Topic: The View From Planetside - Relative Sizes Calculated

The below diagram demonstrates how we view stellar and planetary bodies while positioned on another planetary body.

http://img.photobucket.com/albums/v333/rlongtin/Whatwesee.png

The thing to keep in mind though is that when we see the "size" of something, our eyes don't process length and width effectively because we would first need to have a measure of distance from ourselves to the object we are viewing. Instead, our vision processes everything in angular measures. This is why, for instance, during a Solar Eclipse we can see the Moon, which we know to be many times smaller than the Sun, appear to block the Sun from our view. Obviously the Moon didn't change sizes but its angular measure is close to the Sun's.

These angular measures are known as arcs.

So if we can agree that if I showed you a two cubes that measured 1 cm cubed and 1.001 cm cubed, you would argue that the two look similar in size if you saw them side by side. The same can be said of celestial bodies whose arc lengths are similar in size. Similarly, if one celestial body has a larger arc length than another celestial body, it will appear bigger to us and the other will appear smaller.



Returning to the diagram above, there are two parts of every arc length that determine its value. The distance from the observer to the celestial body's center, and the celestial body's radius. With these in hand, thanks to (the newly updated)The Verse in Numbers, I am calculating the relative sizes of the celestial bodies for our various sims and posting them in the OOC areas.

For now though, to whet your appetite, the average arc length of the Moon from an observer on Earth is 0.0091920195 radians. The average arc length of the Sun from an observer on Earth is 0.0092981618 radians. So to us, the sun is only slightly larger than the moon on average, approximately 1.155% bigger.



Also interestingly, knowing the arc length of celestial bodies tells us how much of the sky they occupy as well. Both the sun and the moon each occupy slightly less than 0.000688% of the sky (more accurately from an observer at sea level with no significant land features to effect the amount of visible sky).



I'll be updating sims as I get more work done on this front.  big_smile

~Robert

Last edited by RLongtin (2012-05-02 17:24:06)

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Re: The View From Planetside - Relative Sizes Calculated

Current requested work

Relative Sizes of Celestial Bodies for:

Relative Luminosity and Color of Stars for:

  • None

Feel free to post requests below. They will be processed in the order received.

***Relative Luminosity refers to how brightly a star would be for a particular planet. Coloration (not given by The Verse by Numbers) is calculated based on three things: surface temperature, radius, and luminosity.

~Robert

Last edited by RLongtin (2012-05-02 17:25:33)

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Re: The View From Planetside - Relative Sizes Calculated

At this time I'm not processing requests for relative Luminosity and Color of Stars - only relative sizes for now. Once those requests have been processed I will begin looking into the Luminosity and Color of Stars.

~Robert

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Re: The View From Planetside - Relative Sizes Calculated

Of course, the relative positions of "stationary" objects change as you move, what is known as parallax. If you know the arc distance and the length you've moved, you can calculate the distance.

An arc movement of one second (very tiny) equates to a distance of 3.08568025 × 10 to the power of 16 metres, or 3.26 light years, aka a "parsec".

Re: The View From Planetside - Relative Sizes Calculated

Correct, although parallax relies on vast distances to acquire its accuracy and requires two "stationary" and one mobile object that revolves around only one of the former objects as references. Also the celestial body to which you are making your parallax measurement cannot orbit your mobile object nor the stationary object about which your mobile object revolves. We typically use Earth and the Sun for our parallax measures to other stars and the assumed distance of 1 AU between Earth and the Sun. Also parallax requires two measurements and it takes a half of a revolution about the sun to acquire each (although I have no doubts that with some high-end expensive technology you can acquire measures in a smaller time frame - but parallax can be done on the cheap without any technology invented in the last 2000 years by waiting a half of a revolution).

But because parallax is only useful for vast distances at least tens of thousands times longer than a star system is wide and has very particular needs regarding its three points of reference, parallax can't possibly be used in determining relative sizes of celestial bodies within the star system they are being made from.

Both my method, Parallax, and one other (false) method were the contents of my presentation and thesis and the pros and cons of each were discussed along with their validity (or lack thereof). Keep in mind I was presenting this to a Mathematical community so proof was of higher value and thus most of my work went into exploring how parallax works, and such.

My method isn't really "mine" though, it's an astrophysics spin on an old method of indirect measurement. My favorite method however is "dissimilar triangles" (that always gets a "huh?" out of my fellow Mathematicians). Not going to toot my own horn very loudly but I put everyone in one of my math classes to shame with that method on one occasion, laying waste to the supposedly superior method of similar triangles. The idea is to have a low error margin and to know which method minimizes your error margin the most given the circumstances.

~Robert

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Re: The View From Planetside - Relative Sizes Calculated

BTW, TVIN has been updated and expanded.

Re: The View From Planetside - Relative Sizes Calculated

Thanks again for all your work on this, Robert, it really is awe inspiring.

Jason, can I request these images get uploaded to the wiki as Robert posts them in the RPE?

Silent, thanks for posting the updated Verse in Numbers. I came across it a few days after linking to the original and hadn't got around to updating here.

Ash

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Re: The View From Planetside - Relative Sizes Calculated

Updated to include a link to the relative sizes of Santo's moons.

Will also be doing stellar bodies as well, but taking everything one step at a time...

~Robert

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Re: The View From Planetside - Relative Sizes Calculated

I figure some people are curious to see what it is I do to get my results. So here's a snapshot of my work on Santo's moons. Basically I create a planet, the Earth's Moon, and all the other moons for the planet in question. I set the distances (from the observer not the planet - the effect this has on the distance is factored in), set the radius of each moon, setup the lines tangent to the moon that pass through the observer's points, and then have the program calculate the angular measure between the tangents. Then I just create circles for the Moon, and each of the planet's moons with a radius set as a scalar multiple of the magnitude of the angle. And...presto! Perfectly proportionate moons based on TVIN 2.0!  big_smile

Of course it's important to observe that the relative sizes are closest to actual when comparing the high-noon positions of each. If one is at high noon and another is not, the relative sizes are (slightly) different, but if each were at high-noon then my diagrams are precise. :-)

http://img.photobucket.com/albums/v333/rlongtin/Phoenix%20Roleplaying/Astronomy/HowIWorkMyMagic.png

Side Note: You'll notice I have the moons shifted in such a way that they are closer to the planet than the actual distance (as mentioned I set the distance from the observer) - this doesn't throw off the numbers at all, but the reason I shifted them is so I can see what I'm doing more clearly!

~Robert

Last edited by RLongtin (2012-02-21 19:59:46)

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Re: The View From Planetside - Relative Sizes Calculated

What software's that you're using there, Robert? Looks to be great for plotting things out.

-Euan

Re: The View From Planetside - Relative Sizes Calculated

Noted about adding this to the wiki.

Just also wanted to say, this assumes standard orbit of those moons (unless the dataset you are using also has elliptical information for the orbits? I don't recall TVIN having that. That would be insane if it did!)

http://www.phoenix-rp.com/img/pips/4.png http://oi60.tinypic.com/5otabo.jpg

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Re: The View From Planetside - Relative Sizes Calculated

Typically if orbit distance is the only thing given it's average orbital distance - so I'm not overly worried, you can freely assume some days it will be (very) slightly larger or (very) slightly smaller. The amount of variation would likely be very minimal.

Thusfar the moons about Deadwood and Santo are significantly closer to their planets of orbit than our Moon is to us - so I have to imagine the orbits are likely close to circular anyways, or else their moons are likely to have a decaying orbit that will one day result in a collision.



And the program is Geogebra - it's free online!  big_smile

~Robert

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Re: The View From Planetside - Relative Sizes Calculated

I've started work on the stars though giving some thought to it, I've decided something.

Rather than continue to do this bit by bit, I'm going to do a full construction of The 'Verse in Geogebra instead. It will be a fairly large project overall but the results will be well worth it I think.  smile

~Robert

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Re: The View From Planetside - Relative Sizes Calculated

Crikey! :-D

Ash

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Re: The View From Planetside - Relative Sizes Calculated

Coooool.  big_smile

Deborah

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Re: The View From Planetside - Relative Sizes Calculated

I wanted to add a note that my project to reconstruct The 'Verse has been "on hold" until I find the time and motivation to set things in motion. It's a terrifyingly large project to undertake that requires only a moment of inspiration to get me going. I will share more info when I actually start it.  big_smile

~Robert

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Re: The View From Planetside - Relative Sizes Calculated

*So* looking forward to it, Robert! Perhaps compartmentalise it, just do a little at a time?

Ash

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Re: The View From Planetside - Relative Sizes Calculated

That's the idea. Much like my book, it got put on the back burner for a long while. Actually a lot of things got put on the back burner in March because my step-mom's condition worsened and since then she's been in and out of the hospital quite regularly (this week alone she was admitted 3 times and sent home twice, and later this week she's supposed to be sent home again). I hadn't flagged LOA because for the most part nothing has changed for me as far as availability goes, but I've managed to forget a number of things I was working on what with having to take care of the house and run the business without the help of my dad for the past month and a half.

~Robert

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Re: The View From Planetside - Relative Sizes Calculated

Yuck, hope things get better soon!

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Re: The View From Planetside - Relative Sizes Calculated

Thanks Jason!

~Robert

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