Horizon Level on Alaalu?

[Gryphon]

The first time Diane Duane brought up that the horizon level was higher on the planet, I reread the text a couple of times, thinking that, no, it probably wouldn't be any higher.

I know from perspective in art class and from other places, that the horizon is always at eye level. I also know that this is true NO MATER YOUR HEIGHT. At this point, so what? The horizon is like that for Earth. That doesn't mean it would be that way for bigger planets too.

But shouldn't it? The Earth and (wazaplanet'sname) are both spheres. Would the size of the planet make a difference?

((Heh. Is anyone willing to try to do a proof to solve this?))

[eveningstar]

Heh. I saw that too and wondered. But I think what Diane meant was that since Alaalu is so much larger than Earth, she wanted to make a comparison. Besides, we might never know how much larger Alaalu is. It says it is barely small enough to have metals on the planet (sorry, don't know the exact quote). Just how small that may be I have no idea.

[Nathan]

Actually, Eveningstar, we do know how large Alaalu is, from one of DD's posts on Out of Ambit, though I think you are correct that it isn't mentioned in the book. The pertinent quote from DD's post is "Alaalu's radius is almost exactly 34,000 km" (for comparison, the Earth's radius is ~6380 km).

It appears that the horizon that Gryphon is referring to (which I have seen referred to variously as the true, natural and astronomical horizon) is, ipso facto, always at eye level, regardless of height. However, on a sphere, the actual horizon (which appears to be properly called the seen, visible, sensible or apparent horizon) is not at eye level and depends upon one's height above the surface (for an infinite plane [which a sphere approaches in the limit of very large radii, where "very large" is in comparison to your distance above the surface] the apparent and astronomical horizons are identical, and thus not height dependent). It's pretty easy to find the horizon dip at a given distance above a sphere (neglecting refraction) --it's done nicely on this page, so I won't bore you with my derivation here (especially as it's identical to the one I linked to and you wouldn't have the benefit of a figure). Putting in numbers (and using the fiducial 1.5 m person from the above website), we have a horizon dip of ~2.36' on Earth's surface and of ~1.02' on Alaalu's, so there is indeed a (small) difference. The final, and perhaps most important, question is whether this difference is large enough to cause the psychological effects mentioned in Holiday. My guess is that it is, but I'm well out of my fields of interest/expertise here, so I'll leave a more detailed analysis to someone more well-versed in such matters.

Nathan

[semiramis]

my guess is that it probably does--something as familiar as the horizon line being even slightly off kilter can probably do that to you. It's like how, if you play a musical instrument, when you pick up someone else's instrument and try to play it-- even if they're the same make and brand, you get so used to your own that they just feel different.

[Xylemicarious]

This really has nothing to do with horizon on Earth. Ok, so think of a cross section of a sphere, a circle. If its a small circle, the curvature of any arc on the circle is tight. The larger the circle, the shallower the curvature. This is the same on a sphere. The horizon will always be at eye level, true, but the amount of things packed into that level are different. Since relative size is a inverse sqaure law, you could have a planet where the horizon radius is huge, because the horizon is just the line where it becomes impossible to see over the curvature of the Earth. On a larger planet, the curvature is more shallow, so a person is able to see things that would be over the curve on planet Earth. The horizon is still eyelevel, but there is more things in the space because of the curvature of the planet.

Xylemicarious

[Gryphon]

Hmmm... The horizon is visible when your line of sight is tangent to the earth. The horizon would actually not be at eyelevel. You'd more have to look upward... nnnnooooo...

Huh. I just lost myself. Nevermind.

[Quill]

Huh. I don't know from art or planetary physics, but when I ride in a passenger jet, the horizon, if visible, is below my eye level. But that may just be cheating.

[Xylemicarious]

Ok, the line of sight rule only applies if your line of sight is on or close to the ground. The higher you go up, the more curvature you are able to see. If you are in space, the horizon doesn't coincide with your line of sight because the earth is below you. The horizon is below you because the entire earth is beneath you. Looking at the horizon of the Earth would be looking down. If you go even farther, the distance of alpha centuri, say, then the horizon of the earth would become a tiny circle in whatever direction the earth was in comparison to yourself.
So yes, the farhter you go up, the more of from eye level the horizon becomes. The horizon will be at eye level as long as the line of sight is tangent to the earth.(Tangent meaning only one point of the nie is touching another point on a circle.) No one's line of sight is perfectly tangent, but the difference is unnoticeable until a person is much higher than the surrounding terrain.

As for the horizon of a bigger planet, as long as you are on the ground, the horizon would remain eye level, becuase the line of sight is still tangent to the sphere, although the arc of the sphere is now longer and more gradual. The horizon would remain at eye level, but there would be the possibility of much more things between you and the horizon.

Since relative size decreases by an inverse square law, you could pack much more units between a point on a sphere and the horizon if the arc was more gradual.
For example: Say that you have a rope with black marks strething all the way to the horizon. For the sake of example, lets say your line of sight is perfectly tangent to the ground, but you are able to see the black marks. All the marks are one meter away from each other, yet the distance between them seems to decrease each time becuase they get farhter and farther away. So the first two would seem a certain length apart, then the second and third would look a certain percentage closer (let's pretend 10%), then the 3rd and 4th would seem 20% closer together than the 2nd and 3rd, and so on. After a certain amount of black marks though, you wouldn't be able to see any more marks because the rope has curved over the horizon. So there is a definite distance between you, and the horizon.
But if the hotizon was farhter away becuase it was a bigger planet, then there would be more marks between you and the horizon, therefore more distance, therfore more space to put things.

This looks completely unreal to Nita and Kit becuase Earthlings are used to having a certain distance between them and the horizon. When the distance is increased suddenly, it's no wonder that it seems strange.

Xylemicarious

[Quill]

Very coherent! Thank you, that makes sense.

Just curious, but am I the only one who thinks it's a bit weird that the planet is so much larger, yet the gravity is less than on Earth?

About the horizon thing: I am not that great at math... I'll stick with music. (How would you use music to determine eye-level... well I have no idea! )

Edit: I should say I'm not great with proof-mathmatics. I'm ok with computer stuff. =D

[Fox]

Chris, My understanding of gravity etc etc is limited but I always thought that gravity is Not depentant on size? For example a mini-black hole in theroy could destroy earth because it has an a large amount of gravity But might be microsopic! Gravity i think is more depentant of density of the planet rather than the size.

Now the planet in wizards holiday had very few metal compounds in the planet! So even though earth is smaller becasue we have (compared to them) a lot more metal our planet is denser and so has a higher gravity! Does any of that make sense? I'm sure I got that all wrong!! One person to ask would be 'PM', that man has a vast amount of knowlege!!
Fox

True, I wasn't thinking of the metal content. (Or the big hole in the middle... or was that a "spirit" hole? *gah* need the book by me for reference. 15, and I'm already loosing my memory. It's a bad sign.)

[Gryphon]

Chris:
Just curious, but am I the only one who thinks it's a bit weird that the planet is so much larger, yet the gravity is less than on Earth?

Hehe, I was just reminded that it said in the book. It's a spoiler part of the book. Normally it probably would have a much greater gravity than Earth, but...

Fox:
Chris, My understanding of gravity etc etc is limited but I always thought that gravity is Not depentant on size? For example a mini-black hole in theroy could destroy earth because it has an a large amount of gravity But might be microsopic! Gravity i think is more depentant of density of the planet rather than the size.

I could be wrong, but wasn't it mass?

No, Fox, it's not the metal content, though that was a good idea. Yep, Chris has it right.

[Fox]

Gryphon your right it is mass, so the denser a object is the more mass it has which in turn means higher gravity! So becasue (I think) metals are denser than rock, becasue earth had far more mental than the other planet it has more mass and a higher gravity! As far as I could tell the other planet was mainly rock so even though it was bigger it has less density and a lower gravity! I'm still proberlly wrong Oh well
Fox

[Gryphon]

Fox:
Gryphon your right it is mass, so the denser a object is the more mass it has which in turn means higher gravity!

Not really... You can have a more dense object with less mass. Density is mass over volume. Water's density is 1.0 g/cm cubed, right? It's always that, no matter how much water you have. You could have an ocean full of water, and its density would be the same as a glass full of water (assuming neither had fishies, pollution, and a lot of other random stuff. Assuming both were water and not much else). So instead of the denser an object is, the more mass it has, let's just settle with the more mass something has, the more mass it has. Remember, density also involves volume, not mass alone. Though you're right about metal being dense so that it contains more mass than what the other planet would.

Oh, Fox, you're dodging the truth. You're so close, but you're going in circles! The planet was <span class="ev_code_WHITE">hollow</span> [&lt;&lt;spoiler]! That's a big chunk of mass missing.