Astroblog: This Full Moon, lets use a simple method to measure distance to the Moon

Tuesday, February 20, 2024

This Full Moon, lets use a simple method to measure distance to the Moon

I don’t know about you folks, but the feed in the social media formerly known as twitter is currently dominated by “cute poop” ads (who seem to have displaced the chemtrailers) and flat earthers.

The former is a mildly puzzling Japanese phenomenon, while the latter appears to be dominated by people who have not progressed past a pre-Babylonian view of the world, but who possess P1000 cameras they don’t know how to focus.

Now as a long-time viewer of the the skies and their wonders, these folks give me the screaming irrits, but I take this as a chance for a teachable moment, and get people involved in measuring the distance to the Moon in a way that anyone can undertake. One of the tenets of the flat earth movement is that the sun and moon are both small and local (that sound you are hearing is the ghost of Aristarchus howling at the said Luna).

Now, Aristarchus used the time it took for earth's shadow to cross the Moon in a lunar eclipse and got a figure that was 1/3 the modern distance, not bad for unaided eye observation without modern clocks (and thousands of times further than the flat earth requirement of “local”).

Now there are no convent total lunar eclipses this year, so we can’t reproduce Aristarchus’s methods.

The most common method for determining the distance to the moon, if you are not bouncing lasers off the mirrors left by the Apollo Astronauts or Soviets, is parallax. For parallax you and a mate a couple of hundred kilometers away have to take an image of the Moon at the same Universal Time, close to one or more bright stars, with equipment that gives an image of roughly the same scale. And you both need clear skies. Then all you have to do is measure the distance between the stars and the moon, do a bit of maths and viola, you have the distance to the Moon.

Probably the next best time for parallax is May 23, when the Moon is close to delta Scorpii. Of course, all this requires a bit of organisation, as does most of the demonstrations of the sphericity of earth.

Fortunately, this is a way to determine the distance to the Moon that one can do just by themselves. All you need is a digital camera with a decent optical zoom function (or attached to a telescope), an accurate timestamp function, a clear horizon, and the patience to take images for most for the night, and an image analysis program like AstroimageJ to measure the Moons diameter https://www.astro.louisville.edu/software/astroimagej/index.html or a Python script.

The basic idea is that the moon at moon-rise is further away than the moon at the zenith by approximately the radius of the earth. (see figure 1, from https://arxiv.org/ftp/arxiv/papers/1405/1405.4580.pdf used under that fair use for research provisions).

All you have to do is measure the radius of the Moon as it rises and the radius of the Moon when it is highest, as well as an accurate measurement of the time the images were taken apply a bit of maths with the radius of the Moon and hey presto, the distance to the Moon! (full details in “The simplest method to measure the geocentric lunar distance: a case of citizen science” at https://arxiv.org/ftp/arxiv/papers/1405/1405.4580.pdf)

(Figure 2, from https://arxiv.org/ftp/arxiv/papers/1405/1405.4580.pdf used under that fair use for research provisions).

Well, of course it’s not that simple. Close to the horizon atmospheric distortion “squashes” the image messing with the accurate measurement of the radius (this is not the horizon illusion, where the Moon appears bigger, when, in fact it isn’t), also, it needs to be a full moon far from apogee or perigee, when there will be enough change in the Moons diameter as it reaches the furthest and nearest points in its orbit to mess up the calculation.

The Full Moon of February 24th is such a Moon, and this is my challenge: to take images of the Moon between moon rise and the Moon at zenith, then measure their diameter (making sure the images a re time stamped in some way, usually file creation data in the image header will suffice, just make sure you cameras clock is set correctly).

(Figure 5. Best fit of the measured apparent sizes (error-bars) to the theoretical model (continuous line. The shaded region
correspond to solutions statistically compatible with the observed apparent sizes at a 5% confidence level, from https://arxiv.org/ftp/arxiv/papers/1405/1405.4580.pdf .used with permission).

Of course then you have to run the Python scripts given in “The simplest method to measure the geocentric lunar distance: a case of citizen science” (at https://arxiv.org/ftp/arxiv/papers/1405/1405.4580.pdf. I did mention you needed python didn’t I? sadly, the links in that paper no longer work, but Jorge Zuluaga has kindly passed the scripts on to me so I can send them on. This link takes you to the Zip file with the Python Scripts. https://drive.google.com/drive/folders/1FXCgbYINt3hBBSU3gPzaY13MgSNIbtL1?usp=sharing

(Figure 6. Instantaneous distance as a function of time elapsed since the first observation. from https://arxiv.org/ftp/arxiv/papers/1405/1405.4580.pdf .used with permission).

You also need more than two Moon shots for the statistical analysis (see the figures and the linked paper). So, what do you think? Are you up for the challenge?

Labels: astrophotography, citizen science, Moon