Solar System Calculator (SSC)
Steve Lewis - May 2021
BACKGROND
=========
SSC is a program to calculate the distance one should depict planets, in order
to scale them to the same ratio as they are in their real distance from the Sun.
This program runs in the Online C compiler, available at:
https://www.onlinegdb.com/online_c_compiler
I did a project with my daughter to paint the planets along our fence. As
a casual art, one could just draw the planets anywhere. But it is more
authentic to draw each planet in the same ratio as they really are, to
appreciate that massive distance between them.
What inspired me was from in my hometown of Gainesville, Florida, the local
astronomy club had erected such a scale model along its NW 8th Avenue.
This scale model is along an uninterrupted span of nearly 1 mile (5280 ft
or 1609.344 meters). For information about the Gainesville model, see:
https://www.alachuaastronomyclub.org/solarwalk.html
There are various online solution for calculating these scaled distances.
some examples are:
https://www.jpl.nasa.gov/edu/teach/activity/create-a-solar-system-scale-model-with-spreadsheets/
https://www.exploratorium.edu/ronh/solar_system/
https://spacefem.com/eris/calculator.php?scale=1&based=Sun
To be even more authentic, a model should also consider the diameter of
each of the planets themselves (and scaled relative to the diameter of the
Sun, which is by far much more massive than all of the planets combined).
But in this regard, it is reasonable for an artist to take certain
liberties, since at small scales it quickly becomes the case that the
planets become too small to be seen at all.
For example, in our fence project, the fence was about 50 feet in length.
At this scale, nearly all the inner planets become too small to be visible
by cars passing on the street. So while the distances there authentic, we
had to enlarge the planets themselves for the sake of being visible (to be
more than just grains of sand).
Another aspect was that for the scale we did end up choosing, we could only
fit up to Saturn along our 50 foot of fence available. We considered
asking our neighbor if we could extend the model along their fence (to
include Uranus and Neptune). But as it turned out, before we had an
opportunity to do so, a storm came and damaged the fence and we had to
replace it entirely with a new fence (and then we had new neighbors shortly
thereafter, and things ended up that so far we never resurrected this model
along the street). The point being that if you only have a finite space to
depict a solar system, the scale you use may vary depending on how many
planets you want to depict (such as just a few of the the inner planets).
USAGE DETAILS
=============
The SSC program is arranged such that it asks these three questions, each
of which also has a default if you just press ENTER:
- what is the "work distance" (in feet)
- what "distance type" (or "category of distances") do you want in the report?
- which first N planets do you want to include in the model?
Further details of the inputs is described as follows:
Work Distance
-------------
This is the distance of your "fence" or "wall" onto which you want to depict
the model of the solar system. The program is flexible in that this distance
can be quite small (0.001 ft) or very large (up to roughly 100,000x larger
than the actual dimater of the solar system itself). In otherwords, you can
both "shrink" or "expand" the model relative to the actual size of the solar
system. These limits are relevant, because they are due to two sets of limitations.
The first limitation is the limit of the computer itself to represent these
very-small or very-large numbers (specifically that we are using a FLOAT type,
not yet even DOUBLE-PRECISION). The second limitation is more artificial, being
due to wanting to keep the OUTPUT of the program to a specific "standard" format.
If the numbers become too small, the output-format doesn't have enough resolution
and you just end up seeing "0" distance. If the numbers become too large, the
output-format is forced to use a larger amount of space on the screen (e.g. 6-digits
instead of the normal 4-digits). It is subjective on how much confusion such
results cause. For instance, if one wanted to fit these results onto a printed
"invoice" that had boxes, it may be necessary to ensure the results did not "overflow"
that box itself.
This is a very important software-design point. While the computer may be
technically capable of a much wider range of calculation, it may be prudent to
reduce that capability to accomodate aspects of how your program interacts with
the human operator. Another reason for doing so is to avoid issues related to
data-overflow, by avoiding situations where the operator requests a calculation
that is larger than the numeric representation can handle. It's another case of
"just because you can do it, maybe you shouldn't do it." in regards to allowing
the full extent of the computational capability of the system. Moderate that
potential down to the more meaningful limits of the visual/reported outputs.
Specifically, the SSC has these thresholds:
Work Distance... Resulting units used for Planet-Scale report...
BELOW 0.001 (not supported, displayed results become 0, even though the FLOAT type technically can support smaller range)
BELOW 9ft millimeters (mm)
BETWEEN 9-9999ft feet inch (' and ")
ABOVE 10000ft miles (mi)
ABOVE 5000000ft "Earth-diameter" (ed)
ABOVE 40000000000ft AU (astronomical unit)
ABOVE 400000000000000ft (not supported, considered as invalid even though the FLOAT type technically supports larger range)
NOTE: This SSC does not get involved with the DIAMETER of any specific
body. The distance are "from the Sun (surface)" and are without regard to
whichever diameter you choose the Sun to be. In our case, the Sun was
simply at the "edge" of the fence.
Distance Type (to Report)
-------------------------
When modeling the solar system, it is a system that is in constant motion and
the orbits are not actual "perfect" circles. So to speak of "distance from the Sun"
it becomes subjective as to what distance you really mean. Specifically, do you
mean "nearest distance", "farthest distance", or just the "average distance" along
the orbit.
The SSC accounts for this, by allowing the user to choose which "type" of distance
that is of interest to them. And it is a "mask" field that means it can be any
combination of these types. The types are "1" (N), "2" (F), "4" (A), but to select
any type just ADD their corresponding number. Examples:
1+2 = 3 (N and F)
1+ 4 = 5 (N and A)
2+4 = 6 (F and A)
1+2+4 = 7 (N and F and A)
There is an input limitation, where if you designate the TYPE by using
LETTERS (N, F, A), only one can be chosen at a time. Whereas if you
specify the TYPE by using a NUMBER (1-7), you can select multiple distance
types to be reported at the same time.
The computation is not that intense, so there is typically no reason to
select anything besides "7" (all of them). But this ended up being an
interesting way to show how multiple options could be handled. Or as a
useful aspect, in a "final report" one may want to focus on specific values
of interest, and "declutter" any other type of distance.
Note that in addition to the calculated scaled-distance-from-the-Sun
result, this SSC also includes additional data with each planet: the
actual distance in mKM (millions of KM) and mMi (millions of miles), as
well as "AU" (astronomical units). When drawing the scale model, it may be
of interest to include these "actuals" in those drawings. And so that
information is available, just in case.
NOTE: If you include Pluto in the calculations, you will see how "odd" of
a planet it is when you see it's NEAREST vs FARTHEST relationship (as it
has a much larger span than the others).
N Planets
---------
From the perspective of this SSC, there are "8" official planets in our
solar system. Since Pluto's initial discovery around 1930, many
"planetoid" dwarf-planet objects have been identified at this "wild" region
past Neptune. That siad, the Pluto data is included for those who are
interested in it.
When preparing a scale model, you may only want to include the "inner
planets" (typically up to Mars), or may not be able to fit the farthest
planets (Saturn, Uranus, and Neptune) for practical reasons (such as if
being inside a classroom). This decision is important since it sets the
"largest value" scale of your model (that being the FARTHEST value of the
designated "Nth" planet). This value is your "100%" reference, the ending
"edge" of your model, and becomes the basis to which all the "real
distance" data is scale to.
NOTE: SSC has no consideration on the moons around each planet. This
would be an interesting future expansion, along with the major asteroid
bodies.
Thank You
---------
Thank You for your interest in this program and overall topic. In my
astronomy work, I am often "looking past the solar system" to explore
things that are "really far" out there: neighbor stars, exoplanets,
nebula, other galaxies.
This project was started as a reference example on the utility of
float-point numbers within a piece of software (and a question of whether
such numbers are vital, or could everything ultimately be represented in
whole-number integers). Aside from that debate, then it becomes a
challenge to address the portability of this solution: not every C
compiler has actually implemented float-point type support for all of their
target systems.
An interesting footnote here is that Bill Gates original BASIC did support
up to 9-digit precision floating-point numbers, with the work of MONTE
DAVIDOFF who wrote the MATH PACKAGE. Performing math functions in a
digital computer becomes a very difficult technical challenge, as math is
fundamentally continuous while the nature of digital computers is
fundamentally bound by discretes (i.e. can achieve extremely high
resolutions, but never quite continuous). So while the first home/office
PC (Commodore PET) could do some scientific computing (financial compound
interest and physics equations), it was "software emulated" and extremely
slow. It took another 5-10 years before things like the 8087
math-coprocessor implemented these capabilities more natively into
hardware, which we now very much take for granted.
Example Output (using Default inputs)
==============
FIRST 8 PLANETS SCALED TO 50.00 FT...
NEAREST FARTHEST AVERAGE
Mercury 000' 006" 000' 009" 000' 007" <-- This is 6", 9", 7" respectively (not .006, .009, etc.)
mKM/mMi 0046/0029 0070/0043 0057/0035 <-- This is just a reference to the static data, not a calculation
AU 00000.307 00000.466 00000.387 <-- This is just a reference to the static data, not a calculation
Venus 001' 001" 001' 002" 001' 002"
mKM/mMi 0107/0066 0109/0068 0108/0067
AU 00000.718 00000.728 00000.722
Earth 001' 007" 001' 007" 001' 007"
mKM/mMi 0147/0091 0152/0094 0150/0093
AU 00000.980 00001.010 00001.000
Mars 002' 002" 002' 008" 002' 006"
mKM/mMi 0205/0127 0249/0155 0228/0142
AU 00001.380 00001.660 00001.520
Jupiter 008' 001" 008' 011" 008' 006"
mKM/mMi 0741/0460 0817/0508 0779/0484
AU 00004.950 00005.460 00005.200
Saturn 014' 009" 016' 006" 015' 008" <-- This is 14 FEET and 9 INCHES, 16ft 6inches, 15ft 8inches.... "from the Sun" (the beginning edge of your model)
mKM/mMi 1350/0839 1510/0938 1430/0889
AU 00009.050 00010.120 00009.580
Uranus 030' 002" 032' 010" 031' 007"
mKM/mMi 2750/1710 3000/1860 2880/1790
AU 00018.400 00020.100 00019.200
Neptune 048' 011" 050' 000" 049' 005" <-- The FARTHEST distance of your Nth planet should match your original work_distance_ft (50ft in this case)
mKM/mMi 4450/2770 4550/2830 4500/2800
AU 00029.800 00030.400 00030.100
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