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 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 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 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 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 ):
validateUnits( mass, 'mass' )
validateUnits( radius, 'length' )
velocity = getRoot( getProduct( [ 2, getNewtonsConstant( ), mass ] ).divide( radius ), 2 )
return velocity.convert( 'meter/second' )
def calculateHorizonDistance( altitude, radius ):
validateUnits( altitude, 'length' )
validateUnits( radius, 'length' )
distance = getRoot( getProduct( [ 2, radius, altitude ] ), 2 )
return distance.convert( 'meter' )
def getPlanckTemperature( ):
return getRoot( getReducedPlanckConstant( ).multiply( getPower( getSpeedOfLight( ), 5 ) ).
divide( getNewtonsConstant( ).multiply( getPower( getBoltzmannsConstant( ), 2 ) ) ), 2 )
def getPlanckCharge( ):
return getElectronCharge( ).divide( getRoot( getFineStructureConstant( ), 2 ) )
def getPlanckTime( ):
return getRoot( getReducedPlanckConstant( ).multiply( getNewtonsConstant( ) ).divide(
getPower( getSpeedOfLight( ), 5 ) ), 2 )