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( getConstant( 'newton_constant' ), mass ), radius ), 2 )
else:
# mass and period
term = divide( getProduct( [ period, period, getConstant( 'newton_constant' ), mass ] ),
getProduct( [ 4, pi, pi ] ) )
velocity = divide( getProduct( [ 2, pi, getRoot( term, 3 ) ] ), period )
return velocity.convert( 'meter/second' )
def calculateOrbitalVelocityOperator( 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( getConstant( 'newton_constant' ), mass ), radius ), 2 )
else:
# mass and period
term = divide( getProduct( [ period, period, getConstant( 'newton_constant' ), mass ] ),
getProduct( [ 4, pi, pi ] ) )
velocity = divide( getProduct( [ 2, pi, getRoot( term, 3 ) ] ), period )
return velocity.convert( 'meter/second' )
def calculateOrbitalMassOperator( 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 ] ), getConstant( 'newton_constant' ) )
return mass.convert( 'kilogram' )
if bRadius:
# radius and period
mass = divide( getProduct( [ 4, pi, pi, radius, radius, radius ] ),
getProduct( [ getConstant( 'newton_constant' ), period, period ] ) )
else:
# velocity and period
mass = divide( getProduct( [ velocity, velocity, velocity, period ] ),
getProduct( [ 2, pi, getConstant( 'newton_constant' ) ] ) )
return mass.convert( 'kilogram' )
def calculateOrbitalRadiusOperator( 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 ), getConstant( 'newton_constant' ), mass ] ),
fmul( 4, power( pi, 2 ) ) )
radius = getRoot( term, 3 )
else:
# velocity and mass
radius = divide( multiply( getConstant( 'newton_constant' ), 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( getConstant( 'newton_constant' ), mass ) )
period = getProduct( [ 2, pi, getRoot( term, 2 ) ] )
else:
# velocity and mass
period = divide( getProduct( [ 2, pi, getConstant( 'newton_constant' ), mass ] ),
getPower( velocity, 3 ) )
return period.convert( 'second' )
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 ), getConstant( 'newton_constant' ), mass ] ),
fmul( 4, power( pi, 2 ) ) )
radius = getRoot( term, 3 )
else:
# velocity and mass
radius = divide( multiply( getConstant( 'newton_constant' ), mass ), getPower( velocity, 2 ) )
return radius.convert( 'meter' )
def calculateOrbitalPeriodOperator( 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( getConstant( 'newton_constant' ), mass ) )
period = getProduct( [ 2, pi, getRoot( term, 2 ) ] )
else:
# velocity and mass
period = divide( getProduct( [ 2, pi, getConstant( 'newton_constant' ), mass ] ),
getPower( velocity, 3 ) )
return period.convert( '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 ] ), getConstant( 'newton_constant' ) )
return mass.convert( 'kilogram' )
if bRadius:
# radius and period
mass = divide( getProduct( [ 4, pi, pi, radius, radius, radius ] ),
getProduct( [ getConstant( 'newton_constant' ), period, period ] ) )
else:
# velocity and period
mass = divide( getProduct( [ velocity, velocity, velocity, period ] ),
getProduct( [ 2, pi, getConstant( 'newton_constant' ) ] ) )
return mass.convert( 'kilogram' )
def calculateBlackHoleLifetimeOperator( measurement ):
validUnitTypes = [
[ 'mass' ],
[ 'length' ],
[ 'acceleration' ],
[ 'area' ],
[ 'temperature' ],
[ 'power' ],
[ 'tidal_force' ],
[ 'time' ],
]
arguments = matchUnitTypes( [ measurement ], validUnitTypes )
if not arguments:
raise ValueError( 'black_hole_lifetime: invalid argument' )
mass = calculateBlackHoleMass( measurement )
lifetime = divide( getProduct( [ getPower( mass, 3 ), 5120, pi,
getPower( getConstant( 'newton_constant' ), 2 ) ] ),
getProduct( [ getConstant( 'reduced_planck_constant' ),
getPower( getConstant( 'speed_of_light' ), 4 ) ] ) )
return lifetime.convert( 'seconds' )
def calculateBlackHoleTemperatureOperator( measurement ):
validUnitTypes = [
[ 'mass' ],
[ 'length' ],
[ 'acceleration' ],
[ 'area' ],
[ 'temperature' ],
[ 'power' ],
[ 'tidal_force' ],
[ 'time' ],
]
arguments = matchUnitTypes( [ measurement ], validUnitTypes )
if not arguments:
raise ValueError( 'black_hole_temperature: invalid argument' )
mass = calculateBlackHoleMass( measurement )
temperature = divide( getProduct( [ getConstant( 'reduced_planck_constant' ),
getPower( getConstant( 'speed_of_light' ), 3 ) ] ),
getProduct( [ mass, 8, getConstant( 'boltzmann_constant' ), pi,
getConstant( 'newton_constant' ) ] ) )
return temperature.convert( 'kelvin' )
def getDodecahedronVolume( n ):
if not isinstance( n, RPNMeasurement ):
return getDodecahedronVolume( RPNMeasurement( real( n ), 'meter' ) )
if n.getDimensions( ) != { 'length' : 1 }:
raise ValueError( '\'dodecahedron_volume\' argument must be a length' )
return divide( multiply( fadd( 15, fmul( 7, sqrt( 5 ) ) ), getPower( n, 3 ) ), 4 ).convert( 'meter^3' )
def getOctahedronVolume( n ):
if not isinstance( n, RPNMeasurement ):
return getOctahedronVolume( RPNMeasurement( real( n ), 'meter' ) )
if n.getDimensions( ) != { 'length' : 1 }:
raise ValueError( '\'octahedron_volume\' argument must be a length' )
return divide( multiply( sqrt( 2 ), getPower( n, 3 ) ), 3 )
def getTetrahedronVolume( n ):
if not isinstance( n, RPNMeasurement ):
return getTetrahedronVolume( RPNMeasurement( real( n ), 'meter' ) )
if n.getDimensions( ) != { 'length' : 1 }:
raise ValueError( '\'tetrahedron_volume\' argument must be a length' )
return divide( getPower( n, 3 ), fmul( 6, sqrt( 2 ) ) )
def getCumulativeListRatios( args ):
first = None
for i in args:
if first is None:
first = i
else:
yield divide( i, first )
def getListRatios( args ):
old = None
for i in args:
if old is not None:
yield divide( i, old )
old = i
def getListRatios( args ):
old = None
for i in args:
if old is not None:
yield( divide( i, old ) )
old = i
def calculateTidalForceOperator( mass, distance, delta ):
mass.validateUnits( 'mass' )
distance.validateUnits( 'length' )
delta.validateUnits( 'length' )
tidalForce = divide( getProduct( [ 2, getConstant( 'newton_constant' ), mass, delta ] ),
getPower( distance, 3 ) )
return tidalForce.convert( 'meter/second^2' )
def calculateTimeDilation( velocity ):
velocity.validateUnits( 'velocity' )
c_ratio = divide( velocity, getConstant( 'speed_of_light' ) ).value
if c_ratio == 1:
return inf
return fdiv( 1, sqrt( fsub( 1, power( c_ratio, 2 ) ) ) )
def calculateTidalForce( mass, distance, delta ):
mass.validateUnits( 'mass' )
distance.validateUnits( 'length' )
delta.validateUnits( 'length' )
tidal_force = divide( getProduct( [ 2, getConstant( 'newton_constant' ), mass, delta ] ),
getPower( distance, 3 ) )
return tidal_force.convert( 'meter/second^2' )
def calculateTimeDilationOperator( velocity ):
velocity.validateUnits( 'velocity' )
ratio = divide( velocity, getConstant( 'speed_of_light' ) )
if ratio == 1:
return inf
return fdiv( 1, sqrt( fsub( 1, power( ratio, 2 ) ) ) )
def getCumulativeListRatios( args ):
result = [ ]
first = None
for i in args:
if first is None:
first = i
else:
yield divide( i, first )
def calculateBlackHoleMass( measurement ):
validUnitTypes = [
[ 'mass' ],
[ 'length' ],
[ 'acceleration' ],
[ 'area' ],
[ 'temperature' ],
[ 'power' ],
[ 'tidal_force' ],
[ 'time' ],
]
arguments = matchUnitTypes( [ measurement ], validUnitTypes )
if not arguments:
raise ValueError( 'black_hole_mass: invalid argument' )
if 'mass' in arguments:
return arguments[ 'mass' ].convert( 'kilogram' )
elif 'length' in arguments:
radius = arguments[ 'length' ]
return divide( getProduct( [ getPower( getConstant( 'speed_of_light' ), 2 ), radius ] ),
getProduct( [ 2, getConstant( 'newton_constant' ) ] ) ).convert( 'kilogram' )
elif 'acceleration' in arguments:
gravity = arguments[ 'acceleration' ]
return divide( getPower( getConstant( 'speed_of_light' ), 4 ),
getProduct( [ 4, getConstant( 'newton_constant' ), gravity ] ) ).convert( 'kilogram' )
elif 'area' in arguments:
area = arguments[ 'area' ].convert( 'meters^2' )
return getRoot( divide( getProduct( [ getPower( getConstant( 'speed_of_light' ), 4 ), area ] ),
getProduct( [ 16, pi, getPower( getConstant( 'newton_constant' ), 2 ) ] ) ), 2 ).convert( 'kilogram' )
elif 'temperature' in arguments:
temperature = arguments[ 'temperature' ]
return divide( getProduct( [ getConstant( 'reduced_planck_constant' ), getPower( getConstant( 'speed_of_light' ), 3 ) ] ),
getProduct( [ temperature, 8, getConstant( 'boltzmann_constant' ), pi, getConstant( 'newton_constant' ) ] ) ).convert( 'kilogram' )
elif 'power' in arguments:
luminosity = arguments[ 'power' ]
return getRoot( divide( getProduct( [ getConstant( 'reduced_planck_constant' ), getPower( getConstant( 'speed_of_light' ), 6 ) ] ),
getProduct( [ luminosity.convert( 'kilogram*meter^2/second^3' ), 15360, pi,
getPower( getConstant( 'newton_constant' ), 2 ) ] ) ), 2 ).convert( 'kilogram' )
elif 'tidal_force' in arguments:
tidal_force = arguments[ 'tidal_force' ]
return getRoot( divide( getPower( getConstant( 'speed_of_light' ), 6 ),
getProduct( [ 4, tidal_force, getPower( getConstant( 'newton_constant' ), 2 ) ] ) ), 2 ).convert( 'kilogram' )
elif 'time' in arguments:
lifetime = arguments[ 'time' ]
return getRoot( divide( getProduct( [ lifetime, getConstant( 'reduced_planck_constant' ), getPower( getConstant( 'speed_of_light' ), 4 ) ] ),
getProduct( [ 5120, pi, getPower( getConstant( 'newton_constant' ), 2 ) ] ) ), 3 ).convert( 'kilogram' )
raise ValueError( 'invalid arguments to black hole operator' )
def calculateAccelerationOperator( measurement1, measurement2 ):
validUnitTypes = [
[ 'velocity', 'length' ],
[ 'velocity', 'time' ],
[ 'length', 'time' ],
[ 'acceleration', 'time' ],
[ 'acceleration', 'length' ],
]
arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes )
if 'acceleration' in arguments:
acceleration = arguments[ 'acceleration' ]
elif 'velocity' in arguments:
if 'length' in arguments:
acceleration = divide( getPower( arguments[ 'velocity' ], 2 ), multiply( arguments[ 'length' ], 2 ) )
else:
acceleration = divide( arguments[ 'velocity' ], arguments[ 'time' ] )
elif 'length' in arguments and 'time' in arguments:
acceleration = multiply( 2, divide( arguments[ 'length' ], getPower( arguments[ 'time' ], 2 ) ) )
return acceleration.convert( 'meter/second^2' )
def calculateAcceleration( measurement1, measurement2 ):
validUnitTypes = [
[ 'velocity', 'length' ],
[ 'velocity', 'time' ],
[ 'length', 'time' ],
[ 'acceleration', 'time' ],
[ 'acceleration', 'length' ],
]
arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes )
if 'acceleration' in arguments:
acceleration = arguments[ 'acceleration' ]
elif 'velocity' in arguments:
if 'length' in arguments:
acceleration = divide( getPower( arguments[ 'velocity' ], 2 ), multiply( arguments[ 'length' ], 2 ) )
else:
acceleration = divide( arguments[ 'velocity' ], arguments[ 'time' ] )
elif 'length' in arguments and 'time' in arguments:
acceleration = multiply( 2, divide( arguments[ 'length' ], getPower( arguments[ 'time' ], 2 ) ) )
return acceleration.convert( 'meter/second^2' )
def getConeVolume( r, h ):
if not isinstance( r, RPNMeasurement ):
return getConeVolume( RPNMeasurement( real( r ), 'meter' ), h )
if r.getDimensions( ) != { 'length' : 1 }:
raise ValueError( '\'cone_volume\' argument 1 must be a length' )
if not isinstance( h, RPNMeasurement ):
return getConeVolume( r, RPNMeasurement( real( h ), 'meter' ) )
if h.getDimensions( ) != { 'length' : 1 }:
raise ValueError( '\'cone_volume\' argument 2 must be a length' )
return getProduct( [ pi, getPower( r, 2 ), divide( h, 3 ) ] )
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 = getKSphereRadius( volume, 3 )
else:
length = getKSphereRadius( arguments[ 'volume' ], 3 )
elif 'volume' in arguments:
# density, volume
volume = arguments[ 'volume' ]
mass = multiply( arguments[ 'density' ], volume )
length = getKSphereRadius( volume, 3 )
else:
# density, length
length = arguments[ 'length' ]
volume = getPower( length, 3 )
mass = multiply( arguments[ 'density' ], volume )
gravity = multiply( divide( mass, getPower( length, 2 ) ), getConstant( 'newton_constant' ) )
return gravity.convert( 'meters/seconds^2' )
def calculateSurfaceGravityOperator( 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 = getKSphereRadius( volume, 3 )
else:
length = getKSphereRadius( arguments[ 'volume' ], 3 )
elif 'volume' in arguments:
# density, volume
volume = arguments[ 'volume' ]
mass = multiply( arguments[ 'density' ], volume )
length = getKSphereRadius( volume, 3 )
else:
# density, length
length = arguments[ 'length' ]
volume = getPower( length, 3 )
mass = multiply( arguments[ 'density' ], volume )
gravity = multiply( divide( mass, getPower( length, 2 ) ), getConstant( 'newton_constant' ) )
return gravity.convert( 'meters/seconds^2' )
def calculateBlackHoleSurfaceGravity( measurement ):
validUnitTypes = [
[ 'mass' ],
[ 'length' ],
[ 'acceleration' ],
[ 'area' ],
[ 'temperature' ],
[ 'power' ],
[ 'tidal_force' ],
[ 'time' ],
]
arguments = matchUnitTypes( [ measurement ], validUnitTypes )
if not arguments:
raise ValueError( 'black_hole_surface_gravity: invalid argument' )
mass = calculateBlackHoleMass( measurement )
gravity = divide( getPower( getConstant( 'speed_of_light' ), 4 ), getProduct( [ mass, 4, getConstant( 'newton_constant' ) ] ) )
return gravity.convert( 'meter/second^2' )
def calculateBlackHoleSurfaceArea( measurement ):
validUnitTypes = [
[ 'mass' ],
[ 'length' ],
[ 'acceleration' ],
[ 'area' ],
[ 'temperature' ],
[ 'power' ],
[ 'tidal_force' ],
[ 'time' ],
]
arguments = matchUnitTypes( [ measurement ], validUnitTypes )
if not arguments:
raise ValueError( 'black_hole_surface_area: invalid argument' )
mass = calculateBlackHoleMass( measurement )
area = divide( getProduct( [ 16, pi, getPower( getConstant( 'newton_constant' ), 2 ), getPower( mass, 2 ) ] ),
getPower( getConstant( 'speed_of_light' ), 4 ) )
return area.convert( 'meter^2' )
def calculateBlackHoleSurfaceGravityOperator( measurement ):
validUnitTypes = [
[ 'mass' ],
[ 'length' ],
[ 'acceleration' ],
[ 'area' ],
[ 'temperature' ],
[ 'power' ],
[ 'tidal_force' ],
[ 'time' ],
]
arguments = matchUnitTypes( [ measurement ], validUnitTypes )
if not arguments:
raise ValueError( 'black_hole_surface_gravity: invalid argument' )
mass = calculateBlackHoleMass( measurement )
gravity = divide( getPower( getConstant( 'speed_of_light' ), 4 ),
getProduct( [ mass, 4, getConstant( 'newton_constant' ) ] ) )
return gravity.convert( 'meter/second^2' )
def calculateVelocity( measurement1, measurement2 ):
validUnitTypes = [
[ 'length', 'time' ],
[ 'acceleration', 'length' ],
[ 'jerk', 'length' ],
[ 'jounce', 'length' ],
[ 'velocity', 'time' ],
[ 'velocity', 'length' ],
[ 'acceleration', 'time' ],
[ 'jerk', 'time' ],
[ 'jounce', 'time' ],
]
arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes )
if 'velocity' in arguments:
velocity = arguments[ 'velocity' ]
elif 'length' in arguments:
if 'time' in arguments:
velocity = divide( arguments[ 'length' ], arguments[ 'time' ] )
elif 'acceleration' in arguments:
acceleration = arguments[ 'acceleration' ]
time = getRoot( multiply( divide( arguments[ 'length' ], acceleration ), 2 ), 2 )
velocity = multiply( acceleration, time )
elif 'jerk' in arguments:
jerk = arguments[ 'jerk' ]
time = getRoot( multiply( divide( arguments[ 'length' ], jerk ), 6 ), 3 )
velocity = getProduct( [ jerk, time, time, fdiv( 1, 2 ) ] )
elif 'jounce' in arguments:
jounce = arguments[ 'jounce' ]
time = getRoot( multiply( divide( arguments[ 'length' ], jounce ), 24 ), 4 )
velocity = getProduct( [ jounce, time, time, time, fdiv( 1, 6 ) ] )
elif 'acceleration' in arguments:
velocity = divide( multiply( arguments[ 'acceleration' ], arguments[ 'time' ] ), 2 )
elif 'jerk' in arguments:
velocity = divide( multiply( arguments[ 'jerk' ], getPower( arguments[ 'time' ], 2 ) ), 4 )
elif 'jounce' in arguments:
velocity = divide( multiply( arguments[ 'jounce' ], getPower( arguments[ 'time' ], 3 ) ), 8 )
return velocity.convert( 'meter/second' )
def calculateVelocityOperator( measurement1, measurement2 ):
validUnitTypes = [
[ 'length', 'time' ],
[ 'acceleration', 'length' ],
[ 'jerk', 'length' ],
[ 'jounce', 'length' ],
[ 'velocity', 'time' ],
[ 'velocity', 'length' ],
[ 'acceleration', 'time' ],
[ 'jerk', 'time' ],
[ 'jounce', 'time' ],
]
arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes )
if 'velocity' in arguments:
velocity = arguments[ 'velocity' ]
elif 'length' in arguments:
if 'time' in arguments:
velocity = divide( arguments[ 'length' ], arguments[ 'time' ] )
elif 'acceleration' in arguments:
acceleration = arguments[ 'acceleration' ]
time = getRoot( multiply( divide( arguments[ 'length' ], acceleration ), 2 ), 2 )
velocity = multiply( acceleration, time )
elif 'jerk' in arguments:
jerk = arguments[ 'jerk' ]
time = getRoot( multiply( divide( arguments[ 'length' ], jerk ), 6 ), 3 )
velocity = getProduct( [ jerk, time, time, fdiv( 1, 2 ) ] )
elif 'jounce' in arguments:
jounce = arguments[ 'jounce' ]
time = getRoot( multiply( divide( arguments[ 'length' ], jounce ), 24 ), 4 )
velocity = getProduct( [ jounce, time, time, time, fdiv( 1, 6 ) ] )
elif 'acceleration' in arguments:
velocity = divide( multiply( arguments[ 'acceleration' ], arguments[ 'time' ] ), 2 )
elif 'jerk' in arguments:
velocity = divide( multiply( arguments[ 'jerk' ], getPower( arguments[ 'time' ], 2 ) ), 4 )
elif 'jounce' in arguments:
velocity = divide( multiply( arguments[ 'jounce' ], getPower( arguments[ 'time' ], 3 ) ), 8 )
return velocity.convert( 'meter/second' )
def calculateBlackHoleLifetime( measurement ):
validUnitTypes = [
[ 'mass' ],
[ 'length' ],
[ 'acceleration' ],
[ 'area' ],
[ 'temperature' ],
[ 'power' ],
[ 'tidal_force' ],
[ 'time' ],
]
arguments = matchUnitTypes( [ measurement ], validUnitTypes )
if not arguments:
raise ValueError( 'black_hole_lifetime: invalid argument' )
mass = calculateBlackHoleMass( measurement )
lifetime = divide( getProduct( [ getPower( mass, 3 ), 5120, pi, getPower( getConstant( 'newton_constant' ), 2 ) ] ),
getProduct( [ getConstant( 'reduced_planck_constant' ), getPower( getConstant( 'speed_of_light' ), 4 ) ] ) )
return lifetime.convert( 'seconds' )
def calculateBlackHoleTemperature( measurement ):
validUnitTypes = [
[ 'mass' ],
[ 'length' ],
[ 'acceleration' ],
[ 'area' ],
[ 'temperature' ],
[ 'power' ],
[ 'tidal_force' ],
[ 'time' ],
]
arguments = matchUnitTypes( [ measurement ], validUnitTypes )
if not arguments:
raise ValueError( 'black_hole_temperature: invalid argument' )
mass = calculateBlackHoleMass( measurement )
temperature = divide( getProduct( [ getConstant( 'reduced_planck_constant' ), getPower( getConstant( 'speed_of_light' ), 3 ) ] ),
getProduct( [ mass, 8, getConstant( 'boltzmann_constant' ), pi, getConstant( 'newton_constant' ) ] ) )
return temperature.convert( 'kelvin' )
def calculateBlackHoleEntropy( measurement ):
validUnitTypes = [
[ 'mass' ],
[ 'length' ],
[ 'acceleration' ],
[ 'area' ],
[ 'temperature' ],
[ 'power' ],
[ 'tidal_force' ],
[ 'time' ],
]
arguments = matchUnitTypes( [ measurement ], validUnitTypes )
if not arguments:
raise ValueError( 'black_hole_entropy: invalid argument' )
mass = calculateBlackHoleMass( measurement )
entropy = divide( getProduct( [ getPower( mass, 2 ), 4, pi, getConstant( 'newton_constant' ) ] ),
getProduct( [ getConstant( 'reduced_planck_constant' ), getConstant( 'speed_of_light' ), getLog( 10.0 ) ] ) )
return getConstant( 'boltzmann_constant' ).multiply( entropy ).convert( 'bit' )
def calculateBlackHoleEntropyOperator( measurement ):
validUnitTypes = [
[ 'mass' ],
[ 'length' ],
[ 'acceleration' ],
[ 'area' ],
[ 'temperature' ],
[ 'power' ],
[ 'tidal_force' ],
[ 'time' ],
]
arguments = matchUnitTypes( [ measurement ], validUnitTypes )
if not arguments:
raise ValueError( 'black_hole_entropy: invalid argument' )
mass = calculateBlackHoleMass( measurement )
entropy = divide( getProduct( [ getPower( mass, 2 ), 4, pi, getConstant( 'newton_constant' ) ] ),
getProduct( [ getConstant( 'reduced_planck_constant' ),
getConstant( 'speed_of_light' ), ln( 10.0 ) ] ) )
return getConstant( 'boltzmann_constant' ).multiply( entropy ).convert( 'bit' )
def getTriangleArea( a, b, c ):
if not isinstance( a, RPNMeasurement ):
return getTriangleArea( RPNMeasurement( real( a ), 'meter' ), b, c )
if a.getDimensions( ) != { 'length' : 1 }:
raise ValueError( '\'triangle_area\' argument 1 must be a length' )
if not isinstance( b, RPNMeasurement ):
return getTriangleArea( a, RPNMeasurement( real( b ), 'meter' ), c )
if b.getDimensions( ) != { 'length' : 1 }:
raise ValueError( '\'triangle_area\' argument 2 must be a length' )
if not isinstance( c, RPNMeasurement ):
return getTriangleArea( a, b, RPNMeasurement( real( c ), 'meter' ) )
if b.getDimensions( ) != { 'length' : 1 }:
raise ValueError( '\'triangle_area\' argument 3 must be a length' )
if add( a, b ).isNotLarger( c ) or add( b, c ).isNotLarger( a ) or add( a, c ).isNotLarger( b ):
raise ValueError( 'invalid triangle, the sum of any two sides must be longer than the third side' )
s = divide( getSum( [ a, b, c ] ), 2 ) # semi-perimeter
return getRoot( getProduct( [ s, subtract( s, a ), subtract( s, b ), subtract( s, c ) ] ), 2 )
def getDodecahedronVolumeOperator(n):
return divide(multiply(fadd(15, fmul(7, sqrt(5))), getPower(n, 3)),
4).convert('meter^3')
def getTetrahedronVolumeOperator(n):
return divide(getPower(n, 3), fmul(6, sqrt(2)))
def getOctahedronVolumeOperator(n):
return divide(multiply(sqrt(2), getPower(n, 3)), 3)
def getConeVolumeOperator(radius, height):
return getProduct([pi, getPower(radius, 2), divide(height, 3)])
def getTriangleAreaOperator(a, b, c):
s = divide(getSum([a, b, c]), 2) # semi-perimeter
return getRoot(
getProduct([s, subtract(s, a),
subtract(s, b),
subtract(s, c)]), 2)
def calculateBlackHoleMass( measurement ):
# pylint: disable=line-too-long
validUnitTypes = [
[ 'mass' ],
[ 'length' ],
[ 'acceleration' ],
[ 'area' ],
[ 'temperature' ],
[ 'power' ],
[ 'tidal_force' ],
[ 'time' ],
]
arguments = matchUnitTypes( [ measurement ], validUnitTypes )
if not arguments:
raise ValueError( 'black_hole_mass: invalid argument' )
if 'mass' in arguments:
return arguments[ 'mass' ].convert( 'kilogram' )
if 'length' in arguments:
radius = arguments[ 'length' ]
return divide( getProduct( [ getPower( getConstant( 'speed_of_light' ), 2 ), radius ] ),
getProduct( [ 2, getConstant( 'newton_constant' ) ] ) ).convert( 'kilogram' )
if 'acceleration' in arguments:
gravity = arguments[ 'acceleration' ]
return divide( getPower( getConstant( 'speed_of_light' ), 4 ),
getProduct( [ 4, getConstant( 'newton_constant' ), gravity ] ) ).convert( 'kilogram' )
if 'area' in arguments:
area = arguments[ 'area' ].convert( 'meters^2' )
return getRoot( divide( getProduct( [ getPower( getConstant( 'speed_of_light' ), 4 ), area ] ),
getProduct( [ 16, pi, getPower( getConstant( 'newton_constant' ), 2 ) ] ) ), 2 ).convert( 'kilogram' )
if 'temperature' in arguments:
temperature = arguments[ 'temperature' ]
return divide( getProduct( [ getConstant( 'reduced_planck_constant' ), getPower( getConstant( 'speed_of_light' ), 3 ) ] ),
getProduct( [ temperature, 8, getConstant( 'boltzmann_constant' ), pi, getConstant( 'newton_constant' ) ] ) ).convert( 'kilogram' )
if 'power' in arguments:
luminosity = arguments[ 'power' ]
return getRoot( divide( getProduct( [ getConstant( 'reduced_planck_constant' ), getPower( getConstant( 'speed_of_light' ), 6 ) ] ),
getProduct( [ luminosity.convert( 'kilogram*meter^2/second^3' ), 15360, pi,
getPower( getConstant( 'newton_constant' ), 2 ) ] ) ), 2 ).convert( 'kilogram' )
if 'tidal_force' in arguments:
tidalForce = arguments[ 'tidal_force' ]
return getRoot( divide( getPower( getConstant( 'speed_of_light' ), 6 ),
getProduct( [ 4, tidalForce, getPower( getConstant( 'newton_constant' ), 2 ) ] ) ), 2 ).convert( 'kilogram' )
if 'time' in arguments:
lifetime = arguments[ 'time' ]
return getRoot( divide( getProduct( [ lifetime, getConstant( 'reduced_planck_constant' ), getPower( getConstant( 'speed_of_light' ), 4 ) ] ),
getProduct( [ 5120, pi, getPower( getConstant( 'newton_constant' ), 2 ) ] ) ), 3 ).convert( 'kilogram' )
raise ValueError( 'invalid arguments to black hole operator' )
def calculateMassEquivalenceOperator( energy ):
energy.validateUnits( 'energy' )
mass = divide( energy, multiply( getConstant( 'speed_of_light' ), getConstant( 'speed_of_light' ) ) )
return mass.convert( 'kilogram' )
def calculateMassEquivalence( energy ):
energy.validateUnits( 'energy' )
mass = divide( energy, multiply( getConstant( 'speed_of_light' ), getConstant( 'speed_of_light' ) ) )
return mass.convert( 'kilogram' )
