_gravity\' requires length and mass measurements' )
if 'mass' in arguments:
mass = arguments[ 'mass' ]
if 'length' in arguments:
length = arguments[ 'length' ]
elif 'density' in arguments:
volume = divide( mass, arguments[ 'density' ] )
length = getNSphereRadius( volume, 3 )
else:
length = getNSphereRadius( arguments[ 'volume' ], 3 )
elif 'volume' in arguments:
# density, volume
volume = arguments[ 'volume' ]
mass = multiply( arguments[ 'density' ], volume )
length = getNSphereRadius( volume, 3 )
else:
# density, length
length = arguments[ 'length' ]
volume = getPower( length, 3 )
mass = multiply( arguments[ 'density' ], volume )
gravity = multiply( divide( mass, getPower( length, 2 ) ), getNewtonsConstant( ) )
return gravity.convert( 'meters/seconds^2' )
def calculateEscapeVelocity( mass, radius ):
validateUnits( mass, 'mass' )
validateUnits( radius, 'length' )
velocity = getRoot( getProduct( [ 2, getNewtonsConstant( ), mass ] ).divide( radius ), 2 )
return velocity.convert( 'meter/second' )
def calculateSchwarzchildRadius( mass ):
validateUnits( mass, 'mass' )
radius = getProduct( [ 2, getNewtonsConstant( ), mass ] ).divide( getPower( getSpeedOfLight( ), 2 ) )
return radius.convert( 'meter' )