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There's a lot of interest with the recent discovery of seven earth sized planets around TRAPPIST-1. I saw this poster, and the NASA video says that in the system you could see a lot of other planets whipping around in their orbits.

It got me wondering:

  • Obviously that poster is exaggerated, but how exaggerated?
  • What would you actually see with the naked eye, standing on TRAPPIST-1g, and looking back toward the other planets?
  • How big would they appear?
  • What might TRAPPIST-1 look like?
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Let's take a look at the star and the planet's characteristics first. We have the star TRAPPIST-1:

  • $M = 0.082 M_{\odot}$
  • $R = 0.117 R_{\odot}$

The planets are all roughly in the scale of $0.7 R_{\oplus}$ to $1.2 R_{\oplus}$ with their semi-major axes of:

  • b: $1.66 \times 10^6 \; \mathrm{km}$
  • c: $2.88 \times 10^6 \; \mathrm{km}$
  • d: $3.14 \times 10^6 \; \mathrm{km}$
  • e: $4.19 \times 10^6 \; \mathrm{km}$
  • f: $5.57 \times 10^6 \; \mathrm{km}$
  • g: $6.73 \times 10^6 \; \mathrm{km}$

So if we would stand on the surface of TRAPPIST-1g and look towards the star, we would be at $1/25$ the distance to the star compared to the sun. The star however is roughly $1/8 R_{\odot}$. That would make the star appear about at about $3$ times the diameter compared to our Sun from the Earth.

TRAPPIST-1f would every few days pass TRAPPIST-1g with a closest approach of $1.16 \times 10^6 \; \mathrm{km} \approx 3 \times r_{\mathrm{Earth-Moon}}$ which is roughly three times the distance to the Moon.

Since $R_{\mathrm{TRAPPIST-1f}} \approx R_{\oplus}$ and $R_{\oplus}/R_{\mathrm{Moon}} = 3.67$ it would seem that TRAPPIST-1f would appear roughly the size of the Moon on closest approach.

The other planets are similar in radius but their distances are $2$ to $5$ times further away and would thus appear smaller by that factor.

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