Cosmic Distances and Scale

How vast is the universe? Let's use our astronomical constants to build intuition.

Earth to Sun

earth_sun_distance = AU
light_minutes_to_sun = AU / c / minute

8.32

Earth is 1.50e+11 m {length} from the Sun. Light takes about 8.32 to reach us.

Proxima Centauri is the closest star beyond our Sun:

proxima_distance = d_proxima
proxima_in_au = d_proxima / AU
light_years_to_proxima = d_proxima / ly

4.2465 [4.2455, 4.2475]

Proxima Centauri is:

How long to reach Proxima Centauri?

walk_speed = 5 km/hour
walk_time_proxima = d_proxima / walk_speed
walk_time_years = walk_time_proxima / year

9.171e+8 [9.148e+8, 9.174e+8]

Walking: 9.171e+8 [9.148e+8, 9.174e+8] years

voyager_speed = 17 km/s
voyager_time = d_proxima / voyager_speed
voyager_time_years = voyager_time / year

74930 [74740, 74950]

At Voyager speed: 74930 [74740, 74950] years

fast_ship = 0.1 * c
fast_time = d_proxima / fast_ship

1.3401e+9 [1.3398e+9, 1.3404e+9] s {time}

At 0.1c: 1.3401e+9 [1.3398e+9, 1.3404e+9] s {time} - much more reasonable!

Our galaxy is enormous:

galaxy_diameter = milky_way_diameter
galaxy_in_ly = milky_way_diameter / ly
num_stars = milky_way_stars

2.0e+11 [1.0e+11, 4.0e+11]

galaxy_volume = (4/3) * pi * (milky_way_diameter/2)^3
stars_per_ly3 = milky_way_stars / galaxy_volume * ly^3

5.7e-4 [2.9e-4, 0.0012]

There are roughly 5.7e-4 [2.9e-4, 0.0012] stars per cubic light year - space is mostly empty!

Let's scale things down. If the Sun (radius 6.9634e+8 [6.9628e+8, 6.9641e+8] m {length}) were a 1mm grain of sand:

scale_factor = 1 mm / R_sun
scaled_earth_distance = AU * scale_factor
scaled_proxima = d_proxima * scale_factor

57694 [57680, 57709] m {length}

Earth would be 0.21483 [0.21481, 0.21485] m {length} away (about 10 meters)
Proxima Centauri would be 57694 [57680, 57709] m {length} away (about 270 km!)

The nearest star is like a grain of sand 270 km from another grain of sand.