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I was thinking about measure the distance to the moon using parallax angle. But I have a confusion. I have read couple of articles about that, but one thing is unclear. Should we take pictures of moon at the same (literally the same, for example, taking both pictures at UTC 16) moment or should we take pictures the same local time (for example, if the timezone difference is 2h then the time difference between two taken pictures should be 2h).

So which one is the correct method for it? I think it is the former one, but I cannot tell why it is not the latter.

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    $\begingroup$ The important part in this calculation is that the two measurements are taken at the same moment, which is simple if you are both using UTC, or some other standard time, without having to worry about timezone changes. $\endgroup$ – IronEagle Sep 30 '20 at 15:21
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The simplest way: take pictures at the same (ie 16UTC). The position of the moon in the sky will be very different for different observers, due to the cuvature of the Earth. But this is not what you are measuring. You need to see the difference in position relative to the stars.

For more accuracy, instead of measuring the difference is position directly, you can time when the moon occludes a star. The absolute time when the moon will occlude a star will differ for different observers, and this can be converted into a difference of position of the moon, and parallax can be calculated from that. It is easier to be accurate in timing than it is to measure position directly. With some clever maths you can just measure the length of the occulution rather than the absolute time, and this means you don't even need a accurate clock, you only need an accurate stopwatch (not so much of an issue now, but significant when these measurements were first being done)

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  • $\begingroup$ Thanks for the answer, but how can we know if the moon is going to occlude a star? $\endgroup$ – spitfire Sep 30 '20 at 18:20
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If the observations occur at the same local time in different time zones (different UTC times), the difference in observed Moon positions has two components: parallax and the Moon's orbital motion. Separating those would involve a prior assumption about the distance which you're trying to measure. Making the observations at the same UTC time eliminates the orbital motion component, leaving only parallax.

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If you're just interested in the distance to the moon, you can find it indirectly given in the Nautical Almanac. For every hour in the year the Nautical Almanac provides a number HP, for horizontal parallax. That's the difference in the moon's apparent position for an observer seeing it directly overhead and an observer seeing it on the horizon. Using plane trig (aren't you glad it's not spherical) you can determine the distance: it's equal to the Earth's radius divided by the sine of HP. The answer will be in units of the Earth's radius. HP is given in minutes of arc with a resolution of a tenth of a minute. All of the HP values will be near 1 degree, 60 minutes.

You won't have any way of measuring parallax unless you know where you are and where the moon is. Knowing where the moon is requires almanac data and exact time.

It wasn't clear to me why you thought you'd need two times rather than one.

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    $\begingroup$ Sorry but I only want to measure distance without looking at any table values. Like in back old days) $\endgroup$ – spitfire Sep 30 '20 at 18:19
  • $\begingroup$ I don't understand this answer yet. As long as you can see the Moon at two places at the same time, you can photograph the Moon and a few nearby bright stars. As long as you can identify the stars you have a scale for the photograph (e.g. pixels per arc second). Then you measure the shift of the Moon's position between the two photographs in pixels, convert to arc seconds, and voila! you have a parallax measurement. Use lat/lon and math to get baseline and you've got an estimate of the distance to the Moon. $\endgroup$ – uhoh Oct 2 '20 at 1:34
  • $\begingroup$ Okay you can check a newspaper to see when the Moon will be up, but I don't see how a Nautical almanac would be needed for this exercise. $\endgroup$ – uhoh Oct 2 '20 at 1:36

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