Bad Astronomy

Neptune is *really* far away

Mike Brown is an astronomer, specifically one who studies Kuiper Belt Objects, those giant frozen iceballs that haunt the solar system out past Neptune.

In fact, Neptune’s biggest moon Triton has a lot of characteristics similar KBOs – it may be one captured by Neptune – so observing it gives an interesting opportunity for a compare-and-contrast study. So this past weekend Mike was using the Keck telescope in Hawaii to observe Triton along with its (adoptive?) parent planet, and took this fantastic image of the pair:


[Click to poseidenate.]

This false-color image shows the two worlds in the infrared, specifically at a wavelength of about 1.5 microns, twice what the human eye can see. Methane strongly absorbs this color of light, so where Neptune (in the upper left) looks dark you’re seeing lots of methane clouds, and where it’s bright there are clouds higher up, above the methane. Triton is in the lower right, and is bright because it’s covered in ice which is highly reflective.


Now this is all very pretty and interesting and sciencey, but if you know me at all you know there’s more to this story.

Mike tweeted about the image, and I oohed and ahhhed at it, of course. But then he tweeted again, saying he was also observing Jupiter’s moon Europa, but it was too bright to get good images using the monster 10-meter Keck telescope. It “saturated the detector” which is astronomer-speak for “overexposed”.


That’s funny, I thought. Neptune looks fine in the image, and the random noisy grain in it makes it clear Mike wasn’t anywhere near saturating the image. Now I know Europa is closer to the Earth, so it should look brighter, but geez, it’s a moon, and a lot smaller than Neptune. How could it be too bright to image?

It turns out my all–too–human and all–too–miserable sense of scale has failed me again. Math to the rescue!

Reflections on reflection

The brightness of an object we see in the solar system depends on a lot of factors, but mostly on three: how big it is, how reflective it is, and how far it is from us and the Sun. The first is obvious: a bigger object should look brighter, since it reflects more light. The same goes for the second; something made of ice is shinier and more reflective than something made of soot, so two objects the same size but with different reflectivities (what astronomers call albedo) will not be the same brightness.


The last bit is little tricky though. Sure, something farther away should look dimmer. A car headlight up close is brighter than one farther away. Normally, that means an object’s brightness drops as the square of the distance – move it twice as far away and it appears 1/4th as bright, move it 10 times farther away and its brightness drops by 100x.

But planets and moons are reflecting sunlight, and the farther they are from the Sun, the dimmer it looks too, and the less light they catch. So not only do they drop in brightness as the square of their distance from us, but also by the square of their distance from the Sun. That drops their light terribly rapidly for remote objects in the solar system.


So let’s put this all together.

Math hysteria

Neptune is 50,000 kilometers across, and Europa is 3100. Since the amount of light they reflect depends on their area, and area goes as diameter squared, Europa reflects (3100 / 50,000)2 = 0.004 times as much light as Neptune.

But, in visible light at least, Neptune reflects 29% of the light it receives, while icy Europa reflects 67%. That ratio is 2.3, meaning Europa is more than twice as reflective as Neptune.


What about distance? Right now, Neptune is about 4.5 billion kilometers from the Sun, and 4.35 billion from the Earth. Europa is 800 million km from the Sun and 650 million from the Earth. That means Europa receives (4.5 billion / 800 million)2 = 32 times more light from the Sun than Neptune does. It’s also closer to us, so distance alone gives Europa a leg up to the tune of (4.35 billion / 650 million)2 = 45 times.


Now we can put these together to see how much brighter Europa really should be from Earth.

( Europa’s brightness / Neptune’s brightness ) = 0.004 x 2.3 x 32 x 45 = 13.

So Europa should appear about 13 times as bright as Neptune to us on Earth. As it happens, Neptune is at about magnitude 8 right now (magnitudes are how astronomers measure brightness, and a star 1 magnitude brighter than another is actually about 2.5 times as bright), and Europa at about 5.2. That’s a factor of 13, so my math worked out just right!

One point: I used the albedo in visible light, but the two objects may have very different reflectivities in the infrared. In fact, I mentioned Neptune has lots of IR-absorbing methane in it, so in reality its albedo in the IR is probably much lower. So it appears even fainter, lending yet more credence to the idea that while Neptune was faint enough to be seen easily using the Keck telescope, Europa might blast it out.


Are we there yet?

Which (finally!) brings me to my main point. Europa is dinky. I mean, it’s about the size of our moon, so it’s a fair-sized world and all, but compared to Neptune it’s pretty small. But because it’s close, it’s a whole lot easier to see.

When I think of the outer solar system, I tend to lump all the planets in my head. Jupiter (Europa’s home planet), Saturn, Uranus, Neptune… sure, they’re far away, but I think of them all just as being “far”. But Neptune is nearly seven times farther away from us than Europa!

That’s a seriously long way off. The spacecraft Juno will take five years to get to Jupiter, so even that planet’s a fair distance. Of course, Juno will orbit Jupiter, so it needs to match speeds with the planet so it can be captured. That lengthens the time of its journey. But even the New Horizons probe, which is screaming through the outer solar system at high speed, will take nearly nine years to cross Neptune’s orbit.



So there you go. A tweet, some math, and boom! The solar system suddenly swells seven sizes inside my head.


And I’ll end by noting that with a decent pair of binoculars you can see Jupiter’s moon Europa shortly after sunset, when the planet rises in the east. Neptune is up as well, and again with good binocs or a small telescope (and a good star chart, try Google) you can spot it pretty handily. The last planet wasn’t discovered until 1846, but now we know where it is… and we can point big telescopes at it, like Mike Brown does, and learn about objects even farther away.

Related posts:

- New Horizons is a long way away
- Home, from the start of a long, lng journey
- Happy birthday, Neptune!
- Jupiter rolls into view