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Helping out a numpty!


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Hello all!

My brain's a bit fuzzy this morning, picked my daughter up from a school trip at 3am.

Confirmation needed on what I'm assuming is a very simple question.

I tend to get all flowery, not necessarily poetic, when describing what I'm observing.

One of the things that crossed my mind was describing high powered observations of the moon as "surfing" across the surface.

I know an object's apparent size is inversely proportional to its distance.

Am I right in thinking I can take a leap and make direct comparisons between magnification and actual distance from the moon's surface?

The moon is roughly 384,000 km away, so at 100x it's 3,840 km and at 384x (! :D ) we'd be "surfing" 1,000 km above the surface?

Is that right, or is there a different method for working out the relationship between magnification and apparent distance?

Cheers

Ps. On a good night, with the 8", a 7mm and a 2x Barlow, it's 375x so 1024km ;) 

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What have I got wrong here, then...?

blob.png.f8067835814d3f63ccd4ef1021955b7b.png

I went on the assumption that at 1x magnification, the moon would have an apparent angular diameter of 0.5183 degrees. At mag 2, this doubles, at 10x mag, it has an apparent angular diameter of 5.183, etc. I then took "apparent diameter / 2 = tan ( radius / distance )" and rearranged to "distance = radius / atan( apparent size / 2 )"

By the time I reach 375x magnification I'm guessing I've got something wrong... nothing can have an apparent angular diameter >180, that would be like looking at a wall in front of you which has infinite width.

I appreciate the calculation above assumes that the moon is flat, which it isn't. Therefore, as you get closer, it becomes more important to take into account that the apparent angular diameter extends only to a line tangent to the surface of the moon. Now I'm getting fuzzy and needing my lunch.

Edit: isn't it the case that as apparent angular diameter tends to 180, you tend to the surface? Ie the definition of a horizon?

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Am I the only one who thinks there's something wrong here? Does magnification make the image on your retina bigger rather than bring the image nearer? I read a thread about photographs, pixels and magnification, which was fascinating. I'm not saying your assumptions are wrong and I'm happy to be corrected. I'd like an imager's view. A bigger picture of the moon might not be a picture of a closer moon. Where is @ollypenrice today?:happy11:

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11 minutes ago, furrysocks2 said:

What have I got wrong here, then...?

blob.png.f8067835814d3f63ccd4ef1021955b7b.png

I went on the assumption that at 1x magnification, the moon would have an apparent angular diameter of 0.5183 degrees. At mag 2, this doubles, at 10x mag, it has an apparent angular diameter of 5.183, etc. I then took "apparent diameter / 2 = tan ( radius / distance )" and rearranged to "distance = radius / atan( apparent size / 2 )"

By the time I reach 375x magnification I'm guessing I've got something wrong... nothing can have an apparent angular diameter >180, that would be like looking at a wall in front of you which has infinite width.

I appreciate the calculation above assumes that the moon is flat, which it isn't. Therefore, as you get closer, it becomes more important to take into account that the apparent angular diameter extends only to a line tangent to the surface of the moon. Now I'm getting fuzzy and needing my lunch.

Edit: isn't it the case that as apparent angular diameter tends to 180, you tend to the surface? Ie the definition of a horizon?

The original post is referring to how magnification relates to apparent distance, so if you magnify something 100x it will in simple terms  look the same as if you just move 100x closer to it. Are  your calculations referring to how magnification relates to the apparent angular size of an object, which would be different (and more complicated!).

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5 minutes ago, Paz said:

The original post is referring to how magnification relates to apparent distance, so if you magnify something 100x it will in simple terms  look the same as if you just move 100x closer to it. Are  your calculations referring to how magnification relates to the apparent angular size of an object, which would be different (and more complicated!).

I thought that magnification inherently related to apparent angular size, and therefore given an apparent angular size, how close would you have to be for that to be the case... I was trying to relate the two and hoping the same numbers would fall out, but they didn't.

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I have these thoughts, my very small brain says, "No, can't possibly be that simple." and usually it isn't! :D

@Domstar: I was only talking about apparent sizes and distances, I know the moon definitely isn't any nearer! It's just a different way of imaging things, especially when viewing with children. Yes 1,000 km may still be beyond their imaginings and experiences, but if you can make links to things that maybe closer to their understanding, it does help. Besides, it just sounds better if your able to say that it's as if you were in orbit only 1,000km away! :)

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@bingevader Sorry if I was being negative and I know what you were saying. My thoughts were 'Gosh, can it really be true?' I suppose I was influenced by a thread which said that magnification is a meaningless term for photography, which surprised me to say the least. 

This is a nice thread and what I want to say is- can it be REALLY true? and if not why not? I'll follow with interest. 

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I think the logic/maths are sound, but the mistake is to imagine that the process can simply be continued to very high magnifications, since turbulence/seeing and resolution-limit effects will kick in well before it feels like you're "surfing" close to the surface!  (And there are other effects like criticality of focus, instability, and dimming.)

Doug.

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1 minute ago, bingevader said:

I have these thoughts, my very small brain says, "No, can't possibly be that simple." and usually it isn't! :D

@Domstar: I was only talking about apparent sizes and distances, I know the moon definitely isn't any nearer! It's just a different way of imaging things, especially when viewing with children. Yes 1,000 km may still be beyond their imaginings and experiences, but if you can make links to things that maybe closer to their understanding, it does help. Besides, it just sounds better if your able to say that it's as if you were in orbit only 1,000km away! :)

Aye, I was just writing that as I understand it, it's all related to the analogy of "being a certain distance away", the partial similarity being "how much bigger something appears"... you could do the same calculation for a single crater on the surface.

For a crater or lunar surface feature 1km in diameter, the following graph shows how large it would appear at a given distance, note log scale on distance axis:

blob.png.9e57b6848a31d6e852549d39ce89df6e.png

So the relationship between how much bigger something appears and how much closer you are to it appears to be non-linear, and tending towards 0 as you move away and tending towards an angular size of 180 degrees as you move towards it.

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Plotting the original "EP mag against equivalent distance from the moon"...

blob.png.8786503a43c996a6f54ad4d7951df324.png

Appreciate you can't read numbers off a log scale, but it shows the relationship - but this is calculated based on the full lunar disc.

 

I think, like magnification for imaging, this becomes meaningless as it depends on what you're comparing it to... ie based on the fact that the relationship is so different for the full lunar disk and a 1km crater, consider then a 10km or 100km crater, you'll get a different answer. Although there is clearly a linear portion so it's an appropriate approximation up to a point. I might conclude therefore that perhaps for all practical magnifications you could happily use the linear relationship for all features you are likely to fit within the field of view. of an EP..?

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33 minutes ago, cloudsweeper said:

I think the logic/maths are sound, but the mistake is to imagine that the process can simply be continued to very high magnifications, since turbulence/seeing and resolution-limit effects will kick in well before it feels like you're "surfing" close to the surface!  (And there are other effects like criticality of focus and dimming.)

Doug.

I did say, "On a good night!" :D

I've done the swimming through soup and floaters the size of chinese dragons, but you'd be surprised (or not)!

My 375x was from experience, maybe not surfing, but definitely at an orbit of 1024km, apparently! :)

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I was using 600x from time to time with my 130 refractor a couple of nights back. That certainly felt visually like I was gliding a few hundred KM above the lunar surface. The feeling was enhanced because my scope was undriven so the moons surface scrolled by quite rapidly.

It's not really serious observing but it is a lot of fun :icon_biggrin:

 

 

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5 minutes ago, furrysocks2 said:

640km above the surface.

Yes - I rounded the figure to "a few hundred" because I thought it sounded more casual :icon_biggrin:

Also the moon - Earth distance does vary slightly.

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1 hour ago, domstar said:

Where is @ollypenrice today?:happy11:

He's here, on top of the Rocher St Michel above Orpierre. He's reflecting on the width of the rocky ridge which leads off it and wondering if it might somehow be magnified...

59fc89eb7ec78_topsmall.thumb.jpg.52d8255ecd1d3b702d34a0aaa0d264ac.jpg

59fc8a1468c1a_TopCairn.jpg.2db8a37952e6daee4d008f0b200d67c8.jpg

Now that I'm down :hello2:I simply agree that the apparent size goes as the inverse square of the distance. In the other thread (about 'magnification' in imaging) my point was that in visual astronomy we have something to magnify, namely the image projected onto the retina. We still have that here, an image of part of the moon, so yes, we can reasonably state a 'distance equivalence' for a magnification by a telescope. I can't see anything wrong with that. It won't work for stars because any angular size they possess in amateur telescopes is an artefact of the optics. They should be points. (Can we see points? I've no idea!)

Olly

 

 

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24 minutes ago, John said:

Yes - I rounded the figure to "a few hundred" because I thought it sounded more casual :icon_biggrin:

Also the moon - Earth distance does vary slightly.

I'll recalculate. That's impressive though!

 

8 minutes ago, ollypenrice said:

It won't work for stars because any angular size they possess in amateur telescopes is an artefact of the optics.

...and seeing?

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The size of a stars airy disk depends on the aperture of the scope. The larger the aperture, the smaller the airy disk. There is no link between the airy disk and the physical size of the star or the distance it is at as far as I know.

Seeing conditions will determine the extent to which a clean airy disk is visible.

 

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1 hour ago, John said:

I was using 600x from time to time with my 130 refractor a couple of nights back. That certainly felt visually like I was gliding a few hundred KM above the lunar surface. The feeling was enhanced because my scope was undriven so the moons surface scrolled by quite rapidly.

It's not really serious observing but it is a lot of fun :icon_biggrin:

 

 

Maybe not serious, but seriously good fun!

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