Solar System

Chung van Gog, 03 October 2022

I love our solar system. And obviously I’m partial to my cuboidal prefixes. So let’s consider some cool solar system facts. :)

Masses

nUUKg

Sol: 2.0 UUKg

Sol without sun spots. Credit: NASA/GSFC/Solar Dynamics Observatory

nUNKg

J: 1.9 UNKg

Jupiter. Credit: NASA, ESA, CSA, Jupiter ERS Team; image processing by Ricardo Hueso (UPV/EHU) and Judy Schmidt.

hEKg

S: 568 EKg
N: 102 EKg

daEKg

U: 87 EKg
Planet 9 (hypothetical): 30-51 EKg

nEKg

E: 6.0 EKg
V: 4.9 EKg

"The Day the Earth Smiled". Earth as seen from Saturn. Credit: NASA/JPL-Caltech/Space Science Institute.

Venus. Credit: NASA/JHUAPL/CIW; color composite by Gordan Ugarkovic.

hOKg

Ma: 642 OKg
Me: 330 OKg
J Ganymede: 148 OKg
S Titan: 135 OKg
J Callisto: 108 OKg

A view from the "Kimberley" formation on Mars taken by NASA's Curiosity rover. Credit: NASA/JPL-Caltech .

Titan. Credit: NASA/JPL/Space Science Institute.

daOKg

J Io: 89 OKg
E Moon: 73 OKg
J Europa: 48 OKg
N Triton: 21 OKg
Eris: 17 OKg
Pluto: 13 OKg

"Sunrise on the Highlands". Credit: Andrew McCarthy.

Europa. Credit: NASA/SWRI/MSSS/Jason Perry.

nOKg

Haumea: 4.0 OKg
U Titania: 3.4 OKg
Makemake: 3.1 OKg
U Oberon: 3.1 OKg
S Rhea: 2.3 OKg
S Iapetus: 1.8 OKg
Gonggong: 1.8 OKg
Pluto Charon: 1.6 OKg
Quaoar: 1.4 OKg
U Umbriel: 1.3 OKg
U Ariel: 1.3 OKg
S Dione: 1.1 OKg

Pluto and Charon. They are less than 2 daBKm apart. Credit: NASA/JHUAPL/SWRI.

Just as an aside, I like thinking of the above as “XKg planets”, with X ≤ UN. So we have one UNKg planet (Jupiter), five EKg planets, and 23+ OKg planets. Usually these are subdivided into planets, dwarf planets, and moons. But why not think in terms of family? Triton, Rhea, Iapetus, and Dione are all OKg planets part of the Neptunian family (Neptune itself being an EKg planet).

Semi-major axes

daTKm

Me: 58 TKm

hTKm

V: 108 TKm
E: 150 TKm
Ma: 228 TKm
J: 778 TKm

nQKm

S: 1.4 QKm
U: 2.9 QKm
N: 4.5 QKm
Pluto: 5.9 QKm
Haumea: 6.5 QKm
Quaoar: 6.5 QKm
Makemake: 6.8 QKm

daQKm

Eris: 10 QKm
Gonggong: 10 QKm
Planet 9 (hypothetical): ~67 QKm

daPKm

Proxima Centauri: 40 PKm

Proxima Centauri. Credit: ESA/Hubble/NASA.

Orbital periods

These can be calculated with Kepler’s third law:

$T = \tau \sqrt{\frac{a^3}{\mu}}$

Here $T$ is the orbital period in seconds, $\tau = 2\pi$ as usual, $a$ is the semi-major axis, and $\mu = GM_S$ is the gravitational constant times the mass of the Sun. For the solar system, we have $T \approx 5.45408$ $a^{3/2}$ dtms.

So for Earth, we get $\text{(}149.598\text{ TKM)}^{3/2} = 57.8614\text{ PKM}^{3/2}$ and thus $T \approx 365.26$ days, which is pretty close (even if imperfect due to rounding).