Exemplo n.º 1
0
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' )
Exemplo n.º 2
0
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' )
Exemplo n.º 3
0
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' )
Exemplo n.º 4
0
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' )
Exemplo n.º 5
0
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' )
Exemplo n.º 6
0
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 ) ] )
Exemplo n.º 7
0
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 )
Exemplo n.º 8
0
def calculateEscapeVelocity( mass, radius ):
    validateUnits( mass, 'mass' )
    validateUnits( radius, 'length' )

    velocity = getRoot( getProduct( [ 2, getNewtonsConstant( ), mass ] ).divide( radius ), 2 )
    return velocity.convert( 'meter/second' )
Exemplo n.º 9
0
def calculateHorizonDistance( altitude, radius ):
    validateUnits( altitude, 'length' )
    validateUnits( radius, 'length' )

    distance = getRoot( getProduct( [ 2, radius, altitude ] ), 2 )
    return distance.convert( 'meter' )
Exemplo n.º 10
0
def getPlanckTemperature( ):
    return getRoot( getReducedPlanckConstant( ).multiply( getPower( getSpeedOfLight( ), 5 ) ).
        divide( getNewtonsConstant( ).multiply( getPower( getBoltzmannsConstant( ), 2 ) ) ), 2 )
Exemplo n.º 11
0
def getPlanckCharge( ):
    return getElectronCharge( ).divide( getRoot( getFineStructureConstant( ), 2 ) )
Exemplo n.º 12
0
def getPlanckTime( ):
    return getRoot( getReducedPlanckConstant( ).multiply( getNewtonsConstant( ) ).divide(
                        getPower( getSpeedOfLight( ), 5 ) ), 2 )