OK, Here is the problem. I'm told that the horizon is approximately 3 miles away, I know this is dependent on height of the person and curve of the earth and what not. I can find numerous formula on the internet.

What I need to know. Say my character is six foot tall, and looking across a desert landscape, I need the horizon to be TWO miles away, so is the planet he is standing on bigger or smaller than earth? I just cannot wrap my head around it. Math and science are not my thing, when I google things like "how far is the horizon" I get formula for Earth, not as if he was on another planet.

help?

- Math help!

brune_hilda2012-05-15 09:11 pm (UTC)

the_physicist2012-05-15 09:21 pm (UTC)

scatteredgray2012-05-15 09:22 pm (UTC)

hourglasscreate2012-05-15 09:29 pm (UTC)

And since I haven't read the comments yet, I bet someone has already beaten me to this answer.

lilacs_roses2012-05-15 09:37 pm (UTC)

hourglasscreate2012-05-16 12:23 pm (UTC)

xolo2012-05-15 09:35 pm (UTC)

xolo2012-05-15 10:17 pm (UTC)

furerin2012-05-15 09:42 pm (UTC)

Now with (a slightly exaggerated) illustration.

The horizon is where the tangent of your sight line touches the planet. So as you can see in my wonderful paint picture, a smaller planet makes the horizon closer. I could go further into the math of it all, but have a feeling that it's not that important to you. But doing some quick and dirty math (with some abbreviations and hoping I did everything correctly) I get that the new planets radius should be about 4/9ths or about half of earths.

stormsdotter2012-05-15 10:17 pm (UTC)

The elevation of the desert will also influence the distance your person can see. Just because the ground looks flat doesn't mean there isn't a very slight slope; most people won't notice a 5

^{o}incline outdoors.Even if your world is 4/9ths of Earth, it may have a similar gravity depending on its density and composition.

zibblsnrt2012-05-16 01:34 am (UTC)

volumewould be much smaller than 4/9ths - around a tenth, if my math is right - so it'd need to do some interesting things with composition to be close to Earth's gravity.lederhosen2012-05-16 08:37 am (UTC)

At 4/9ths Earth's radius, assuming it has a similar composition, gravity would be 4/9ths Earth-normal. (Volume and hence mass scale with the r-cubed, but gravity scales with mass on r-squared, so the net effect is that under constant composition, gravity scales with r.) So, noticeably lighter than Earth, but you're not going to go floating off into space.

To get earthlike gravity at that mass, you'd need a composition about as dense as lead. That seems to be possible (there are plenty of things more dense than lead) but I don't think it's common among rocky planets.

hourglasscreate2012-05-16 12:24 pm (UTC)

nanini2012-05-15 10:33 pm (UTC)

"The distance to the horizon can be calculated, in metric units, using the formula d = sqrt(h(2r+h)), where sqrt is the square root, h is the height of the observer (or rather his eyes) above sea level and r is the radius of the planet. All units are in meters. The distance (d) you get out of this formula is the distance in direct line from the observer's eyes to the horizon. It is not the distance along the curvature of the planet. The difference between these two figures is, however, very small for moderate values of h (i.e., values below 100 kilometers)."

calcitrix2012-05-16 03:28 am (UTC)

Lol, also--I looked up all that info writing my pirate AU. :) But it sounds like you've got it.

dorsetgirl2012-05-16 08:14 am (UTC)

verysimple formula, and it's annoyed me ever since that I can't remember it!lederhosen2012-05-16 08:24 am (UTC)

dorsetgirl2012-05-16 08:27 am (UTC)

hippypaul2012-05-16 10:30 am (UTC)

They teach it to the Army as well - Grin.

dorsetgirl2012-05-16 11:19 am (UTC)

Although of course all the stupid maps have shown contour lines in metres for years...

Edited at 2012-05-16 11:33 am (UTC)