Plotting the brightest 200 stars

Grabbing our libraries

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
plt.style.use('seaborn-v0_8-darkgrid')

Solar System

Generating our data, wherein all the density is in the initial bin (the Sun)

aus = np.arange(0.1, 5, 0.1)
m_sun = 2E30
d_init = m_sun / (4/3 * np.pi * 0.1**3)
dens = np.zeros(shape=aus.shape)
dens[0] = d_init

ss_data = pd.DataFrame({'R_au': aus, 'density': dens})
ss_data.head()

ss_data.to_csv('L19_solar.csv', index=False)

Plotting it up:

plt.bar(ss_data.R_au, ss_data.density, width=-0.1, align='edge')
plt.show()

Computing the mass and then cumulative mass:

ss_data['mass'] = 4/3 * np.pi * ss_data.R_au**3 * ss_data.density
ss_data['cmass'] = ss_data.mass.cumsum()
ss_data.head()

	R_au	density	mass	cmass
0	0.1	4.774648e+32	2.000000e+30	2.000000e+30
1	0.2	0.000000e+00	0.000000e+00	2.000000e+30
2	0.3	0.000000e+00	0.000000e+00	2.000000e+30
3	0.4	0.000000e+00	0.000000e+00	2.000000e+30
4	0.5	0.000000e+00	0.000000e+00	2.000000e+30

Computing the velocity:

G = 6.602E-11
au = 1.496E11
ss_data['vel'] = np.sqrt(G * ss_data['cmass'] / (ss_data.R_au * au))
ss_data.head()

	R_au	density	mass	cmass	vel
0	0.1	4.774648e+32	2.000000e+30	2.000000e+30	93947.874955
1	0.2	0.000000e+00	0.000000e+00	2.000000e+30	66431.179459
2	0.3	0.000000e+00	0.000000e+00	2.000000e+30	54240.830895
3	0.4	0.000000e+00	0.000000e+00	2.000000e+30	46973.937477
4	0.5	0.000000e+00	0.000000e+00	2.000000e+30	42014.766948

Graphing it up:

plt.plot(ss_data.R_au, ss_data.vel, 'o')
plt.xlabel('Distance away (AU)')
plt.ylabel('Velocity (m/s)')
plt.show()

Sanity check: how long for Earth to go around?

dist = 2*np.pi * 1 * au
time = dist / ss_data[ss_data.R_au == 1].vel
time / 86400

9    366.193607
Name: vel, dtype: float64

Galaxy

Generating our data, where the bulge will have a constant density that will then drop off

rs = np.arange(10,20000,10) # lyrs
dens_init = 4E30 / (4/3 * np.pi * 10**3)
dens = dens_init/(1+np.exp((rs - 3000)/500))

gal_data = pd.DataFrame({'R_ly': rs, 'density': dens})
gal_data.head()
gal_data.to_csv('L19_galaxy.csv', index=False)

Plotting it up?

plt.bar(gal_data.R_ly, gal_data.density, width=-10, align='edge')
plt.show()

Computing the mass and then cumulative mass:

gal_data['mass'] = 4/3 * np.pi * gal_data.R_ly**3 * gal_data.density
gal_data['cmass'] = gal_data.mass.cumsum()
gal_data.head()

	R_ly	density	mass	cmass
0	10	9.525209e+26	3.989910e+30	3.989910e+30
1	20	9.524724e+26	3.191766e+31	3.590757e+31
2	30	9.524229e+26	1.077165e+32	1.436241e+32
3	40	9.523723e+26	2.553144e+32	3.989385e+32
4	50	9.523208e+26	4.986340e+32	8.975725e+32

Computing the velocity:

G = 6.602E-11
ly = 9.461E15
gal_data['vel'] = np.sqrt(G * gal_data['cmass'] / (gal_data.R_ly * ly))
gal_data.head()

	R_ly	density	mass	cmass	vel
0	10	9.525209e+26	3.989910e+30	3.989910e+30	52.765590
1	20	9.524724e+26	3.191766e+31	3.590757e+31	111.930185
2	30	9.524229e+26	1.077165e+32	1.436241e+32	182.777276
3	40	9.523723e+26	2.553144e+32	3.989385e+32	263.810580
4	50	9.523208e+26	4.986340e+32	8.975725e+32	353.931328

Graphing it up:

plt.plot(gal_data.R_ly, gal_data.vel, 'o')
plt.xlabel('Distance away (lyrs)')
plt.ylabel('Velocity (m/s)')
plt.show()