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 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 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 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 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 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 getDodecahedronSurfaceArea( n ): if not isinstance( n, RPNMeasurement ): return getDodecahedronSurfaceArea( RPNMeasurement( real( n ), 'meter' ) ) if n.getDimensions( ) != { 'length' : 1 }: raise ValueError( '\'dodecahedron_area\' argument must be a length' ) area = getProduct( [ 3, getRoot( add( 25, fmul( 10, sqrt( 5 ) ) ), 2 ), getPower( n, 2 ) ] ) return area.convert( 'meter^2' )
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 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 getConeSurfaceArea( r, h ): if not isinstance( r, RPNMeasurement ): return getConeSurfaceArea( RPNMeasurement( real( r ), 'meter' ), h ) if r.getDimensions( ) != { 'length' : 1 }: raise ValueError( '\'cone_area\' argument 1 must be a length' ) if not isinstance( h, RPNMeasurement ): return getConeSurfaceArea( r, RPNMeasurement( real( h ), 'meter' ) ) if h.getDimensions( ) != { 'length' : 1 }: raise ValueError( '\'cone_area\' argument 2 must be a length' ) hypotenuse = getRoot( add( getPower( r, 2 ), getPower( h, 2 ) ), 2 ) return getProduct( [ pi, r, add( r, hypotenuse ) ] )
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 calculateEscapeVelocity( mass, radius ): mass.validateUnits( 'mass' ) radius.validateUnits( 'length' ) velocity = getRoot( getProduct( [ 2, getConstant( 'newton_constant' ), mass ] ).divide( radius ), 2 ) return velocity.convert( 'meter/second' )
def calculateEscapeVelocityOperator( mass, radius ): mass.validateUnits( 'mass' ) radius.validateUnits( 'length' ) velocity = getRoot( getProduct( [ 2, getConstant( 'newton_constant' ), mass ] ).divide( radius ), 2 ) return velocity.convert( 'meter/second' )
def getPlanckLength( ): return getRoot( g.h_bar.multiply( g.G ).divide( getPower( g.c, 3 ) ), 2 )
def calculateHorizonDistanceOperator( altitude, radius ): altitude.validateUnits( 'length' ) radius.validateUnits( 'length' ) distance = getRoot( getProduct( [ 2, radius, altitude ] ), 2 ) return distance.convert( 'meter' )
def getPlanckAcceleration( ): return getRoot( getPower( g.c, 7 ).divide( g.h_bar.multiply( g.G ) ), 2 )
def getConeSurfaceAreaOperator(radius, height): hypotenuse = getRoot(add(getPower(radius, 2), getPower(height, 2)), 2) return getProduct([pi, radius, add(radius, hypotenuse)])
def getPlanckVoltage( ): return getRoot( getProduct( [ 4, pi, g.e0, getPower( g.c, 6 ) ] ).divide( g.G ), 2 )
def getPlanckCharge( ): return getConstant( 'electron_charge' ).divide( getRoot( getFineStructureConstant( ), 2 ) )
def getPlanckTemperature( ): return getRoot( g.h_bar.multiply( getPower( g.c, 5 ) ). divide( g.G.multiply( getPower( g.k, 2 ) ) ), 2 )
def getPlanckMomentum( ): return getRoot( g.h_bar.multiply( getPower( g.c, 3 ) ).divide( g.G ), 2 )
def getPlanckTime( ): return getRoot( g.h_bar.multiply( g.G ).divide( getPower( g.c, 5 ) ), 2 )
def getPlanckLength( ): return getRoot( g.h_bar.multiply( g.G ).divide( getPower( g.c, 3 ) ), 2 )
def getPlanckMass( ): return getRoot( g.h_bar.multiply( g.c ).divide( g.G ), 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 getPlanckElectricalInductance( ): return getRoot( g.G.multiply( g.h_bar ).divide( getPower( g.c, 7 ). multiply( getPower( getProduct( [ 4, pi, g.e0 ] ), 2 ) ) ), 2 ).convert( 'henry' )
def getPlanckTemperature( ): return getRoot( g.h_bar.multiply( getPower( g.c, 5 ) ). divide( g.G.multiply( getPower( g.k, 2 ) ) ), 2 )
def getPlanckTime( ): return getRoot( g.h_bar.multiply( g.G ).divide( getPower( g.c, 5 ) ), 2 )
def calculateHorizonDistance( altitude, radius ): altitude.validateUnits( 'length' ) radius.validateUnits( 'length' ) distance = getRoot( getProduct( [ 2, radius, altitude ] ), 2 ) return distance.convert( 'meter' )
def getPlanckVolume( ): return getRoot( getPower( g.h_bar.multiply( g.G ), 3 ).divide( getPower( g.c, 9 ) ), 2 )
def getPlanckMass( ): return getRoot( g.h_bar.multiply( g.c ).divide( g.G ), 2 )
def getPlanckMomentum( ): return getRoot( g.h_bar.multiply( getPower( g.c, 3 ) ).divide( g.G ), 2 )
def getPlanckCharge( ): return getConstant( 'electron_charge' ).divide( getRoot( getFineStructureConstant( ), 2 ) )
def getPlanckEnergy( ): return getRoot( g.h_bar.multiply( getPower( g.c, 5 ) ).divide( g.G ), 2 ).convert( 'joule' )
def getPlanckVolume( ): return getRoot( getPower( g.h_bar.multiply( g.G ), 3 ).divide( getPower( g.c, 9 ) ), 2 )
def getPlanckAngularFrequency( ): return RPNMeasurement( getRoot( getPower( g.c, 5 ).divide( g.h_bar. multiply( g.G ) ), 2 ).value, 'radian/second' )
def getPlanckEnergy( ): return getRoot( g.h_bar.multiply( getPower( g.c, 5 ) ).divide( g.G ), 2 ).convert( 'joule' )
def getPlanckVoltage( ): return getRoot( getProduct( [ 4, pi, g.e0, getPower( g.c, 6 ) ] ).divide( g.G ), 2 )
def getPlanckMagneticInductance( ): return getRoot( getPower( g.c, 5 ).divide( getProduct( [ g.h_bar, getPower( g.G, 2 ), 4, pi, g.e0 ] ) ), 2 ).convert( 'tesla' )
def getPlanckMagneticInductance( ): return getRoot( getPower( g.c, 5 ).divide( getProduct( [ g.h_bar, \ getPower( g.G, 2 ), 4, pi, g.e0 ] ) ), 2 ).convert( 'tesla' )
def getPlanckViscosity( ): return getRoot( getPower( g.c, 9 ).divide( getPower( g.G, 3 ).multiply( g.h_bar ) ), 2 ).convert( 'pascal*second' )
def getPlanckElectricalInductance( ): return getRoot( g.G.multiply( g.h_bar ).divide( getPower( g.c, 7 ). \ multiply( getPower( getProduct( [ 4, pi, g.e0 ] ), 2 ) ) ), 2 ).convert( 'henry' )
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 getPlanckViscosity( ): return getRoot( getPower( g.c, 9 ).divide( getPower( g.G, 3 ).multiply( g.h_bar ) ), 2 ).convert( 'pascal*second' )
def getDodecahedronSurfaceAreaOperator(n): area = getProduct( [3, getRoot(add(25, fmul(10, sqrt(5))), 2), getPower(n, 2)]) return area.convert('meter^2')
def getPlanckAcceleration( ): return getRoot( getPower( g.c, 7 ).divide( g.h_bar.multiply( g.G ) ), 2 )