Proof that the moon is closer to Earth than the sun

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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berkeman
Mentor
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!
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!

mp3car and Stephanus
wabbit
Gold Member
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

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mp3car and marcus
William Henley
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
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.

marcus
Gold Member
Dearly Missed
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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
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.

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wabbit
wabbit
Gold Member
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 : )

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Monsterboy, billy_joule and berkeman
wabbit
Gold Member
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 :)

William Henley
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 : )
Why don't you start a new thread then?

berkeman
russ_watters
Mentor
Define "proof". To me the fact that we've sent people to the moon and spacecraft near the sun is pretty good proof.

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.

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".

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wabbit
Staff Emeritus
2019 Award
I think you can't do much better than Russ' answer. We've gone to the moon.

wabbit
Gold Member
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.

russ_watters
Mentor
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.
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.

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wabbit
Gold Member
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 )

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mfb
Mentor
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.

wabbit
Gold Member
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.

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 :)
I did this with my 5 year old and he got it.

wabbit
Chronos
Gold Member
Se lunar laser ranging experiment for evidence man has been to the moon.

wabbit
Gold Member
Se lunar laser ranging experiment for evidence man has been to the moon.
I agree this is a good answer, though a tennis ball is easier to get hold of than than a laser ranging apparatus : )

ShayanJ
Gold Member
Define "proof". To me the fact that we've sent people to the moon and spacecraft near the sun is pretty good proof.
A 9 year old girl still doesn't trust NASA(or any other such organization) as much as you do. That's simply another thing she should learn. So what you say, can't be a proof for her. She should understand things herself now.
Also, a more important thing she should learn now, is how to think logically and draw conclusions from demonstrations and reasons. Telling her people went to moon and said it is as such, so you should accept it, doesn't help that.

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Monsterboy and wabbit
Se lunar laser ranging experiment for evidence man has been to the moon.
Those could have been placed there by an automated probe. Footprints on the otherhand...

Non-NASA probes have photographed the landing sites in high enough resolution to show the footpaths of the astronauts:

How did the ancients know that the moon was closer than the Sun?

It really would be interesting to hear from an "early childhood education" researcher on this topic. It's a great question. What does "prove" mean to a four year old. Is she being obstinate about it? If so why. Is she defending a perception or just devoid of any? If she's open to it, what would be the most effective/important/valuable experience? and what would be the real goal? Would it be so she wouldn't fall prey to false authority? Would it be to develop a positive sense memory of questioning something with/to her father? Would it be to find out just how abstract she can get? Would it be so she can look at the moon, close her eyes and get dizzy. The last one would be my wish for her, but that's because it means a lot to me. Kids are as different as adults. What would suit her way of approaching things?

I just heard a thing on the radio about Big Bird from Sesame Street. Oscar the Grouch showed up... (the real guy who does the voice and mannerisms did both) Oscar was a brilliant character. They both were. And it brought back that very sensual memory of listening to them as a kid. Kids brains are doing something pretty different than adult brains I think.

nitsuj
wabbit
Gold Member
I think kids are curious and interested in learning, but sometimes they learn that it is better not not ask too many questions and just accept the authorities answer, whether it is "The earth if flat, don't listen to heathens who deny the word of God", or "The earth is round, don't listen to bigots who deny the word of Science".
But they can keep asking new and interesting questions when they're told "the earth is round as you can see when you look at the horizon at sea, or in a vast plain, from lower and higher ground, and as you see the top of that mountain appearing over the sea before its base does as we approach it".

To me the goal would be to foster learning and understanding and fuel that thirst for it, which recourse to authority quells.

Then again, I m not involved in teaching kids, so I do not have any representative sample. I agree it would be great to hear from someone who does.

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I would think that would be a relic of our evolution. We had no concept of experiment and observe, so the major reason we think the way we do is about survival. Learning that from our parents is far more efficient than having the brain figure it out intellectually. Our intellect evolved over the past million years; monkey see, monkey do behavior however evolved many times longer, so that's what our brains are really fine tuned to do.

The bible says the moon isn't really there at all, it's just a ball of light. Bill Nye got boo'd in Texas for casually mentioning this followed by the fact that we now know it simply bounces light from the sun. These were adults who's parents watched men walk on the moon.