def calculateDistance( measurement1, measurement2 ): validUnitTypes = [ [ 'length', 'time' ], [ 'velocity', 'time' ], [ 'acceleration', 'time' ], [ 'jerk', 'time' ], [ 'jounce', 'time' ] ] arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes ) if not arguments: raise ValueError( '\'distance\' requires specific measurement types (see help)' ) time = arguments[ 'time' ] if 'length' in arguments: distance = arguments[ 'length' ] elif 'acceleration' in arguments: # acceleration and time distance = getProduct( [ 0.5, arguments[ 'acceleration' ], time, time ] ) elif 'jerk' in arguments: # jerk and time distance = calculateDistance( getProduct( [ 0.5, arguments[ 'jerk' ], time ] ), time ) elif 'jounce' in arguments: # jounce and time distance = calculateDistance( getProduct( [ 0.5, arguments[ 'jounce' ], time ] ), time ) else: # velocity and time distance = multiply( arguments[ 'velocity' ], time ) return distance.convert( 'meter' )
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 calculateKineticEnergy( measurement1, measurement2 ): validUnitTypes = [ [ 'velocity', 'mass' ], ] arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes ) if not arguments: raise ValueError( '\'kinetic_energy\' requires velocity and mass measurements' ) mass = arguments[ 'mass' ] velocity = arguments[ 'velocity' ] energy = getProduct( [ 0.5, mass, velocity, velocity ] ) return energy.convert( 'joule' )
def calculateAcceleration( measurement1, measurement2 ): validUnitTypes = [ [ 'velocity', 'distance' ], [ 'velocity', 'time' ], [ 'distance', 'time' ], [ 'acceleration', 'time' ], [ 'acceleration', 'distance' ], ] arguments = matchUnitTypes( [ measurement1, measurement2 ], validUnitTypes ) if 'acceleration' in arguments: acceleration = arguments[ 'acceleration' ] else: acceleration = RPNMeasurement( '1.0', 'meter/second^2' ) return acceleration.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 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' )