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>>Introduction
objects.rsm>text>
Introduction to the Dance Demo
Welcome to the `Dance of the Planets' demo. This demonstration version of the
program will show you a selection of simulations illustrating much of the
detail and scope of Dance. In the demo you will see:
* 20 selected asteroids and comets. The complete program has over 5500 -
virtually all numbered asteroids and recorded comets.
* The nine planets as seen from afar, and closeup views of the Saturn system.
Of course in the complete program all the planets can be viewed up close.
Date input is inoperative in the demo, but in the complete program it can be
set from 1,000 BC to AD 10,000. Even with these demo limitations, there is a
lot to see and do. And in the process you will learn how Dance operates. If
this is your first time through, just press [Page Down] whenever you are ready
for the next screen, following the comments and instructions you find there.
So [PgDn] now to proceed with demo. At any time you can also press [Home] to
see the demo contents and from there, jump directly to a particular simulation.
- Thomas Ligon 11 Nov 1989
>>A Starship Perspective
SM>0>->100>0.5>-10>270>00000000000000000000>
On the screen is a familiar sky. The bright star at the center is the Sun, some
3 light-days away. Press [o] to see orbits. Adjust the monitor for dark space,
faint orbits showing. Over 100 stars are on the screen; can you see them? In
the Control Bar below, note date, ecliptic coordinates and lowest Zoom setting.
>>Basic Viewing Operations
Space and Earth Viewing Modes.. Basic Viewing Operations
The Space Mode view in the previous screen is from outside the solar system.
At 1X (next screen), the apparent size of the constellations and orbits are
much what they would be out a spaceship window, 270 a.u. away from the Sun.
As you will see later, there is also an `Earth View' selected from the popup
(main) menu, providing Earth views of orbiting bodies against the starry sky.
Viewing/Operating Options..
* Speed, magnification (Zoom), Latitude, and longitude (Rotate) are selected
with hot keys and changed with the cursor keys. Active selections are high-
lighted & simulation is suspended. Pressing any key will resume simulation.
* Zoom, Latitude, and Rotate can be changed faster from the popup Menu. Select
the option, change with the cursor keys, [Enter] to de-select. Then select
another or [Enter] a second time to exit the menu and resume simulation.
* SET SPEED TO SUIT. Some of the following simulations will be too fast if the
coprocessor is present, too slow if it isn't. For accuracy, what is import-
ant is how many gravitational calculations are performed for the distance
traveled. So fast settings may be notably less accurate for some objects.
* Objects on the screen can be labeled by using [I]dentify from the menu.
A quick reference guide to operation is available by pressing [H]elp. Now try
some of these viewing/operating options on the next screen.
>>The Solar System at 1X
SM>1>->100>1>-17>270>00000000000000000000>
THE SOLAR SYSTEM at 1X ** This text can be restored by pressing Enter. *
Make Zoom active by pressing (Z). Advance to 4X with the Up cursor key. Select
(M)enu and then (I)dentify to label the planets. Note that Saturn, Uranus and
Neptune are all in rough alignment. (S)peed up to see orbital motion. [PgDn]
>>From the Earth's Sky
EM>1>01/01/1990>1000>0.5>-3>270>00000000000000000000>
AN EARTH PERSPECTIVE ** Orbits should be toggled on.
The same part of the sky from Earth. Here in the morning sky we'll find a grand
planet rendezvous in early Feb 1990. Use Menu (I)dentify. Change Speed to suit.
Note ra/dec coordinates of center cross, Sun with 1hr long rays.
>>Viewing Planets Up Close
Viewing Planets Up Close
You may Zoom and view the solar system from any angle, but the Sun will always
be in the center as long as the program is in `Space Mode'. To view a planet up
close, lock on to the planet by moving the box cursor (which appears when you
press [T]rack) over the planet and then press [Enter]. The program will then be
in `Planet Mode' with the planet at the center (the planet's name will be shown
in the control bar) and you can Zoom up to 32kX. From 270 a.u., the planets are
all nearly the same distance away, so at a given magnification they will appear
scaled to each other. When Jupiter is golfball-sized, Earth will be pea-sized.
In the next screen Saturn will already be locked in, so you don't need to do
the Track operation. You will also see the solar system with all the asteroids
and comets included with the demo. An interesting sight, but because it takes
some time for the program to calculate and draw so many orbits, there will be a
pause any time the screen is changed.
>>Tracking on to Saturn
Saturn>1>11/16/1989>200>16>-6>300>111111111>11111111111111110000>
TRACKING ON TO SATURN
Using [T]rack, Saturn has been locked on for close viewing. Dance is now in
PLANET MODE. Even at this distance the orbit of Saturn's outer most satellite,
Phoebe, can be seen. All asteroids/comets included with the demo are shown.
>>Saturn's Satellites
Saturn>1>07/01/1990>200>1k>0>293>
SATURN'S MAJOR SATELLITES
At 1000X from our distant location, Phoebe's orbit is partly off screen. You
can (I)nvert for north to be down (note north-pointing arrowhead). Identify
from Menu labels satellites. Zoom up. Press any other key to resume simulation.
>>Saturn Up Close
Saturn>0>11/16/1989>200>32k>0>343>
SATURN UP CLOSE Subtle shades and shadows for a nice view. Watch as Titan
moves up from below. Toggle orbits on/off. (I)dentify the satellites, (R)otate
to better see the rings. At this time the rings are highly tilted to the Sun,
so Saturn casts a short shadow on the ring-satellite plane.
>>Comets Revealed
SM>1>->100>0.5>-13>90>00000000000101110000>
COMETS REVEALED
A small comet sampling as seen from afar. Note the two parabolic orbits. Such
comets, seen only once, may approach from any direction. The orbits of period-
ic comets Halley and Encke are also present. Zoom up and Identify.
>>Halley Perihelion
SM>1>10/15/1985>1k>32>-10>330>111110000>00000000000100000000>
COMET HALLEY PASSING THROUGH PERIHELION ** Set Speed to suit. Orbits on.
Looking down Halley's long orbit toward the sun. The comet moves north of the
ecliptic only near perihelion, and plunges south through the ecliptic between
the orbits of Venus and Earth. Never close to any planet, its orbit is stable.
>>Halley Apparition 123456789012
EM>1>12/15/1985>1k>0.5>-3>313>111110000>00000000000100000000>
HALLEY REVISITED - AN EARTH VIEW ** Label objects with menu Identify.
The 1986 apparition wasn't great; you can see why. Watch while the comet passes
through perihelion, Feb 8, 1986 (your PC will bleep). Notice the apparent speed
increase as the comet angles down for its southerly ecliptic plunge.
>>Halley Loops
EM>1>01/01/1990>10k>0.5>-8>143>111110000>00000000000100000000>
A LINGERING LOOK AT COMET HALLEY ** Identify from the menu.
Below Leo you can still find Halley cycling its way to the far reaches of its
orbit. Such epicycles are due to the parallax caused by the Earth's orbital
revolution. Watch for several years; speed the simulation up if you wish.
>>Orbital Simulation
The Simulation Nature of Dance
Dance is an orbital simulator. This means that whenever you are viewing the
Dance heavens, the program is constantly calculating the gravitational effects
that the various bodies have on one another and moving them accordingly. In the
program `real' distances, masses and velocities are operating according to
Newtonian gravitation in three dimensional space, and the results are scaled
and transformed to the two dimensions of your screen. Dance is a detailed work-
ing model of the solar system that can not only show views and events that are
calculable, but also simulate perturbations and other complex multiple-bodied
orbital interactions that are generally not. Being able to predict orbit-
changing encounters of the past and future is an exciting and unique aspect of
Dance. With the full database of asteroids and comets you can discover events
and causes that very likely no one else knows about.
The next simulation shows an interesting future event with comet Kojima that
many know about now because its been used as a Dance example on many occasions.
Comet Kojima was discovered in 1970, has a period of nearly eight years, and
has been very regular for the previous three apparitions. During the encounter,
simulation will slow as Dance performs more calculations to maintain accuracy.
The strongest change to the comet's orbit will be an increase of inclination to
the ecliptic plane. You may slow speed to 2000-5000 for better accuracy. [PgDn]
>>Comet Futures
SM>1>09/01/1995>10k>8>-35>90>111111000>00000000000010000000>
A STRONG PERTURBATION Kojima's orbit, like most periodic comets, is chaotic.
Simulation reveals a strong orbit-changing Jupiter encounter during 1996-1997.
Result: an earlier, brighter apparition. Encounter distance (in planet radii)
will appear upper left. Jupiter's outermost satellites are out about 320 radii.
>>Bright Asteroids
SM>1>09/20/1990>5k>8>-90>90>111110000>11111000000000000000>
BRIGHT ASTEROIDS Ceres is the largest; nearly 1000 km diameter. Only Vesta is
ever brighter than mag 6. Change Latit from Menu to 10°S (select, cursor and
[Enter] twice). Note orbit of Pallas. Object Status shows location/ magnitudes
for the date. Vernal equinox direction (0° Longitude) is shown at 90° N/S Lat.
>>Asteroids in the Sky
EM>1>03/01/1989>2k>0.5>-10>270>111111110>00111000000000000000>
ASTEROIDS IN A STARRY SKY Looking towards Sagittarius from Earth in 1989.
The motion and paths of several bodies are seen. Watch the epicycles through
1989. Planet coordinates are on the (A)ccess screen; asteroid position/magn on
the Object Status screen. In June-July Vesta was at maximum brightness.
>>Asteroid 1989FC
SM>1>02/01/1989>200k>64>-20>45>111110000>00000000001000000000>
1989 FC - A CLOSE ASTEROID Our closest known brush with an asteroid, 400,000
miles, occurred in March 1989. Though small, 1989FC would have caused havoc had
it struck. Dim and fast moving, Earth-crossers are hard to find. You can check
out dozens in DANCE. Note date and minimum distance (Earth radii) for 1989FC.
>>Orbital Resonances
Orbital Resonances
Asteroids with periods that are a simple ratio to Jupiter's are regularly
perturbed by it. Resonances have depopulated the Kirkwood gaps, but resonances
with ratios near one can provide an island of orbital stability. These `island'
resonances provide one classification for Asteroids. Trojan asteroids, with a
ratio of 1:1, essentially share Jupiter's orbit. This is the Lagrangian reson-
ance with the asteroid nominally 60° ahead or behind Jupiter. There are over
100 known. Hildas are another large group with 3:2 resonances.
Resonances are also found among the satellites of the Jovian planets. The
Galilean satellites have period ratios very nearly 1:2:3:4 (check the Access
information screen for Jupiter when in Planet Mode). Like the hands of a clock,
they have regular `meeting places'. The Saturnian system is full of resonances;
and only there are satellites found with Lagrangian (co-orbital) resonances.
When you have the Saturn system on the screen in some of the following simul-
ations, press [A]ccess to see satellite information. Note the periods for co-
orbital satellites and other resonances. Return to the simulation with [Esc].
>>Tuned Asteroids
SM>1>07/01/1987>20k>8>-90>270>000010000>00000111000000000000>
ASTEROID RESONANCES - LIVING WITH JUPITER (inner planets are off for speed)
Some stable resonances. Shown: Hilda, the first 3:2 resonance found; Achilles,
the first 1:1 Trojan asteroid. Thule, the only known 4:3, is rather strongly
perturbed every 3 Jupiter (36 Earth) years. Watch through 2018.
>>Tuned Satellites
Saturn>1>07/01/1990>5k>4k>-70>35>00000000000001100>
SATELLITE RESONANCES ** Toggle orbits on/off to see Hyperion. Slow down?
With a 3:4 resonance, Hyperion receives a kick from larger Titan every three
revolutions causing precession of its eccentric orbit. Refresh with (E)rase to
see current paths. Inner satellites are off for speed.
>>Solar Precession
Saturn>1>07/01/2005>20K>512>-90>270>00000000000000001>
The Sun causes relatively rapid orbital precession for Saturn's Phoebe and the
outer 8 Jupiter satellites. As these weakly-bound bodies move toward the Sun,
they accelerate, expanding the orbit slightly. The effect reverses as they move
away. Watch this produce a precession of Phoebe's periapse. Note Sun direction.
>>Doing Orbital Experiments
Doing Orbital Experiments
Orbital elements of real or hypothetical objects orbiting the Sun can be
placed in a text file and loaded into Dance. On the next screen you will see
four hypothetical objects with the same period but with very different eccen-
tricities. Such examples can vividly illustrate basic principles of orbital
mechanics. An introduction to the basic theory, along with simulation examples,
can be found in the Dance manual.
Examples of other enlightening experiments: 1) using hypothetical objects to
see whether regularly spaced, nearly circular orbits between the Jovian planets
are stable. 2) How, with a `primordial' distribution of asteroids (near-circu-
lar and regularly spaced), the Kirkwood gaps arise. Such experiments involve a
lot of objects and time. A reasonably fast PC with coprocessor is recommended.
Very long simulations can be saved in Resume files and run over several nights.
>>Orbital Experiments
SM>1>->10k>8>-90>90>000000000>00000000000000001111>
Four hypothetical objects with the same period. Note the semimajor axes are the
same, as expected from basic orbital theory (the period is determined solely by
the semimajor axis and mass). High speed simulation error is also illustrated.
SP4 precesses due to too few calculations as it zips through perihelion.
>>The Complete Solar System
Dance - The Complete Solar System
In the above presentation you have seen a small sampling from what is prob-
ably the most complete, detailed, dynamic solar system model ever created.
Perhaps you found some terminology and phenomena with which you aren't yet
familiar. This shouldn't bother you in the least; Dance can be enjoyed at many
levels and for many purposes, and its a great way to learn and instruct.
Dance is a graphical working model of the solar system for anyone with the
interest and curiosity in the family of objects that orbit our sun. With Dance:
Observe the `dance' of planets, asteroids and comets against the starry sky.
View the planets and their satellites from exotic and revealing perspectives.
Watch comets being flung into new future orbits. Check out asteroids that can
pass close to Earth. Use Plot Asteroid to see the fascinating distribution of
4200+ asteroids on the date you have just entered (something we couldn't do in
the demo), or use it to identify an asteroid you have found in your telescope.
Plan an evening's observing agenda, or a season's. Discover special future
viewing opportunities for planets, satellites, comets and asteroids. Enter the
orbital elements of a newly discovered asteroid or comet and see where it has
been, and where it can be found. Design and run orbital experiments to eluci-
date orbital phenomena and processes. It goes on and on. Never before has the
solar system been so accessible.
>>Ordering and Updates Info
Ordering and Updates
DANCE OF THE PLANETS, version 1.3, is available for $165 plus shipping from:
A.R.C. Software
P.O. Box 1974D
Loveland, CO 80539
For information or ordering call 1-303-663-3223. MC/VISA accepted as well as
authorized purchased orders. Postage paid on domestic orders paying by check or
money order. Foreign orders must be prepaid (charge cards accepted) and include
$25 for shipping and handling.
Version 1.5 is scheduled for March, 1990. Among the many new features:
* Properly scaled telescopic views from Earth with detailed images of the
inner planets.
* A large stellar/non-stellar database with supporting features (constellation
lines and labels, a FIND and object information facility, etc.).
* Planet-centered views of close encounters with comets and asteroids.
1.5 with the extended data bases will be $195 plus postage, and a $75 upgrade
for owners of version 1.3 and earlier. Inquire as to availability and a special
pre-release offer. Club, institution, dealer and distributor inquires welcomed.
>>End
SM>1>->100>0.5>-10>270>111111111>00000000000000000000>
This is the end of the demo. Press [Home] for demo contents. Or put some aster-
oids in the simulator that you haven't seen yet: Press [A]ccess, select Object
Status. Toggle Hidalgo and Icarus on and [Esc] back to the simulator. At the
time of their discovery these were the farthest and closest to the Sun.