Units in Python

The Astropy package includes a powerful framework that allows users to attach units to scalars and arrays, and manipulate/combine these, keeping track of the units.

Astropy has a lot of built-in units. A complete list can be found here.



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import numpy as np

from astropy.table import QTable

from astropy import units as u
from astropy import constants as const

from astropy.units import imperial
imperial.enable()

Note: because we imported the units package as u, you cannot use u as a variable name.

You can use the units by themselves:



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u.m    # The unit of meters



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u.s    # The unit of seconds



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u.m / u.s    # combine them into a composite unit

For any unit you can find all of the built-in units that are equivalent:



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u.m.find_equivalent_units()

The `units` package is much more useful when you combine it with scalars or arrays to create `Quantities`



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time_1 = 0.25 * u.s

time_1



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position = np.arange(1,6,1) * u.m    # np.arange(x,y,z) - create an array of numbers between x and y in steps z

position



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velocity = position / time_1

velocity

You can access the number and unit part of the Quantity separately:



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velocity.value



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velocity.unit

At example problem: How long would it take to go 100 km at velocities in `velocity`?



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distance = 100 * u.km

time_2 = distance / velocity

time_2

Notice that the units are a bit strange. We can simplify this using `.decompose()`



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time_2.decompose()

Unit conversion is really easy!



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time_2.to(u.h)



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velocity.to(u.cm / u.h)



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velocity.to(imperial.mi / u.h)



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velocity.si                     # quick conversion to SI units



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velocity.cgs                    # quick conversion to CGS units



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density = 3000 * (u.kg / u.m**3)     # From last week's homework

density.to(u.kg / u.km**3)

Units make math with Time easy!



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u.s.find_equivalent_units()



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time_3 = 29 * u.day + 7 * u.h + 56 * u.min + 12 * u.s
time_4 = 2 * u.fortnight + 1.33 * u.day



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time_3 - time_4



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(time_3 - time_4).to(u.min)

You can define your own units



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ringo = u.def_unit('Ringos', 3.712 * imperial.yd)



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position.to(ringo)



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velocity.to(ringo / u.s)

Dimentionless Units



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dimless_y = (1 * u.m) / (1 * u.km)

dimless_y



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dimless_y.unit



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dimless_y.decompose()   # returns the scale of the dimentionless quanity

Some math functions only make sense with dimentionless quanities



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np.log(2 * u.m)



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np.log((2 * u.km) / (1 * u.m))



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np.log10((2 * u.km) / (1 * u.m))

Or they expect the correct type of unit!



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np.sin(2 * u.m)



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np.sin(2 * u.deg)

Using units can save you headaches.

All of the trig functions expect all angles to be in radians.
If you forget this, it can lead to problems that are hard to debug



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np.sin(90)               # not really what I expected



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np.sin(90 * u.deg)       # better

Tables and units

Astropy tables are constructed to use units



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planet_table = QTable.read('Planets.csv', format='ascii.csv')



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planet_table[0:3]



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planet_table['a'].unit = u.AU
planet_table[0:3]



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planet_table['a'].to(u.km)



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planet_table['a'].to(u.km)[2]

Constants

The Astropy package also includes a whole bunch of built-in constants to make your life easier.

A complete list of the built-in constants can be found here.



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const.G



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const.M_sun

An Example: The velocity of an object in circular orbit around the Sun is

$$ v=\sqrt{GM_{\odot}\over d} $$



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distance = planet_table['a'][0:3]  # Mercury, Venus, Earth



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orbit_v = np.sqrt(const.G * const.M_sun / distance)

orbit_v



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orbit_v.decompose()



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orbit_v.to(u.km/u.s)



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orbit_v.to(ringo/u.ms)

Functions and Units - (Last week's homework)



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def find_diameter(H,A):
    result = (1329 / np.sqrt(A)) * (10 ** (-0.2 * H))
    return result * u.km



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H = 3.34
A = 0.09

asteroid_diameter = find_diameter(H,A)
asteroid_diameter



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def find_mass(D):
    p = 3000 * (u.kg / u.m**3)
    result = p * (1/6) * np.pi * D**3
    return result



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asteroid_mass = find_mass(asteroid_diameter)
asteroid_mass



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asteroid_mass.decompose()



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moon_mass = u.def_unit('Lunar\ Masses', 7.34767309e22 * u.kg)



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asteroid_mass.to(moon_mass)



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