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Visual respresentations of topics in Astronomy

  1. Dec 3, 2012 #1
    Hello everyone. It is exciting to discover your forum here.

    I am hoping someone might be able to point me in the right direction for finding any symbols, charts, diagrams, written formulas, et cetera (ANYTHING) that represents or communicates or otherwise serves to explain any of the following concepts:

    The habitable zone - both general and specifically for our solar system
    Earth's rotation and/or a body not being tidally locked
    Earth:Moon size ratio (especially how this is unique compared to other planet:moon ratios)
    How the Moon slowed Earth's rotation during formation
    How the heating and cooling of Earth because of its rotation creates weather
    Moon's tractive force

    This diagram that represents the relationship between the size of the Earth and Moon is an example of the type of thing I am hoping to find.

    GP EARTH MOON 345.jpg

    Sorry if this is too vague or not clear. Any help is appreciated.

  2. jcsd
  3. Dec 3, 2012 #2


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    In order for me to attempt some contribution may I first please understand exactly how the posted diagram represents the relationship between the size of the Earth and Moon?
    Thank you for your attention.

  4. Dec 4, 2012 #3
    The two circles in solid black lines seem to represent Earth and Moon. Their radii ratio is about 0.27, which seems consistent with the diagram. Everything else in the picture looks like a geometrical build-up from the two circles.
  5. Dec 4, 2012 #4
    A - C Earth Diameter
    B - C Earth Radius
    C - E Moon Diameter
    C - D Moon Radius
    F - G - H – 345 Triangle
  6. Dec 4, 2012 #5


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    Yes, but the implication of the diagram is that there is some significance to

    1) the isoceles triangle that has the earth's diameter as its base
    2) the right triangle

    I see no significance to either one. The fact that you can draw them is not meaningful unless there is some significance to their dimensions and I don't see any. If the moon were twice as big as it is, you could draw exactly the same two triangles, they would simply have different angles.

    If in fact there is no significance to the triangles, then putting them into the figure is misleading.
  7. Dec 4, 2012 #6
    Here is some more info. Does it apply? For the purposes of my project it is enough to know that the dimensions all fit together as they do.

    Does anyone know of any charts, diagrams, formulas, etc for any of the other topics I posted?

    If we take the 3,4,5 triangle with the area of*6*we can calculate the measurements of the earth and moon.

    Take 3+4+5=12 and 3X4X5=60 and multiply those two 12X60=72 which adds up to nine. Now, multiply 72 times a factor of 10 you get 720. Take this 720 and multiply the ratio between earth and moon*11 to 3*to get the measurements of the earth and moon but simply put the 3,4,5 triangle holds the measurements to the earth and moon.

    The perimeter of the square around the Earth is 4 x 7920 = 31,680 miles.
    The circumference of the outer, dotted line circle is 2 x pi x radius = 2 x 22/7 x (3960 + 1080) = 44/7 x 5040 = 31,680 miles as well.
    Thus this ideal description of the Earth and Moon "squares the circle" by producing an equal perimeter and circumference.
  8. Dec 4, 2012 #7
    @tractive: The context is still unclear. Let's try not to miss each other. Some things to consider:

    1) You can always reduce a complex relationship to a simple one, by throwing away information. Keep information that isolates and describes a distinct element of the problem.

    2) The problem is physical. The peculiarity of the moon and Earth raises a question about the moon's origin, not about numbers. I'm not sure what you mean by ideal, but I don't think it relates to the question.

    3) No matter what you draw, the dimensions will all "fit together as they do". That's not about the Earth or Moon. There's nothing wrong with your diagram, it's just unclear what it expresses.

    4) Some different ways of measuring size: mass, volume, surface area, perimeter. Averages, maximum, minimum. ..."in the x direction." The word 'size' is in the way.

    5) So , for
    "Earth:Moon size ratio (especially how this is unique compared to other planet:moon ratios)". I think the unique relationship you are looking for is:

    Moon/Earth > {any other moon}/{its planet}
    (I'm measuring mass)
    So the diagram is missing the comparison to the other planets and moons. The "greater than" sign is more important than the exact numbers involved. Also the ratio Earth/Moon is substantially to vastly greater.

    Two objects with intersecting orbits will eventually collide. The planets in our solar system have cleared their orbits of "debris". Moons are small enough to be tag-along debris. Our moon is too massive.

    Mass isn't necessarily conveyed by average radius/circumference. Density matters! Some objects are highly irregular.

    The same side of the moon always faces the earth. It is as if the moon is a direct extension of the Earth's own rotation, instead of exhibiting its own, distinct motion. :)

    We aren't looking for a unique ratio; we're looking for reasonable ways the moon could have come to orbit the Earth. Large objects in close proximity tend to have unstable interactions, or just collide. There are some good introductory videos about the three-body-problem and lagrange points (NASA orbited one with a satellite for the first time recently, and talk about it in a clear way), that don't require the maths (which I don't know).

    I hope that helps a little. Your ideal description of earth and moon doesn't relate to the question. In general, with physics, whatever happens in the universe, happens. The moon is just that-size. This is a physical fact we are presented with. It happens to raise questions about origin. We cannot reach back in time and see what happened, so we have to investigate. These and other facts have led astronomers to hypothesize that the moon was once part of the Earth. So, in this case, a good representation of the "unique" relationship is multifaceted.

    To me, as long as we mistrust our own conclusions --especially if we can explain everything-- we can find the scientific method on our own.

    I'm not trying to be hard on you, just flag you down before you get too far down a particular road.

    Hope that's of some use. I think nobody's sure what you're up to. No foul.

    Be well!

    P.S. I teach myself math and physics, so if you have any questions about how to tackle these subjects alone, don't hesitate to drop me a line.
    In general, Khan Academy is amazing.
    Last edited: Dec 4, 2012
  9. Dec 4, 2012 #8
    No, this is all good information. Thank you.

    The diagram I posted is not my own. I am not looking to develop my own charts, rather I am just working on a visual story of why we have ocean waves on Earth. The factors I would like to represent, the list I first posted, are what my research has lead to and I thought astronomers and physicists might know symbols or diagrams commonly used to communicate the concepts. For example, just as the pi symbol represents pi, maybe astronomers have a shorthand symbol to communicate the habitable zone of a solar system. Or I could even use a written formula of, say, calculating the moon's gravitational pull. If there is one.

    I apologize, I really know too little. But I was posting here assuming I would get pointed in the right direction. I will check out Kahn. Thanks!
  10. Dec 4, 2012 #9
    Oooooooooooooooooh. I get it. You're kind of hunting for iconography? But not just icons. Representations that express the essential qualities AND measured relationships -- because it's physics -- maybe?

    now that strikes me as a very interesting question.

    I'll trim down my previous answer a bit so nobody gets put off. Maybe somebody knows.

    Have you thought about inventing some, as an art project or something? Good design is catchy. Creating symbols is tough, but fascinating. It could be wonderful to see what someone comes up with to communicate these ideas.

    My friend, we all know very little.

    Don't have time for it right now, but I'm interested in your question. Bug me about it if you don't find what you're looking for. For example, in a game level I'm designing (personal project, it'll never be done), "this direction currently down" is communicated by a plumb line with a bob. :)
    Put angle marks on the wall, and now you know how far off this line is from what's "supposed" to be down. Just information, but concise and physical. Those are just pretend answers, too. But maybe that's what you need, here.
  11. Dec 4, 2012 #10
    Okay, not to spam you, but I admit to being obsessed with this problem (expressing math and physics in a natural way). For example:
    Don't bother to read the blog. The cards, the hanging pentagon and the puzzle are all physical solutions to the problem. ;)

    Some things that come to mind (hope this isn't too random)

    1) The origins of circular motions can be distinguished.
    This realization is the basis for Classical Mechanics.
    You're on a boat. Go to your cabin, put your book on the bedside table, lie down, go to sleep. If the sea is calm, you can do these things exactly as if you were on dry land, not-moving. The book is next to you on the table when you wake. Moving at a constant speed in a straight line, we experience no force. We can't tell. There are also an infinite number of ways we could have been pushed, and then drifted.

    Now get on a Gravitron. You're mashed against the wall. No matter where you stand, you are pushed away from one, exact point.

    Newton built a bridge between straight-line measure and curves, using Classical geometry.
    Symbols are efficient and powerful, but the groundwork is geometry.

    A good starting place is to assume that distinguishable force will be an Origin (or Focus) of a conic section. Khan Academy has good videos on this.

    2) Don't believe anyone who says a relationship can't be visualized.

    3) Tell a story. When we tell stories we fill in details. To figure out the different forces operating on the oceans, talk yourself through a tide chart. Where are the high and low tides? How long are the cycles, and what is the moon up to?

    4) There is a fundamental kind of equation that all waves satisfy that is conveniently called the Wave Equation. This is a little tricky. Modeling physical phenomena means Partial Differential Equations, but let's say we want to avoid that at all costs. It can be very VERY frustrating to read about wave mechanics without some experience with Partial Differential Equations.
    A couple of things to note:
    a) Waves pass through media. If you hear a train whistle from a mile a way, the air didn't move a mile to bring you the whistle. Each molecule pushes toward its neighbor AWAY from the whistle (the unique origin of the force :) ), then the imbalance in pressure pulls it back more or less where it started.
    b) Waves transmit differently in liquids and solids. Air is extremely pliant; it can be compressed. Waves that strike an incompressible medium transmit perpendicular to their original direction, along the surface. Drop a stone in water, and the waves go sideways along the surface, even though the motion of the pebble was vertical.
    c) One way the motions are the same is that ocean waves pass through the water, leaving the molecules in the same place. A buoy bobs up and down on the waves. It does not move in the direction of the waves.
    d) In general, waves travel at a constant rate of speed over time, and are only slightly attenuated by transmission through a medium. In fact, the FIRST assumption to make about waves is that they don't lose any force at all, and THEN worry about how much force is lost by transmission. Transmission loss in air is very high because the air molecules are actually pushing back and forth.
    e) Some other force must be operating, to cause the tides. It's not necessarily obvious at first that waves are a result of other motions, and that the forces causing the rise and fall of the tides does so independently of the waves crashing on the beach.

    f) in air, we don't usually consider displacement of the medium a signal. To a microphone, wind is noise. You use a totally different device to measure that. With ocean waves, that's probably not a good assumption. A tsunami is a signal we want to keep track of. It may be caused by a sudden displacement of ocean water: an undeground eruption; a chunk of land sliding into the water, etc. I believe the size of the oceans, and the difference of medium (the displacement may spread in a similar manner to a signal in air, to balance the sudden change in volume: an outward radius from a point. Quite unlike wind) are factors which determine what kinds of phenomena create waves in an imcompressible fluid. I'm not there yet with the math.

    g) the distances are vast. If 10 people talk at once, the sound waves all interact. In the oceans, waves can add to each other in and randomly create super massive waves which didn't exist before.

    h) Oscillatory motion is Harmonic Motion. A buoy bobbing up and down is a perfect example. I know some good mental pictures for this, but let me start by saying that an oscillation is a circular motion. The circle does not exist in any real plane: its origin is imaginary. How do we know it's circular? Paint a dot on a bicycle wheel and spin it. Look at it straight down the front, where you can no longer see the circle. The motion of that dot is oscillatory.

    Don't know how widely you're casting the net, but here are a couple of thoughts about collecting and presenting information:
    Edward Tufte, "The Visual Display of Quantitative Information" is excellent. He focuses on clean graphic design, and putting many variables together in a natural and accurate way.

    There is an old idea called "situational geometries". Consider a puzzle like, "you have a wolf, a goat, and a cheese one one side of a river and they have to get to the other side. THe riverboat can carry only two passengers. If you leave the wolf alone with the goat, he'll eat it. If you leave the goat alone with the cheese, HE'll eat it. How do you get them across the river?"
    Different kinds of problems are naturally expressed in different ways. A river, a wolf, a goat and a cheese are not just easy to understand, they make the problem easier to solve than if you write it in abstract algebra.

    Unique geometries for particular problems. Here, "eating one another", obstacle/river, and "only x can fit on the boat", "one side of the river and the other" are immediately accessible. They are more than that: SOLVING the problem is easier with a riverboat, a wolf, a goat, and a cheese, than abstract algebra.

    For physics, the natural language is generally Vectors, but the ideas expressible with vectors do not require vectors to communicate. For example, with fluids, the vector operations for determining "circulation" and "flow" are probably exactly what you picture in your mind about water when you read those words.

    Let me know what you find, eh? Maybe we can do better if it's dissatisfying.
    Last edited: Dec 5, 2012
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