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Proof that the moon is closer to Earth than the sun

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  1. May 1, 2015 #1
    How can I prove to my 9 year old daughter that the moon is closer to earth than the sun? At the moment, she has read it in books and this information has the same status as unicorns and fairy princesses!
     
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  3. May 1, 2015 #2

    berkeman

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    Welcome to the PF.

    Explain the 2 types of eclipses to her, and show her pictures and animations. And find out when the next solar eclipse is -- Road Trip! :smile:
     
  4. May 2, 2015 #3

    wabbit

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    Great question. I agree with berkerman, eclipses would be the best proof, and even better if she can verify it by witnessing a partial solar eclipse and the associated lunar eclipse.

    Another proof, a little harder to grasp but based on readily available evidence, is the phases of the moon : if the Sun was closer, the moon would be more or less always fully illuminated. Drawing some diagrams with relative positions and light rays, we can see that the succession of phases only happens when the moon is closer.

    This can actually be extended to Aristarchus' calculation of the ratio of their distance (off by a factor 20 but only as a result of measurement imprecision), but this requires some geometry.
    http://en.m.wikipedia.org/wiki/Aristarchus_of_Samos
     
    Last edited: May 2, 2015
  5. May 2, 2015 #4
    I agree with Wabbit, a solar eclipse would be the best proof, you could show her a video of one or it would be even better to actually witness one.
     
  6. May 2, 2015 #5

    marcus

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    It might work to go straight to drawing skinny right triangles, like Aristarchus. His way is not so abstract and you don't have to wait for an eclipse or accept other people's accounts and lore about eclipses. You can actually see for yourself that it is farther.

    By spreading your arms to measure an angle and drawing a skinny triangle in the dirt.

    Samos is an island just off the coast of what is now Turkey. Pythagoras was born and grew up on Samos.
    The city Miletus was in sight on the mainland, across the bay. Thales was born in Miletus and was Aristarchus teacher.

    On a half-moon late afternoon when the sun is nearly ready to set, the moon is still fairly high in the sky.
    In the late afternoon, the next time there is an exact half moon, spread your arms and point with your right arm at the sun and your left at the moon. It's a big angle! Clearly more than 80 degrees, nearly a square corner!

    At that moment you have a right triangle sun-moon-earth with the right angle at the moon, and a large angle at the earth. The insight is that the angle at the sun is small, so the triangle must be skinny.

    Try drawing right triangles EMS with the right angle at M, and the angle at E really big, like your widespread arms, more than 80 degrees.
    The only way the triangle can be is long skinny, with a very small angle at S

    the distance ES has to be way longer than the distance EM

    it's empirical about triangles, we experience triangles. Let your daughter directly experience a right triangle the next afternoon there is an exact half moon high in the sky and the sun is down near the horizon.

    Aristarchus got it right.
     
    Last edited: May 2, 2015
  7. May 2, 2015 #6

    wabbit

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    Maybe we should do a thread about elementary astronomy relying on naked eye observations following in the footsteps of the ancients. I don't know how much of that is taught in school (approximately none that I know of...), but it is a pity not every schoolkid can actually prove that the earth is round, that the sun is farther than the moon, or understand phases of the moon and perhaps retrograde motion and so many other things that are accessible with basic geometry and concrete observations. And it even gives a reason to look up up at the stars : )

    And when you look at the Almagest or the remnants of the Antikythera, it's obvious they made a lot of those observations and geometry.

    In any case, @Rabbani, if you have more questions like this please come back, the wabbit for one loves them : )
     
    Last edited: May 2, 2015
  8. May 2, 2015 #7

    wabbit

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    About the phases argument : I think this could be made concrete with just a light source and a ball in a darkened room - this might beat a drawing :)
     
  9. May 2, 2015 #8
    Why don't you start a new thread then?
     
  10. May 4, 2015 #9

    russ_watters

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    Define "proof". To me the fact that we've sent people to the moon and spacecraft near the sun is pretty good proof.
     
  11. May 4, 2015 #10
    Show her a youtube video of a solar eclipse. The moon visibly moves in front of the sun, even the ancients knew that the moon was closer than the sun.
     
  12. May 4, 2015 #11
    I like the tennis ball with a flashlight. I don't know what exactly made it snap, but once you see that lit side, then shaded side, then the full one, then "where did it go", you follow the way it goes from one to the other, the the time of night and day it is visible, and at the same time you see (or experience) the tennis ball circling your head and the flashlight (or streetlight) way off - I just sort of saw it. And it practically made me dizzy. Still to this day it makes me dizzy. My dad used to point to the partial moon (often) and ask, "Where is the sun (flashlight)?" I just think being able to "see a machine operate" is going to be more effective than any terms or descriptions. It doesn't "prove it" in the abstract but it makes you believe it and feel it (which is most important in this case IMHO).

    There was one time we were laying on a warm concrete foundation looking toward Sagitarius on a moonless night. This was In Illinois, where it is 360degrees flat so literally my entire field of vision was sky and stars (which is key). We were looking at that crazy dark river of the Milky way, talking about how "right over there is Downtown" and... BAM! I literally felt like I was about to slide off the planet toward the Galactic South Pole, like I was back up against a wall and nothing below me. The perception of "It's way over there across an empty sparkling gulf" was just so clear that in a particular instant my visual cortex and limbic loop agreed, "well - that indicates extreme vertiginous peril. Grab hold of something while you enjoy this adrenalin".
     
    Last edited: May 4, 2015
  13. May 4, 2015 #12

    Vanadium 50

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    I think you can't do much better than Russ' answer. We've gone to the moon.
     
  14. May 4, 2015 #13

    wabbit

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    I don't quite agree - we're told that we've gone to the moon, we saw it on TV - that's hearsay, or an argument of authority(*). A concrete demonstration like the tennis ball is quite something else, it allows her to really understand things, not just accept them.

    (*) just in case someone wonders - no I am not doubting that we went to the moon, yes pictures are a bit more than hearsay - but still, reported evidence, not direct experience.
     
  15. May 4, 2015 #14

    russ_watters

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    Unless she's seen a solar eclipse herself, the tennis ball demonstration is just hearsay too. The other possible problem that not using an argument from authority* presents is that kids often have too much imagination and not enough logic to properly process such things. You can show her the demonstration, but that may not convince her that The Gods didn't just flip the sun over, exposing the dark side.

    *Note: argument from authority is usually not a logical fallacy. When to trust it is also something important to teach children.
     
    Last edited: May 4, 2015
  16. May 4, 2015 #15

    wabbit

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    Of course argument of authority can't be entirely avoided - but here, for one thing witnessing a partial eclipse is doable and a nice extra even - but the tennis ball proof doesn't require that : just look at a thin crescent moon. How is it illuminated ? Where can the light source be ? Soon enough she will "see" the Sun "behind" the moon, for it can only be there.

    Well you may include authority to say it is a sphere - but not quite : look at the succession of phases. Can you find a better explanation than a spherical shape illuminated by a distant source ?

    (Bracing for the too imaginative kid here - maybe strike that last question :wink: )
     
    Last edited: May 4, 2015
  17. May 4, 2015 #16

    mfb

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    You don't have to see a solar eclipse to understand the phases of the moon.
    In addition to the proof of the different distance, the child can learn and understand something about the universe.
     
  18. May 4, 2015 #17

    wabbit

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    About this, something a I found rather sad happened recently here in France for the recent eclipse : many schools had done no preparation whatsoever to use the event as a teaching opportunity, and had not made any provision for viewing it safely - so they actually kept the kids inside during recess for fear they would damage their vision if allowed to look at the eclipse.
     
  19. May 4, 2015 #18
    I did this with my 5 year old and he got it.
     
  20. May 4, 2015 #19

    Chronos

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    Se lunar laser ranging experiment for evidence man has been to the moon.
     
  21. May 5, 2015 #20

    wabbit

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    I agree this is a good answer, though a tennis ball is easier to get hold of than than a laser ranging apparatus : )
     
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