# BAFact math: how big does the Sun look from Pluto?

By Phil Plait | March 16, 2012 10:16 am

[On January 4, 2012, I started a new features: BAFacts, where I write an astronomy/space fact that is short enough to be tweeted. A lot of them reference older posts, but some of the facts need a little mathematical explanation. When that happens I’ll write a post like this one that does the math so you can see the numbers for yourself. Why? Because MATH!]

Today’s BAFact:

From Pluto, the Sun is so far away it would appear to be a point in the sky like a star, though an incredibly bright one.

Yesterday, I showed how the Sun would still be painfully bright even from Pluto, far brighter than the full Moon looks from here on Earth. But how big would it look in the sky?

It turns out, that math is even easier than it was to find the brightness! The size of an object on the sky depends on how big it really is, physically, and how far away it is. If you double the distance to an object, it will appear half the size. Easy peasy*.

So, as I established yesterday, on average Pluto is about 39 times farther from the Sun than the Earth, so if you were standing on Pluto (hopefully, in a well-heated and insulated spacesuit!) the Sun would appear 1/39th as big, or 0.026 times as big as it does from Earth.

What would that look like?

Well, the size of the Sun in the sky from Earth is about a half a degree — remember, there are 360° in a circle. So from the horizon to the zenith is 90°, and your outstretched fist is very roughly 10°. The Sun is about 0.5°, so you can block it with a single finger held at arm’s length.

From Pluto, though, it’s far smaller: less than 1 arcminute in size (a degree is divided into 60 arcminutes, so from Earth the Sun is about 30 arcmin across). That brings up an interesting point: the smallest size the human eye can easily resolve is something about an arcminute across. Anything smaller than that looks like a dot.

So from Pluto, the Sun would look like a star — that is, a point of light — albeit an intensely bright one. Looking at it would certainly be painful, and probably make your eyes tear up.

But wait! I also mentioned yesterday that Pluto’s orbit is an ellipse, and it goes from 4.4 billion to 7.3 billion km from the Sun. That’s a factor of 29 to 49 times the Earths distance from the Sun. So that shrinks the size of the Sun accordingly. When Pluto is farthest from the Sun (called aphelion) the Sun is far less than an arcminute in size, and looks like a dot. When Pluto is closest to the Sun (perihelion) it will actually be just about one arcminute in diameter. Someone with sharp eyes might be able to perceive it as a disk rather than a point of light… though that would still be really tough to do, because the Sun’s still so bright. If you had a filter in your spacesuit visor you’d be able to see the disk of the Sun.

If you’re curious, blogger Burton MacKenzie made a simple diagram showing how big the Sun is from each of the planets (thumbnail shown here; click to ensolarnate). He didn’t put Pluto on it, but from there the Sun would look even smaller on average than it does from Neptune.

Never forget: the solar system is big! The New Horizons probe was launched in early 2006, is screaming across the solar system at 15 km/sec (fast enough to cross the entire US in about 5 minutes!) but still won’t pass Pluto until mid-2015.

Space is deep, vast, and empty. From far enough away, even the Sun itself would be dimmed to invisibility. If there’s a life lesson in there somewhere, feel free to find it.

Image credit: ESO, annotated by me

* Well, almost easy peasy. This only works well if the object is far enough away that it appears small to you. There’s actually a trigonometric formula to do this exactly, but it hardly matters; for something the size of the Sun, even at Mercury’s distance, saying its apparent size changes linearly with distance is OK.

CATEGORIZED UNDER: Astronomy, BAFacts, Cool stuff, Debunking
MORE ABOUT: angular size, Pluto, Sun

1. Kimberly

New Horizons will make its closest approach to Pluto in July 2015 not 2014, specifically July 14, 2015.

In 2014, the spacecraft does cross the orbit of Neptune. Specifically, on August 25, 2014 — exactly 25 years after Voyager 2 made its historic exploration of that giant planet.
(http://pluto.jhuapl.edu/mission/whereis_nh.php)

It’s hard to imagine it traveling at 15 km/s (34,000 mph), snapping images & taking data as it goes, but that is precisely what the scientists have designed the instruments aboard New Horizons to do for encounter fly-by.

New Horizons: a mission of extremes. Takes a very long time to get there (9.5 years) for a brief (9 days of core science, with ancillary science plus/minus a few months) visit, followed by up to 300+ days to get the data down to Earth due to the immense distances and slow data rates supported by the Deep Space Network. In the post-Pluto era, New Horizons has enough fuel and power to move on to the next terra incognita, the realm of the icy Kuiper Belt Objects, after a few more years. The solar system is indeed very large and empty, but it is home.

2. D’oh! Typo. Thanks Kimberly, I fixed it.

3. Somehow these two posts about the Sun from Pluto have been reminding me of my new 3-D-cell LED flashlight—the actual LED element is about the size of a pinhead, but it’s so bright I can’t look at it, and it lights up the whole room even with no lens or mirror and in the daytime!

4. booboo

Remember that the apparent surface brightness of the solar disk is independent of the distance…..

So, we can simulate the pluto sun by putting a 1′ hole in a plate. Held at a 1 m distance from the eye, that would be about 1 mm (1 mrad) in diameter. So, get a piece of foil and punch a 1 mm hole in it and hold it at arms length in front of the solar disk. Voila–simulated plutonian sol.

Of course, on a sunny day you are not dark adapted…..you could foil over a window in a dark room, and survey the plutonian sun from a dark adapted state…..does it ‘hurt’ to look directly at it? Might be dangerous (for the same reason as a partial eclipse is dangerous).

Of course, luminous flux associated with sunlight is about 10^5 lux. Divided by 40^2, the luminous flux of daylight on Pluto is about 60 lux, not really dark at all…many household interiors in the US run ~100 lux at night.

5. Cyphern

I doubt this is the book you referred to in your previous post (since you mentioned pluto and this story took place on a oort cloud object), but these last couple posts have reminded me of the book Camelot 30k (http://en.wikipedia.org/wiki/Camelot_30K)

6. Aren’t Venus and Jupiter about 1 arcminute across when best seen from Earth?

7. Hephaestus

Space is big
Space is dark
It’s hard to find
A place to park

– Burma Shave

8. K. Halse

“so if you were standing on Pluto (hopefully, in a well-heated and insulated spacesuit!)”

How insulated would it really have to be? Aside from the part where your feet are touching the ground, (where you can lose heat through conduction) how much colder would it be on the surface of Pluto; in comparison to a astronaut, on a spacewalk, in Earth’s shadow.

9. Chris A.

@Andrew W (#6):
“Aren’t Venus and Jupiter about 1 arcminute across when best seen from Earth?”

Venus, a tad more (62 arcsec). Jupiter, considerably less (47 arcsec).

10. Burton MacKenzie’s “The Sun as seen from other Planets” diagram caused me to stop and think for a minute… Pluto, Mercury and Mars have orbits that are pretty highly elliptical (as do many of the Trans-Neptunian objects), so the Sun looks accordingly bigger when they are at aphelion versus perihelion. Pluto is also closer to the Sun than Neptune at times so the Sun could occasionally look bigger from Pluto than from Neptune. (The Sun even looks 3.4% bigger at Earth’s perihelion than its aphelion due to our nearly circular orbit.) So I created a new diagram with all the planets (plus the dwarf planets), with the Sun scaled to show the relative maximum and minimum size as seen from each orbit. These images can be found at: calgary.rasc.ca/images/Sun_Angular_Size_From_Planets_Scaled.png (similar size to Burton’s) and calgary.rasc.ca/images/Sun_Angular_Size_From_Planets_Full.png (larger and clearer)

11. Messier Tidy Upper

Great post BA – Cheers!

@11. Kimberly Says:

In 2014, the spacecraft does cross the orbit of Neptune. Specifically, on August 25, 2014 — exactly 25 years after Voyager 2 made its historic exploration of that giant planet. .. ( link snip) .. It’s hard to imagine it traveling at 15 km/s (34,000 mph), snapping images & taking data as it goes, but that is precisely what the scientists have designed the instruments aboard New Horizons to do for encounter fly-by. New Horizons: a mission of extremes. Takes a very long time to get there (9.5 years) for a brief (9 days of core science, with ancillary science plus/minus a few months) visit, followed by up to 300+ days to get the data down to Earth due to the immense distances and slow data rates supported by the Deep Space Network. In the post-Pluto era, New Horizons has enough fuel and power to move on to the next terra incognita, the realm of the icy Kuiper Belt Objects, after a few more years. The solar system is indeed very large and empty, but it is home.

Cheers for that informative comment too.

I can’t wait to see Pluto – my fave planet – examined in close-up detail and New Horizons sure is a wonderful mission. Any word on whether /which Edgeworth-Kuiper cometary belt objects New Horizons might be visiting after its Pluto fly-by yet?

12. Jeffersonian

How bright would it be standing on Pluto – bright enough to read a book?

13. Nigel Depledge

MTU (11) said:

I can’t wait to see Pluto – my fave planet . . .

[Inhales]

[Thinks again]

No, I won’t open that can of worms again.

14. Nigel Depledge

Jeffersonian (12) said:

How bright would it be standing on Pluto – bright enough to read a book?

Booboo (4) said:

Of course, luminous flux associated with sunlight is about 10^5 lux. Divided by 40^2, the luminous flux of daylight on Pluto is about 60 lux, not really dark at all…many household interiors in the US run ~100 lux at night.

Hey, who’d ‘a thunk it, Jeffersonian? Your question was already answered in a previous comment.

15. Leon

Hey Phil! Wouldn’t it be cool if NASA turned the probe and got a shot of the Sun from out there? Maybe when it’s made its flyby and they’re mostly done taking pictures of the Pluto system, they could turn the probe, take a couple pictures, and publish photos of the Sun from (roughly) Pluto’s orbit. I bet that would get some public interest, or at least curiosity. I know I’ve wondered what it would look like–and if I remember right, Heinlein speculated about it himself in “Have Spacesuit, Will Travel”.

16. Matt B.

I hope that New Horizons will look back at the Sun, and that other stars will be visible in the shot. That would be amazing.

Burton MacKenzie somewhat mistakenly says “confronted by that giant ball of nuclear radiation”. In terms of what it looks like, the Sun is a ball of thermal radiation. That diagram is really interesting, though, because it also shows the inverse of the sizes of the planets’ orbits.

NEW ON DISCOVER
OPEN
CITIZEN SCIENCE