Multiple Lighting Bug: no accounting for phase angle

[Malenfant]

OK, here's an illustration of something I mentioned elsewhere: I believe that the multiple lighting implementation is flawed. The images below are taken using my Spica STC file.

SpicaABCD are four stars that are effectively one light source (they're very close in the sky, within a degree of eachother), E is the primary of spicaworld (the planet that the view is centred on).

In the views below, the camera is between SpicaABCD and Spicaworld, so we are looking at the hemisphere that is illuminated only by SpicaABCD. SpicaE is 180 degrees away, on the other side of the planet - so we are not seeing any light from E at all. In all cases, SpicaABCD are about 10,000 AU from the planet - but I'm changing the distance of the planet from E in each image. I'm using A as a reference magnitude for ABCD.

This image is with the planet at 20 AU from E. The appmag of E is -17.49, and the appmag of A is -17.07:




This image is with the planet at 10 AU from E. The appmag of E is -18.99, and the appmag of A is -17.06:




This image is with the planet at 5 AU from E. The appmag of E is -20.50, and the appmag of A is -17.06:




This image is with the planet at 2.5 AU from E. The appmag of E is -22.00, and the appmag of A is -17.06:




In all cases, Spica E is directly behind the planet (it'd be where the red diamond marker is if we could see it), so we're not seeing any of the light from there. But in all cases, the side that we can see - that is purely illuminated by ABCD - is getting dimmer as the planet gets closer to E, even though the apparent magnitude of A isn't changing.

(the fact that there's really four stars in ABCD there is irrelevant - they're not changing their positions relative to eachother in any of these images, and they're basically one light source that is a very similar magnitude to A alone. Either way, the illumination from these stars shouldn't be decreasing as the planet is moved into a closer orbit around E).

I know that the idea is to simulate the response of the human eye here, and that basically what we see on the darkside is all relative to the dayside illumination, but there's a problem here because we're not seeing the 'true' dayside at all in these images, and yet the 'illuminated darkside' is getting dimmer even though its brightness isn't changing.


There seems to be a 'standard light level' that all planets around any stars are illuminated by. What seems to be happening is that if there was just one star, then one side of the planet would get 100% of this light. If there's two stars, then each side gets a fraction of this 'standard light level' that is determined by the relative apparent magnitudes of each star. If the app mags are the same and we looked at in this case, then the illumination each side gets 50% of this 'light level'. You can see this in the images below.

In this image, Spica E is to the right and ABCD is to the left. Spicaworld is at 2.5 AU from Spica E. As you can see, the E-illuminated side is pretty bright.




In this image, Spica E is to the right and ABCD is to the left. Spicaworld is now at 20 AU from Spica E. As you can see, both sides are about equally illuminated, and the E-illuminated side is definitely dimmer than it was in the previous image when the planet was in a closer orbit to E.




What I think should be happening is that the phase of the planet relative to its Primary should be accounted for. As less of the bright primary-illuminated side is visible as you rotate around the planet relative to the stars in the system, the companion-illuminated side should become brighter. In the first four images I posted, the companion-illuminated side that we are looking at should be as bright as the primary-illuminated side, since our eyes are not being forced to account for another brighter light source.

So basically, when determining how brightly a planet is illuminated by stars in a multiple system, we need to include a factor that accounts for the phase angle of the planet that you are looking at. This is currently missing, so we're getting nonsensical results like what I show in the first four images.

[Malenfant]

43 views, and no comments. Either people aren't convinced or they're taking my word for it - so here's some numbers. I THINK my logic is correct here - if it's not then please point out where I'm going wrong:


Say you have two stars, a Primary with brightness of 1.0 at the planet's location and a distant companion with brightness of 0.01 at the planet's location. Say the two stars are 180?° apart, so that they are on exact opposite sides of the planet, like in the examples above.

All things being equal, the two hemispheres of the planet are also going to be different in brightness by a factor of 100, so let's say also that a full primary-lit disk has a brightness of 1.0 and a full companion-lit disk has a brightness of 0.01 of the full primary disk. i.e. A full disk lit only by the primary is going to be 100 times brighter than a full disk lit only by the companion.

But when you factor in eye-adaptation, things get tricky. The first thing to realise is that the brightness of the illuminated parts of the planetary disk are what's important here, not the magnitude of the stars.

Now, let's say you're looking at the planet at a phase angle of 90 degrees relative to the primary. Again, remember that in this case the primary and companion are on opposite sides of the planet, so we'd be looking at a disk that is half illuminated by the primary and half by the companion. What is the brightness ratio between the primary-lit side of the disk and the companion-lit side?

Well, we have half a primary-lit disk. So that's 1.0 divided by 2, so that half is 0.5 the brightness of the full primary lit disk obviously. The companion-lit half has a brightness of 0.01/2 = 0.005 of the brightness of the full primary lit disk. So if we divide 0.5 by 0.005 we get a ratio of 100. So the primary-lit half of the disk is 100 times brighter than the companion-lit half of the disk. So Celestia should render the companion-lit half at 0.01 the brightness of the primary-lit half. Making sense so far?

However, this ratio is not constant with phase angle!. The primary-lit portion is not always going to be 100 times brighter than the companion-lit portion.


Let's now say that we're looking at a phase angle of 162?° relative to the primary, with the stars in the same place relative to the planet. This means that 10% of the disk is lit by the primary, and 90% is lit by the companion (so we're looking at a primary-lit crescent, and a companion-lit gibbous phase, and no portion of the disk is unlit). Now, the brightness of the primary-lit crescent is going to be 0.1 of the brightness of a full primary-lit disk (since there's 10% of the area lit). The brightness of the companion-lit gibbous phase however is now going to be 0.009 of the full primary-lit disk (ie 90% of 0.1). Taking the ratio of these two brightnesses, we get 0.1/0.009 = 11.1. So the primary-lit crescent is now only 11.1 times brighter than the companion-lit gibbous phase - not 100 times brighter - and should be rendered by celestia as such.

As the phase angle approaches 180?° the companion-lit side will get brighter relative to the primary-lit side. And as the phase angle approaches 0, the opposite is true (at phase angle of 90?° the ratio is equal to the brightness ratio of the stars). So a 90% primary-lit gibbous phase (0.9) will be 900 times brighter than the 10% companion-lit crescent (0.001).

So basically, the brightness of the companion lit portion of the disk IN THIS SCENARIO is not always going to be 100 times smaller than the brightness of the primary lit portion of the disk, even though that is what the ratio of the brightnesses of the two stars is at the planet. As the ratio gets smaller (when the phase angle increases from 90?° to 180?°) the companion-lit portion of the disk will become brighter relative to the primary-lit portion. And that is what is currently missing from Celestia.

Obviously you're not always going to have the two stars on directly opposite sides of the planet - they're going to be at other angles relative to eachother, which makes it more complicated (you'd have to add the companion-lit component to the brightness of the primary-lit disk when they're both illuminating part of the planet). But this example should illustrate what I'm getting at, I hope.

[Malenfant]

I just realised I can't actually demonstrate this in Celestia very well because of the inaccurate shaders it uses - a 10% illuminated crescent isn't even visible in Celestia because of the way that the planet unrealistically darkens near the day/night terminator.

At a phase angle of 162 degrees you should be able to see a very thin crescent (like a new moon - the moon was at this phase angle to Earth on 2nd December 2005), but you can't in Celestia.

e.g. this photo was taken on Jul 19th 2004, from:
http://www.air-and-space.com/Moon%20200408.htm



The phase angle is about 166?° in this picture, but if you look at the moon in Celestia, you can only barely see the limb of the moon and can't see any crescent at all.

[Malenfant]

Chris? I'd be interested to hear your detailed opinion on this...