cpotting wrote:Who would have thought it would be so complicated. I would have thought the variables would simply be a) the absolute magnitude, b) the distance from the sun, c) the phase angle and d) the distance from the planet.
Well, you're right, and they are - those are the values that vary for each planet
. In the equation, Absolute magnitude is V(1,0), distance from the sun is r, and distance from the planet is d. What's different are the constants that they are multiplied by - which are in the phase function Dm(i).
I'm still not sure why there are different phase functions for each of the planets. A reflecting ball is a reflecting ball is a reflecting ball.
Hate to tell you this, but nope.
This all goes back to photometry - the way an object/surface reflects and scatters light. Celestia doesn't handle this realistically at all - to illustrate this have a look at the full moon in Celestia. You'll notice that it's brightest at the subsolar point and dims around the edges? Now compare that with how the full moon really looks - you'll see that the real moon
doesn't get dimmer around the edges, and that actually (surface variation notwithstanding) it's the same brightness throughout the lit hemisphere. The brightness of the moon doesn't change with distance from the sub-solar point.
You can also see this by looking at photos from the surface of the moon. If you look at photos taken with the sun directly behind the astronaut you'll see that there's a lot of glare - the ground is brightest directly ahead of the astronaut's shadow. That's because the lunar regolith is strongly back-scattering - photons bounce back off it in the direction they came from.
Atmospheres also scatter light in odd ways (next time you're in an aeroplane flying over clouds, take a look at how they reflect the sunlight).
All of these factors are different for each planet, and are subsumed into the Dm(i) function.
The absolute magnitude should account for the albedo, any differences in colour, reflectivity, etc.
It does. But remember, the absolute magnitude is the (theoretical) magnitude of the object at
zero phase angle, at a distance of 1 AU from both sun and earth. the
5log(rd) term tells us how that changes with real distance, and the Dm(i) term tells us how that changes when the phase angle isn't zero.
The only other factors I could see coming into it are the planetography - different amounts of light reflected from one area as opposed to another, and the oblateness. Both of these should have very minor effects for the major planets though.
There's about two pages of text explaining about oblateness in the chapter from the Explanatory Supplement that I'm using for all this
- it changes the size of the disk seen from Earth. Surface variations also do change the visible magnitude - the surface markings on Mars (and dust storms) for example can cause a variation of up to 0.25 magnitudes.
(Personally, I think these scientists just complicate things to keep us laypeople on the outside. Come on! Who's with me for simplifying pi to 3.0, using circular orbits, and changing all these trigonometric curves to linear functions? Think about it - if we did, we could hack so much
extraneous code out of Celestia that it could be loaded as a Java applet and run on your cell phone!
)
*Slapslapslap* Get a grip man, science is supposed to be complicated!
Did your contact give a reason for the need for separate phase functions? Why doesn't the equation for Mercury work for Venus, etc? I would be interested in knowing.
See above
. It's all down to photometry - Venus' atmosphere reflects light in a different way to the regolith on the surface of Mercury. For example:
V(1,0) for Mercury: -0.60
V(1,0) for Venus: -4.40
(these values are the most up-to-date. In fact, they're not even used in the almanac yet, but they will be from next year so they give slightly different (but much more realistic) results to the official ones we know today).
Dm(i) for Mercury: 4.98(i/100) - 4.88(i/100)^2 + 3.02(i/100)^3
Dm(i) for Venus: 1.03(i/100) + 0.57(i/100)^2 + 0.13(i/100)^3
And technically, Venus actually starts to get
brighter at high phase angles (when it's nearly new) because the atmosphere scatters light through it that increases its magnitude. But I've not accounted for this in the script.
. In the meantime, congrats on getting your script going.
Wow 