Jupiter and Venus still blaze in the west

By Phil Plait | March 14, 2012 11:35 am

If you’ve been outside just after sunset and faced west, you’ve almost certainly seen two bright "stars" glaring back at you. Those aren’t stars: they’re Venus and Jupiter, the 3rd and 4th brightest natural objects in the sky (after the Sun and Moon, of course, and I say "natural" because the space station can in fact look brighter than both). As they circle the Sun, every year or so the orbital geometry of the two (and the Earth) sets things up such that they appear very close together in the sky. This is called a conjunction, and when it involves planets this bright, it’s really something to see!

[Click to enaphroditenate.]

That stunning shot was taken by German astrophotographer Robert Blasius, and it’s part of an incredible set of photos gathered by Astronomers Without Borders.

Getting pictures of the two planets together is not hard; I rested my phone on a chair at a party in the middle of downtown Austin, Texas, and got a decent shot myself, shown here (click to embiggen). If you have a real camera, great pictures are a tripod and a click away.

The two will be close together for the next few days, too, so you have time.

I’ve been getting a lot of email and tweets about the pair, asking me about them. Venus is the brighter of the two planets, which is interesting: it’s far smaller than Jupiter, and reflects less sunlight overall. So why is it so much brighter?

Because it’s closer!

The brightness of a planet in our sky depends on a handful of things: how big it is, how reflective it is (an icy object is brighter than a rocky one), how far from the Sun it is, how far from us it is, and even our viewing angle. These can all be calculated, so what the heck. Let’s do a little math!


Area of my expertise

The total light reflected by a planet depends on the surface area of that planet, which depends on the radius squared (remember your algebra? The area of a circle is π x (radius)2). Jupiter has a radius about 71,500 km, and the radius of Venus is about 6050 km.

Squaring those two and getting the ratio, we get

area of Venus / area of Jupiter = 0.0072

So all things being equal, Venus should only be 0.0072 times as bright as Jupiter, or, flipping it, Jupiter should be about 140 times brighter than Venus! But all things are not equal…


A planet’s day in the Sun

Jupiter is farther from the Sun than Venus, and that means it gets less sunlight than Venus does. The amount of light an objects gets from the Sun depends on its distance from the Sun squared (this is called the inverse square law of light). We can figure that out too! Just divide the distance of Jupiter from the Sun by Venus’s distance from the Sun, and square that:

Jupiter’s current distance from the Sun is about 746 million km, and Venus is about 108 million km. So,

(746 million / 108 million)2 = 47.7

So Venus receives about 47.7 times as much sunlight as Jupiter does, and all things being equal should be 47.7 times as bright. But we’re not done…


Long way home

The light from each planet also has to get from there to here, to Earth. Again, that goes as the square of the distance! So we have to account for that. Right now, Jupiter is about 846 million km from Earth, and Venus is about 121 million km distant. Let’s square those and see what happens:

(846 million / 121 million)2 = 48.9

Yikes, another factor of almost 50! So again, due to their respective distances from the Earth, Venus should be 48.9 times brighter than Jupiter. But wait! There’s more …


Pause to reflect

Both Venus and Jupiter are highly reflective — both are covered in clouds, though the clouds of Venus are somewhat more reflective than those of Jupiter. Venus has a reflectivity (called its albedo) of about 67%, and Jupiter is about 52%. That’s pretty close. The ratio is

.67 / 0.5 = 1.29

So Venus wins there too.

And still there is one more thing: phase! We see Venus roughly "half full" right now because it’s off to the side of the Sun, while Jupiter is "full". According to the US Naval Observatory, 57.6% of Venus is lit right now from our view. So we have to account for that by throwing a factor of 0.58 on Venus.

And now we’re ready to put them all together!


So let’s figure out how much brighter Venus is than Jupiter by putting these all together. All we have to do is multiply them all, making sure we do it in terms of Venus to be consistent:

Venus brightness / Jupiter brightness = 0.0072 x 47.7 x 48.9 x 1.29 x 0.58 = 12.6

So Venus should be a bit less than 13 times brighter than Jupiter according to my calculations.

Is that right? Looking up the actual numbers on Heavens Above, I get that Venus is actually about 8 times brighter than Jupiter. My number’s off, but not by much. That’s not bad, considering I just threw some numbers together based on straight geometry and did some very rough math.

I love this aspect of astronomy: using nothing more than a few first principles — how light gets dimmer with distance, how objects reflect that light, and how we see them — I was able to predict that Venus should be brighter than Jupiter, and even by how much! The actual amount may be off, but I wasn’t wrong by a factor of ten, say. Just that basic knowledge got me pretty close, and no doubt there are a handful of other factors that, when accounted for, get this much closer if not bang on the right number.

After all, the Universe knows what it’s doing. And science is a great way — the best way — to understand what the Universe is doing. Make a few assumptions, test them out, see how well they fit what’s really going on, and then look more deeply into the problem. I’ll hold off here from going deeper into the numbers above (though I’ll bet I see some folks in the comments diving in), but this is a great example on how science zeroes in on a solution.

And honestly, you don’t have to do all the math to go outside and take a look. Please do! The math isn’t hard, but what’s easier is facing west and looking up. That is the heart of astronomy.

Look up!

Image credit: Robert Blasius/Astronomers Without Borders; me

CATEGORIZED UNDER: Astronomy, Pretty pictures

Comments (38)

  1. Tara Li

    “Keep Looking Up!” – Jack Horkheimer, the Star Hustler (Boo! Porn searches making him change his show name!)

  2. “And honestly, you don’t have to do all the math to go outside and take a look. Please do! The math isn’t hard, but what’s easier is facing west and looking up. That is the heart of astronomy.”

    That’s what I try to do every week on my website; show people where to look up, and be able to identify what they can see: Naked eye, with simple binoculars or small telescopes. The idea being that if more people can identify what is up there, the more likely they are to 1) voluntarily reduce light pollution and 2) support professional astronomer’s work.

  3. Tom

    Good read, interesting maths (some of which I couldn’t have thought to include, like the phase of the planets), but the area of a circle isn’t 4 pi r^2, just pi r^2. Not that it matters since it cancels in the ratio, just thought I’d nitpick.

  4. Keith Bowden

    I’m going to blow up the Earth’s clouds; they obstruct my view of Venus. (This is very appropriate today as I’m wearing my Marvin the Martian sweater.)

  5. JaberwokWSA

    Phil,

    You might want to rephrase your comment about the area of a circle. I believe you are giving the surface area of a sphere. It may be a bit confusing to some. What you say and what you mean don’t really match.

  6. Gary

    Phil, I would suggest using × (ampersand+times+semicolon) for the multiplication operation in lieu of the letter ‘x’. It will probably look cleaner, and it will be less confusing for those of us who hardly remember algebra. :)

  7. Worlebird

    “The area of a circle is 4 x π x (radius)^2″ – Um, sorry Phil, but the area of a circle is π x (radius)^2. You’re multiplying by an extra 4. it doesn’t change the ratios, of course, but the formula is wrong…

  8. Webhead

    So them bright and clear over Madison last night, looking out over the UW campus. Amazing.

  9. Jaberwok WSA is right. I stumbled over that point too. The error doesn’t affect the result, though, because the extraneous term makes no difference to the proportion that was being calculated.

  10. Heh. I did write down the area of a sphere; I was trying to do too many things at once there and wrote the wrong thing down. As Tom points out it cancels, so the numbers should still work out.

    I’m still trying to figure out where the numbers go wrong, but I can’t come up with anything. I suspect it’s albedo, since that’s highly variable, but when i look at that it makes the numbers farther off!

  11. What might be throwing the numbers off is that we are not getting the full reflected light from the surface area visible to us. Remember that the light is bouncing off of a spherical surface. How much of that light comes our way depends not only upon the albedo, but also the specularity.

  12. Robert

    Maybe you’ve just provided the ultimate proof for the existance of dark matter? :)

  13. Other Paul

    Wouldn’ t you get a better estimate by using the square of the phase – on the grounds that, from earth, the phase should factor twice? Once as the proportion of reflected light that we see (which is the factor already used) and once more because it’s that (relative) proportion that we’re seeing?

    Clear as mud – try this, From the sun’s PoV only half the surface areas of the planets are illuminated (and that half – of course – cancels out, so you’re still left with .0072) but from our PoV we’re only seeing .576 of that ‘solar exposure’ of Venus. The .576 reflected is on top of that. On the face (hah!) of it, it looks like the same thing being double counted, but is it really? Anybody see what I’m getting at who could explain it better?

  14. mike burkhart

    I got a good view of both last night ,Its unuasual to see Venus and Jupiter in the sky so close to each other .Of course I thats how they appear in the sky the two Planets are actually very far from each other.

  15. ceramicfundamentalist

    i also think it’s the specularity thingy. remember that a full moon is much more than twice as bright as a half moon even though its albedo doesn’t change based on phase. venus should be the same – it always has an albedo of about 67%, but we should recieve less than half as much light from it when it is in half phase as when it is in full phase. your calculations are based on a full phase venus, which is why you have calculated a brighter-than-observed venus.

  16. Brian

    Brian Williams said on the NBC Nightly News last night “because its closer”, and I immediately said to my wife “really? what about the distance from the sun, what about the surface area, what about the albedo”?

    She, of course, ignored me. Its good to know somewhere folks understand me!

    (Although I’m ashamed I didn’t think of the phase.)

  17. Doug

    “(remember your algebra? The area of a circle is 4 x π x (radius)2)”

    I must have taken a different algebra class than you. That, or you’re just trolling us on pi day.

    However, what matters here is the r^2 factor, not whether or not we’re talking about the surface area of a sphere or the area of a circle, so you got lucky.

  18. Brent Hagany

    I am saddened that the specularity argument has been put forward before I could do it myself. I wanted my nerd cred :(

  19. Chris A.

    Phil:

    Did you take into account that the apparent radius of Venus should include its atmosphere, not just the solid body of the planet? But, seems to me that will also make your ratio bigger, not smaller. :

  20. lunchstealer

    What about angle of incidence of the light to the planet? Does albedo vary by the angle the light strikes the atmosphere?

    If Venus is 58% full right now, then the part that’s facing directly toward the sun, and thus has the highest insolation per sq km, is pointing away from us at something like a 60 degree angle. The part that’s pointing at us is getting low-angle late-afternoon or early-morning sunlight. In fact, I suspect that this is the case. If you fly, and see clouds below you, they’re always brightest in the direction opposite the sun, surrounding the shadow of your aircraft (if you’re close enough to cast a shadow).

    Also, if the surface of the clouds are uneven, with the equivalent of thunderheads towering above the surrounding clouds, those clouds will cast shadows across the neighboring clouds. on the parts of the planet where the sun is close to zenith, those shadows will be very short, and will not reduce the overall sunlight reflected by very much. However, if they’re close to the terminator, the shadows are longer, and will shade much of the neighboring clouds, as viewed from earth.

    Both those effects should serve to reduce the albedo of Venus to some extent, relative to the albedo of Jupiter.

  21. Phil H.

    Not to mention the beauty of Mars right now, too. It’s so bright in the night sky right now that it’s easy to pick up on the red hue with the naked eye. Beautiful skies right now.

  22. molybdenumfist

    Would brightness be linear with phase? It isn’t for the moon, maybe that factor should be a little less than 0.58, making this estimate even closer.

    My nerd cred is here somewhere… I seem to have misplaced it :(

  23. lepton

    Phil,

    I think phase makes a bigger different than you assumed.

    Jupiter is almost full, so it is in a favorable position/angle to reflect more light to earth.

    Venus is half, so, it is in a less favorable position/angle.

    That can certainly make 12.6x to 8x.

  24. Randy Owens

    Same thing that explains heiligenschein would come into play. The bodies reflect preferentially back towards the Sun, because e.g. when we look at Jupiter, the area closest to normal is also closest to normal to the Sun’s light. But looking at Venus, the area normal to us is almost parralel to the Sun’s light. So, that will give Jupiter a boost, in comparison to Venus, much like (but not as extreme as) the dew on the grass behind your head reflects & refracts much more light back at you than dew to the side.

  25. Jeffersonian

    Phil, (or anybody)
    I have a question and am hoping it can be answered here.

    Was out again tonight looking at Jupiter/Venus and turned around and pointed out Mars to a family member who, when asked how I knew it was a planet and not just a star, I responded “well it’s clearly red plus it glows and doesn’t twinkle” (I knew the current position of Mars anyway but didn’t want to explain the current chart). So I started wondering who first figured out that the planets were not stars. I know that there’s a whole long history, but it appears from history that it was only after telescopes that people figured out that “wandering stars” were not twinkling. How can that be? Isn’t it obvious they are not “on fire”?

    TL;DR > Q: Hasn’t it always been clear that planets don’t twinkle, and if so, who first figured out why (i.e. that they weren’t on fire or were planets and not stars)?

  26. Tara Li

    @Jefferson – That’s a fun question! The “ancients” certainly knew the planets were different (planet meaning wanderer, in ancient Greek IIRC), but that they were separate worlds, round solid bodies, is a far different matter. It was certainly known, as far back as the same Greeks, that the Earth and Moon were spherical bodies, and there’s some question whether the Sun was known to be so – there are various reports that are interpreted as being of sunspots, but it’s believed that a lot of such literature was burned during the middle ages as challenging the perception of the Sun as a perfect and eternal Celestial Body. But I think it was noticed that they did not twinkle – or at least, twinkled less (they seem to twinkle at least somewhat to me, but that’s perhaps my eyesight, which is far from the best.)

    Galileo is the first in current history to have developed the telescope to an extent that lead people to investigate the wanderers, and to suggest that at least Jupiter was a separate world – as he charted the Galilean Moons circling it. He also noted the phases of Venus, but it’s less certain whether he connected that with it being a spherical body. However, Jupiter & Venus are at the edge of being resolvable as disks by the naked eye under optimum conditions (which occurred much more regularly way back when, when light pollution was less of a problem), and the Galilean satellites are actually bright enough to be seen by themselves, save for the glare of Jupiter itself (unless blocked by a tree limb or some such) – so might well have been seen many times, and just not recorded.

    TL; DR > A: Galileo – and I’m somewhat surprised that the development of the telescope went so immediately to astronomy, and less quickly to terrestrial war applications.

  27. Checkmate1

    Nonsense, all nonsense!!
    Clearly, the brighter one is Niburu; you’re just afraid to admit The Truth.
    ( ducking and running for cover) ;)

  28. Jeffersonian

    Tara,
    good answer.
    fun for me, too – history of discovery’s often my focii d’surf.
    But just googling and wiki-ing isn’t getting me anywhere.
    Once I pointed out the planets yesterday to people who never look up, they agreed that it was obvious that the 3 were not stars; that they were clearly different, even to the naked eye. (We were at a person’s cabin at high altitude and colors were apparent). So, clearly others in antiquity would have noted the same for the wandering stars. Didn’t it occur to anybody that the glowing ones were somehow like Earth as opposed to stars? Seems obvious, given the other sidereal knowledge of certain eras and civilizations. ex. Anaxagoras knew the Sun was flaming and that moon glowed from its reflected light 2000 years before Galileo*, adding to my confusion!

    *It’s weird we refer to Galilei by his first name. We don’t call Copernicus “Nicky” , Newton “Izzy” or Darwin “Chuck”.
    ———-

    TL;DR> I guess the better questions would be:
    *Who discovered that stars were on fire and therefore different than the wandering stars?

    *Who first figured out that stars are “suns”?

  29. Peter Davey

    “Sunset and evening star, and one last call for me, and may there be no moaning at the bar, as I put out to sea.” – Tennyson (he asked that that poem always be placed last in any collection of his works.

  30. abadidea

    The ancients could tell the planets were different because

    a) They are slightly larger than stars to the naked eye, and have different colors

    b) They follow the path of the sun

    c) They move at a different speed than the background stars (which all appear to move as a single unit from Earth)

    Which led to the general believe of “celestial spheres”, with the stars being plastered on an “outermost” sphere, and the planets being on internal tiers.

  31. Chris A.

    @Tara Li (#27):

    “…Jupiter & Venus are at the edge of being resolvable as disks by the naked eye under optimum conditions (which occurred much more regularly way back when, when light pollution was less of a problem)…”

    Um, no. While Venus’s diameter at closest approach slightly exceeds the limit of resolution of the human eye (generally cited as 1 arcmin), Jupiter is not even close (47 arcsec, or 0.78 arcmin). So, while a few sharp-eyed observers have reported resolving Venus as a crescent without optical aid, it’s a safe bet that no one has ever resolved Jupiter’s disk with the unaided eye, in Galileo’s time or otherwise.

    And, I’m stymied as to why you think light pollution should matter in this case, given that Venus and Jupiter are the two brightest planets, and are generally visible from even the worst light-polluted cities.

  32. Planets do twinkle under some conditions, though it’s true that the effect isn’t as pronounced as with stars, because of the greater angular size of a planet’s disc compared with the scale of atmospheric turbulence.

    The last time I spotted Mercury, about a week and a half ago, it was definitely twinkling. (Mercury’s angular size is generally considerably smaller than that of Venus, Mars or Jupiter, and from the Northern Hemisphere it is only visible with quite a low elevation above the horizon, so you’re looking through a lot of air.)

  33. BoulderBob

    Time lapse from East Boulder — a co-worker’s hobby.

    http://vimeo.com/38224668

    Cheers

  34. Can I offer an opinion of a complete amateur? Sometimes knowing too much of a subject creates false fluency and bias.

    I have been observing night sky with my own eyes for 30 years. I have never seen anything looking as Bright as alleged Venus does. Is there a possibility that there is another object hiding in the sight of Venus?

    Don’t be square and imagine the possibility of a large object that is on approach but remains in such trajectory that makes people on Earth see it as a single object, namely Venus itself?

  35. Greg Kane

    You note the formula for the area of a circle, adding “remember your algebra?” I think what we’ve got to remember here is our geometry. (Not to say that I do.)

  36. Greg Kane

    You note the formula for the area of a circle, adding “remember your algebra?” I think what we’ve gotto remember here is our geometry. (Not to say I do.)

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