# Units and Quantities¶

## Objectives¶

• Use units
• Create functions that accept quantities as arguments
• Create new units

## Basics¶

How do we define a Quantity and which parts does it have?

In [1]:
from astropy import units as u

In [2]:
# Define a quantity length
# print it

In [3]:
# Type of quantity

In [4]:
# Type of unit

In [5]:
# Quantity

In [6]:
# value

In [7]:
# unit

In [8]:
# information


Quantities can be converted to other units systems or factors by using to()

In [9]:
# Convert it to: km, lyr


We can do arithmetic operations when the quantities have the compatible units:

In [10]:
# arithmetic with distances


Quantities can also be combined, for example to measure speed

In [11]:
# calculate a speed

In [12]:
# decompose it


## Challenges

1. Convert the speed in imperial units (miles/hour) using:
from astropy.units import imperial
2. Calculate whether a pint is more than half litre
You can compare quantities as comparing variables.
Something strange? Check what deffinition of pint astropy is using.
3. Does units work with areas? calculate the area of a rectangle of 3 km of side and 5 meter of width. Show them in m^2 and convert them to yards^2
In [13]:
#1

In [14]:
#2

In [15]:
#3


## Composed units¶

Many units are compositions of others, for example, one could create new combinationes for ease of use:

In [16]:
# create a composite unit

In [17]:
# and in the imperial system


and others are already a composition:

In [18]:
# what can be converted from s-1?

In [19]:
# or Jules?

In [20]:
# Unity of R


Sometime we get no units quantitites

In [21]:
# no units


What happen if we add a number to this?

In [22]:
# arithmetic with no units

In [23]:
# final value of a no unit quantity


## Equivalencies¶

Some conversions are not done by a conversion factor as between miles and kilometers, for example converting between wavelength and frequency.

In [24]:
# converting spectral quantities

In [25]:
# but doing it right


Other built-in equivalencies are:

• parallax()
• Doppler (dopplr_radio, doppler_optical, doppler_relativistic)
• spectral flux density
• brigthness temperature
• temperature energy
• and you can build your own
In [26]:
# finding the equivalencies

In [27]:
# but also using other systems


## Printing the quantities¶

In [28]:
# Printing values with different formats


## Arrays¶

Quantities can also be applied to arrays

In [29]:
# different ways of defining a quantity for a single value

In [30]:
# now with lists
# and arrays
# and its arithmetics

In [31]:
# angles are smart!


## Plotting quantities¶

To work nicely with matplotlib we need to do as follows:

In [32]:
# allowing for plotting
from astropy.visualization import quantity_support
quantity_support()

%matplotlib inline
from matplotlib import pyplot as plt

In [33]:
# Ploting the previous array


## Creating functions with quantities as units¶

We want to have functions that contain the information of the untis, and with them we can be sure that we will be always have the right result.

In [34]:
# Create a function for the Kinetic energy

In [35]:
# run with and without units


## Challenges

1. Create a function that calculates potential energy where *g* defaults to Earth value, but could be used for different planets. Test it for any of the *g* values for any other planet.
In [36]:
#4

In [37]:
# run it for some values

In [38]:
# on Mars:


# Create units for a laugh scale

1. Convert the area calculated before rectangle_area in Hectare (1 hectare = 100 ares; 1 are = 100 m2).
#5