How to Verify that the Sun is a Distant Sphere, with Binoculars & Sunspots

[Mick West]

From past the orbit of Mars, the solar system looks a bit like the above. Earth is just a speck, not even visible here (at the end of the blue line). The sun is much larger than the earth, yet still seems small and far away. Its light shines equally in all directions.

Can we actually verify this? Can we prove the sun is not actually a spotlight shining on only half of a flat earth, like some people claim to believe?

Yes, we can do this in various ways but I like practical science experiments that are (relatively) easy to perform, so I'm going to focus on a few here, things that you can do yourself. We shall demonstrate:

1. The size of the sun is the sky remains almost exactly the same all day long, meaning the relative change in distance is very small, so it's very far away.
2. The Sun looks circular from every direction, so the Sun is a sphere
3. Over a single day sunspots remain in about the same position as the sun moves from horizon to horizon, so the Sun is very far away.
4. Over the 26 days sunspots move over the surface of the sun in a spherical path, so the sun is a sphere.

To verify the first two is relatively straightforward. All you have to do is take measurements (like photos) of the size and shape of the sun throughout the day and see if it varies.

Now the sun is incredibly bright so you can't just take a normal photo. You need to use a filter in front of the lens so you can block out most of the light. Still though you need a good zoom to be able to measure the size well (and to see sunspots, more on which later). But you can certainly do all of this with a camera if you have the right equipment.

A practical alternative is to use something most people will have access to - a pair of binoculars (or a telescope). Now it goes without saying you should never look at the sun though binoculars. Permanent eye damage could result. So instead of projecting an image of the sun permanently onto your retina you can instead project it onto a piece of paper.

This is a 2x4 piece of wood, about three feet long, attached to a tripod with cable ties (you don't need the tripod, it's just convenient). Each end of the 2x4 has some cardboard stapled to it. The top piece has a hole cut in it, aligned with one side of the binoculars, which are firmly fixed to the 2x4 with tape (and cable ties). You point it at the sun, and an image forms on a piece of white paper on the bottom card. You focus this image using the binoculars' focus knob.

This gives you a very safe and pretty high quality image of the sun. You can measure how big it is, and see if it changes through the day (it doesn't). You can also see if it implausibly changes shape (it remains circular)

For measuring the size, you can use some squared paper, as it gives a nice visual record.

Because the distance from the binoculars to the paper is fixed, then any change in the size of the sun would be reflected in the size of the projected image. No such changes were observed, and the sun stayed the same size and shape size from horizon to horizon.

We normally think of the sun as just a very bright light, but if you look closely you can see some detail in the surface of the sun - sunspots. We can observe how these move through the day, and see if they indicate the Sun is a sphere.

Now for reference, I recommend you get a recent image of the sun from the SDO, here's the one corresponding with today's images.

Just a couple of small spots, but enough to work with. I've got the SDO app on my phone, and used that as a reference. You can just make out the two spots in each image.

Now at first glance it might look like the spots are in the wrong place, but because we are projecting wth the binoculars rather than looking through them the image is inverted, it's upside down. Also the orientation of the SDO image isn't going to match the orientation of this image from Earth, as your latitude and the time of day will alter your viewing angle. So if we flip my image vertically and rotate it a bit you'll see that it lines up exactly. Drag the slider below to see this.
[compare]

[/compare]

So what happens to sunspots over the course of the day? Very little. They rotate based on the angle of the viewer, like the moon and the stars do (this is known as field rotation - you are rotating, so your field of view seems to rotate). They also move slightly to the right due to the rotation of the Sun. But basically the same side of the Sun is a facing you all day long, and since it's a sphere, and the same side is facing everywhere on the Earth, then that means it's a very large and far away sphere. Many times further away than the size of the Earth.

One thing we should be able to do after taking a few observations is to trust the SDO images match our images. This is what the sun looks like from everywhere in the world. It has been verified countless times because taking photos of sunspots is something people do hundreds of times a day, and something you can do yourself. But if you really want to, you can verify the following just by taking lots of photos for a couple of days.

Here's two days of photos of the sun, made into a time-lapse movie. It the 48 hours prior to the above SDO image which we verified:


Source: https://www.youtube.com/watch?v=AERs0LuANAQ


You'll notice that the sun is rotating from west to east, to the right. People often don't realize that the sun rotates. Viewed from Earth the Sun completes a full revolution every 26.24 days. So this two day period is about 1/13th of a full rotation (although with no fixed surface this does not have quite the same meaning as the rotation of a rock planet).

What is significant here is that we can see the rotation in the SDO images (and verify it with our own images). We can also see that this is the rotation of a sphere by observing sunspots (particularly larger ones in groups) and seeing that they move exactly as we would expect on a rotating sphere. You can see this somewhat with the sunspot on the right as it approaches the edge. However to really get a sense of the Sun's rotation (and roundness) have a look at a longer period, with more sunspots.

Source: https://www.youtube.com/watch?v=oInoNnPsxcA


Now you might argue this is "just an animation", but it's just a series of SDO images, images that are quite easily independently verified as I did above. This is verifiably what the sun looks like from everywhere on the globe, and verifiably how sunspots move around it.

One more thing we can do if we take photos of the sun with the same settings is compare them, and see they don't change though the day.

When there's some nice visible sunspots we can see how much the sun's image appears to rotate from my perspective (because of the rotation of the earth). Again, note the absolute lack of any change in size.

Hence we have demonstrated that the sun is a large distant rotating sphere, and by extension we have demonstrated yet again that the Earth is not flat.

 

[Henk001]

Years ago some of my students did a science project that goes even further. They indeed measured the solar diameter a bit like you did -- with a projection (through a small telescope) of the solar disk on a white paper upon which a circle was drawn almost matching the size of the sun and then measuring the time it took the suns image to cross this circle with a stopwatch -- and they continued to do so through a whole year. When they plotted the results in a graph you could clearly see that the suns diameter is largest in the beginning of january and smallest in the beginning of july -- the difference being a bit more than 3%. For observers living in the southern hemisphere this will turn out to be exactly the same. It is caused by the fact that the earth moves in an elliptical orbit around the sun with its perihelion in january.
This result also contradicts the FE model, because the sun is supposed to be further away in winter and the southern and northern hemisphere should see opposite changes.

 

[OTACHI]

The size of the sun is the sky remains almost exactly the same all day long,

What do you mean by "almost"?

 

[Mick West]

What do you mean by "almost"?

I mean the sun varies in apparent diameter by about around 3.28% over six months due to the path of the earth around the sun being slightly elliptical. So over a 24 hours day it with vary by (on average) approximately 0.018%, or 0.009% over a 12 hour daylight period. This amount is far too small to notice day to day, and can only be seen over six months by taking good photos

See:
http://webpages.charter.net/darksky25/Astronomy/Articles/sun/sunindex.html

Here are the two images side by side, where the size difference is subtle, but unmistakable. The image on the right, perihelion, is clearly larger. Carefully measuring the two images reveals that the aphelion (July) sun is about 96.38% of the diameter of the perihelion (January) sun. Calculations carried out using predicted differences in the distance to the sun at aphelion and perihelion (using Starry Night Pro) give a predicted change of 3.28%.

 

[Mick West]

I'm glad you brought it up though, as this variation in the size of the sun is another great verification of the size, motion and shape of the solar system. A DIY experiment could be performed like John Rummel did in the link above, and the values compared with the expected values for the real heliocentric model.

A camera like the Nikon P900 (with a solar filter) would be ideal for this, as you could simply take a photo every week or month for a year at full zoom (2000mm), and then plot the diameters on a graph (and make an animation of the change). Use a high sun to minimize refraction.

I just ordered a solar filter in anticipation of the August eclipse, so I can give that a go. I hope to make my own video of sunspot rotation.

The P900 is great as at maximum optical zoom the sun is about half the height of the frame, so it's easy to have a very consistent zoom setting with a measurable sun. Also lots of Flat Earth folk have a P900.

I experimented yesterday with using an IR filter which is pretty dark, but I was concerned about all the IR getting though and frying my camera, so I only took one shot which was still overexposed (at 1/2500 f/8 ISO 100).

The point of these experiments is to let people check the solar system themselves as easily as possible - and to also create experiments that are reasonably verifiable just by looking at a photo or video.

 

[Greylandra]

Mick, could you explain these relative terms in your conclusion please... (1) Large and (2) distant. Compared to what exactly? Further, it'd be really swell if you could provide the math work that might equal a radius of 696,000km and a distance of 149 million km for the sun based on your science experment above. Lastly could you also show how a subjective "Large and distant" sun might disprove a flat earth because a "Rotating sphere" shaped sun definatly doesn't cut it. Smacks of 3 year old logic... "that thing is round, ergo all the things must be round" heh.

 

[Mick West]

Mick, could you explain these relative terms in your conclusion please... (1) Large and (2) distant. Compared to what exactly?

Compared to the size of the Earth.

 

[Henk001]

could you also show how a subjective "Large and distant" sun might disprove a flat earth

In the flat earth model the sun is supposed to be hovering above the FE disk at a height of say 3000 mi. This is required in order to explain results of experiments like that of Erathosthenes. [ by the way: for every latitude when doing an Erathosthenes-like experiment you will find another height -- another failure of the FE model] In that case its distance to any observer should change significantly in the course of a day, and with it, its apparent size. Mick's experiment shows it doesn't.

it'd be really swell if you could provide the math work that might equal a radius of 696,000km and a distance of 149 million km for the sun based on your science experment above

It only shows that the sun has to be far away, and therefore very big compared to the size of the earth. The exact values of the distances in the solar system have been determined with other methods:

Short version: What we actually measure is the distance from the Earth to some other body, such as Venus. Then we use what we know about the relations between interplanetary distances to scale that to the Earth-Sun distance. Since 1961, we have been able to use radar to measure interplanetary distances - we transmit a radar signal at another planet (or moon or asteroid) and measure how long it takes for the radar echo to return. Before radar, astronomers had to rely on other (less direct) geometric methods.

for more see f.i.:
http://curious.astro.cornell.edu/ab...stance-between-earth-and-the-sun-intermediate

 

[Mick West]

I just used a very cheap ($12 for 10) solar filter for this, held in front of the camera (P900, maximum zoom).

WARNING: Don't do this with a camera with an optical viewfinder, as it could burn your eyes, causing vision loss or blindness. The P900 has a digital viewfinder, so is safe. Even so, incorrect usage may damage your camera.

Unfortunately there's practically zero sunspots today.

 

[Mick West]

Using it with an iPhone was rather poor if just held in front of the lens. Holding it far away worked out better.

Not sharp, but you could at least use it to verify there's no apparent change in the sun's diameter from sunrise through noon to sunset.

 

[Mick West]

Hmm, that's not even in focus . Here's a better focussed shot compared with a normal iPhone photo of the sun.
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Notice in the unfiltered shot there's an actual image of the sun from internal reflections.

 

[Trailblazer]

Further, it'd be really swell if you could provide the math work that might equal a radius of 696,000km and a distance of 149 million km for the sun based on your science experment above.

That would be very easily done with the P900 shot above. You can use the same full zoom setting and take a photo of an object of known size and distance and thus work out the angular diameter of the image frame at full zoom.

Then measure what fraction of the images diameter the image of the sun takes up. It wouldn't prove that that was the actual size and distance but it would prove that it wasn't consistent with what we see. (And the distance can be calculated using other methods.)

And, as @Henk001 says, a large and distant sun means that it cannot be hovering "inside the dome" as the FE model requires.

(Similarly, the FE model sun orbit requires it to move from a circle around the Tropic of Cancer in the northern summer to one around the Tropic of Capricorn in the northern winter. So the sun as seen from the northern hemisphere ought to shrink in size during the northern winter. In fact, we see the reverse: a slightly larger sun.)

 

[Mick West]

That would be very easily done with the P900 shot above. You can use the same full zoom setting and take a photo of an object of known size and distance and thus work out the angular diameter of the image frame at full zoom.

Then measure what fraction of the images diameter the image of the sun takes up.

The sun takes up 2448/4608 pixels. or 53.125% of the photo. At this zoom (2000mm). I'd previously measured that the FOV is 160mm at 8000mm or .16m at 8m

Hence at 149,000,000 km away the diameter = 149000000*.53125*.16/8 = 1.583 million km, which is wrong as it should be about 1.3914 million km.

This led me to discover an error in my previous assumptions (and hence the above diagram). The camera is not an idealized pinhole camera, it's a complex compound lens camera, so the FOV need not converge to a focal point in the camera. While the field of view at full zoom scales linearly, it does not scale down to zero at the camera. It scales down to zero at what I have initially experimentally determined to be about 2.5/5m behind the camera! This changes the equation a bit.

I'll need to do some more tests tomorrow to get an accurate value.

 

[Mick West]

This led me to discover an error in my previous assumptions (and hence the above diagram). The camera is not an idealized pinhole camera, it's a complex compound lens camera, so the FOV need not converge to a focal point in the camera. While the field of view at full zoom scales linearly, it does not scale down to zero at the camera. It scales down to zero at what I have initially experimentally determined to be about 2.5/5m behind the camera! This changes the equation a bit.

Well that was wrong too, it's NOT linear. I carefully measured the FOV at 5,6,7 and 8 meters and got a line that curved slightly. It turns out that the field of view of a Nikon P900 varies with focus. So measuring when focussed on a nearby object will give you a different FOV compared to a far away object. You need to find the FOV at a much larger distance.

That's the measurements I've taken so far. You can see the FOV converging as the distance increases. the 31.85m was the longest I could get in my yard on a level surface.

I suspect the 1.025° is close to the actual FOV at infinity as it gives a much more reasonable 149000000*.53125*.0179 = 1.4169 million km, suggesting the actual FOV at infinity is slightly narrower.

 

[Mick West]

This solar position calculator:
http://www.instesre.org/Aerosols/sol_calc.htm

Gives. 1.007759 AU for yesterday's photo. one AU is 149597870700m, so the distance to the sun was 150758575662 meters.

The Sun's diameter is constant, at 1,391,400,000, given this covers .53125 of the frame then a full frame is 1391400000/.53125 = 2619105882m.

Hence the field ratio (width of field at a distance / distance) of a P900 at infinity is 2619105882/150758575662 ~= 0.01737, with a FOV angle of 0.9953°

This matches the converging FOV as seen above. 0.01737 should be an accurate value for any far focussed image (like > 100m away)

 

[Greylandra]

That would be very easily done with the P900 shot above. You can use the same full zoom setting and take a photo of an object of known size and distance and thus work out the angular diameter of the image frame at full zoom.

Then measure what fraction of the images diameter the image of the sun takes up. It wouldn't prove that that was the actual size and distance but it would prove that it wasn't consistent with what we see. (And the distance can be calculated using other methods.)

And, as @Henk001 says, a large and distant sun means that it cannot be hovering "inside the dome" as the FE model requires.

(Similarly, the FE model sun orbit requires it to move from a circle around the Tropic of Cancer in the northern summer to one around the Tropic of Capricorn in the northern winter. So the sun as seen from the northern hemisphere ought to shrink in size during the northern winter. In fact, we see the reverse: a slightly larger sun.)

Right... so could you please show me the assumption free measurement that isn't self referential for either the suns radius or its distance from earth that would allow for a precise calculation here?

 

[Mick West]

Right... so could you please show me the assumption free measurement that isn't self referential for either the suns radius or its distance from earth that would allow for a precise calculation here?

The point is simply to demonstrate it's a faraway sphere, not to measure it exactly.

 

[Greylandra]

The point is simply to demonstrate it's a faraway sphere, not to measure it exactly.

ok so lets run with your [..speculative statement with no evidence removed..] conclusion, the sun = "far away sphere"... got it. Now how did this dismantle the flat earth argument again?

 

[Mick West]

ok so lets run with your [...] conclusion, the sun = "far away sphere"... got it. Now how did this dismantle the flat earth argument again?

The Flat Earth argument is that the sun is nearby, like within a dome sufficient to enclose the known Earth. It's also frequently claimed the sun is a flat disk. This disproves both.

Now as the sun is a faraway sphere, then that makes sense in the normal model of the solar system. But how does it work in the Flat Earth model. How does the sun make time zones - one area dark, one light from millions of miles away. Can you draw a diagram?

 

[Mick West]

A bit better filter. This is just a sheet of "black polymer" filter from Thousand Oaks Optical. $20. I got it to make a cheap filter for my 500mm Sigma lens on my Canon 7D. This photo is using the filter on my Nikon P900 by just holding it in front of the camera.

We are at a bit of a minimum for sunspots right now, but that will change. The point about sunspots again is that this image is the same regardless of where on Earth you view it from. So it's a faraway sphere.

 

[Trailblazer]

The point about sunspots again is that this image is the same regardless of where on Earth you view it from. So it's a faraway sphere.

Yes, unless @Greylandra can show us otherwise, there is no way for a nearby sun (à la flat Earth) to appear the same size and shape, and with the same face presented towards the viewer, from anywhere in the sunlit portion of Earth.

(As for measuring the distance to the sun from first principles, both Flamsteed and Cassini managed to do this to within better than 10% as long ago as the 1670s, using different methods.)

 

[Whitebeard]

Binoculars strapped to a 2x4 with a couple sheets of cardboard including rough cut holes may look like its based on scientific method to you... this is 2017!

Its the most basic form of solar observation, its called the projection method, I did it at school in the 1970's as part of a science project and its still the easiest way for those who are interested to start solar observation

Most folks use a small telescope, but what are binoculars but two small telescopes strapped together?

 

[Mick West]

A comparison of the size of the sun at sunrise (at least when the sun was first visible), and local solar noon here.

 

[Mick West]

Dang bird got in the way of the sun!

It does illustrate another way of taking photos of the sun - through cloud. I'd not really recommend it though. This was an accidental shot. I was actually photographing the bird.

 

[Neil Obstat]

View attachment 26521

Just a couple of small spots, but enough to work with. I've got the SDO app on my phone, and used that as a reference. You can just make out the two spots in each image.
View attachment 26522

Now at first glance it might look like the spots are in the wrong place, but because we are projecting wth the binoculars rather than looking through them the image is inverted, it's upside down. Also the orientation of the SDO image isn't going to match the orientation of this image from Earth, as your latitude and the time of day will alter your viewing angle. So if we flip my image vertically and rotate it a bit you'll see that it lines up exactly. Drag the slider below to see this.
[compare]View attachment 26523 View attachment 26524 [/compare]


View attachment 26523 View attachment 26524

So what happens to sunspots over the course of the day? Very little. They rotate based on the angle of the viewer, like the moon and the stars do (this is known as field rotation - you are rotating, so your field of view seems to rotate). They also move slightly to the right due to the rotation of the Sun. But basically the same side of the Sun is a facing you all day long, and since it's a sphere, and the same side is facing everywhere on the Earth, then that means it's a very large and far away sphere. Many times further away than the size of the Earth.

One thing we should be able to do after taking a few observations is to trust the SDO images match our images. This is what the sun looks like from everywhere in the world. It has been verified countless times because taking photos of sunspots is something people do hundreds of times a day, and something you can do yourself. But if you really want to, you can verify the following just by taking lots of photos for a couple of days.

Hence we have demonstrated that the sun is a large distant rotating sphere, and by extension we have demonstrated yet again that the Earth is not flat.

This material regarding sunspots reminds me of a flat-earther who has been repeating for years that the sun and moon "roll like a wheel" as they move across the sky every day. Since this phrasing is found in the Bible it becomes all the more obsessive for some. At first I didn't know what she was talking about, or why it seemed to be so important to her. Eventually it became evident that she was presuming that one can simply stand in the same place and observe the sun or moon, then return to that same place off and on all day long making observations, and then conclude by the various observations that you see them "rolling like a wheel" across the sky. As if this is really relevant to support the "flat" earth hypothesis.

But simply standing in the same place is insufficient, when you pivot on your feet to face the sun and moon through the day. The fact that you are turning on your feet is the REASON that the sun and moon appear to "roll like a wheel." It is your body pivoting on your feet that is causing the apparent rotation of the sun and moon!

In order to get an unbiased, objective view of the sun and moon, one must orient the pivot axis of one's head parallel to the axis of the earth, from true north to true south. In the northern hemisphere, that means facing south and leaning your head backwards the same number of degrees as your latitude, so that the top of your head has Polaris directly above it. Then to view the moon (don't be looking directly at the sun) as it rises in the east, turn your head to the left and keep your eyes straight forward, not turned left. As the moon rises, you then turn your head keeping Polaris directly over the top of your head and your head angled back at your latitude degrees. As the moon moves, you then slowly turn your head to the right, keeping the moon in front of your eyes because you don't turn your eyes. You don't pivot on your feet. You only turn your head.

This is what a camera mounted to a star tracking apparatus does. When viewed in this way, the moon does not "turn like a wheel." The moon's face keeps the same orientation all the way across the sky. The same rules apply to viewing the sun, but you shouldn't be looking at the sun with your eyes because that causes permanent blindness.

So the flat-earther perception problem turns out to be a stubborn insistence to ignore corrective measures and to continue looking at the sun and moon with a biased and improper method based on laziness. It is non-scientific, IOW nescience, opposed to knowledge.