Where can I find free/open data for the observed (not calculated/theoretical) distance between the Earth & Moon?
I want to see the observed distance of the Moon, hour by hour.
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1$\begingroup$ Distance measurements between fixed points on the surfaces of the Earth and Moon are regularly measured by time-of-flight of laser pulses beamed from Earth towards retroreflector arrays left on the Moon by several missions such that a few of the photons returning to Earth are measured and carefully timed. When compared to the most thorough models of solar system motion, agreement has been within a few centimeters over 30 years.Tracking down the 30 years of data will take a bit of searching. $\endgroup$– uhohCommented Jan 1, 2018 at 0:46
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1$\begingroup$ One might start that search looking at the papers Lunar laser ranging: the millimeter challenge and also Progress in Lunar Laser Ranging Tests of Relativistic Gravity. In the mean time, you can read more about this in the question How is a result of no time variation in the gravitational constant $G$ related to a measurement of no local expansion? $\endgroup$– uhohCommented Jan 1, 2018 at 0:47
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$\begingroup$ Apache Point observatory in New Mexico may well have the data you seek: tmurphy.physics.ucsd.edu/apollo/apollo.html $\endgroup$– Wayfaring StrangerCommented Jan 2, 2018 at 16:01
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3 Answers
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Found laser ranging data here: http://www.geoazur.fr/astrogeo/?href=observations/donnees/lune/brutes
Here you can search for data for an arbitrary time period.
The data is what they call "MINI" format, which is hard to read, its basically a long string of numbers.
Here is a sample line:
5120160113152419452625024340653926601301910034002705017 087323+04325 5320a0702
Luckily there is a specification for this format here: http://www.geoazur.fr/astrogeo/observations/donnees/lune/mini-format.html
The spec says the time-of-flight for the laser is charcters 24-37 from each line, measured in .1 picoseconds. So for the above line, the laser's round-trip flight time is 24340653926601 (.1 ps).
The data does not contain the distance, so to calculate the distance from the flight time, I do the following:
Divide 24340653926601/2 to get 1-way flight time in .1 ps.
Multiply the result 1.2170327e+13*.1 to get ps.
Multiply the result 1.2170327e+12*1.0e-12 to get seconds.
Multiply the result 1.2170327*299792458(the speed of light) to get the distance in meters: 364857224.599
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1$\begingroup$ It seems you are making good progress! The one-way time from the center of the Earth to the center of the Moon will range between roughly 1.2 and 1.35 seconds, since the orbit is eccentric. Since these measurements are from specific locations on the surfaces of these two bodies, the time will be roughy 0.02 to 0.03 seconds less than that. $\endgroup$– uhohCommented Jan 5, 2018 at 1:48
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$\begingroup$ I found this cyrano-se.obspm.fr/pub/1_llr_analysis/2_llr_residuals/… $\endgroup$– uhohCommented Jan 10, 2018 at 0:19
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$\begingroup$ It would be perfectly reasonable to accept your own answer in this case! In fact it's preferred because in future searches by others, they will then see that an answer has been accepted. I've added a supplementary answer below that fairly well confirms your interpretation of the data. $\endgroup$– uhohCommented Jan 10, 2018 at 0:47
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$\begingroup$ Slightly related links in this answer, particularly ilrs.cddis.eosdis.nasa.gov/data_and_products/formats/crd.html although this is about CRD format and it looks like you have something different. $\endgroup$– uhohCommented Jun 21, 2018 at 3:20
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Here's a rough check on that, offered as a supplementary answer. Using the Python package Skyfield one can calculate the distance to the center of the Moon. Right now I don't know how to calculate the distance to the specific location of the Apollo 15 reflectors on the Moon, but the distance from the observatory to the closest point on the Moon is about 200 km shorter than the distance determined from laser pulses as described in the other answer. This seems about right considering the radius of the Moon is about 1767 km.
Output:
altitude: 37.6454136245
azimuth: 193.116013331
distance (to center of Moon): 366418.551453
distance to closest point on moon: 364652.0
compare to: 364857
Python script
import numpy as np
import matplotlib.pyplot as plt
from skyfield.api import Loader, Topos
load = Loader('~/Documents/fishing/SkyData')
data = load('de421.bsp')
ts = load.timescale()
planets = load('de421.bsp')
earth = planets['earth']
moon = planets['moon']
Grasse = earth + Topos('43.753698 N', '6.922998 E', elevation_m = 372.)
time = ts.utc(2016, 1, 13, 15, 24, 19.4526250)
alt, az, dist = Grasse.at(time).observe(moon).apparent().altaz()
print "altitude: ", alt.degrees
print "azimuth: ", az.degrees
print "distance (to center of Moon): ", dist.km
print "distance to closest point on moon: ", round(dist.km, 0) - 1767.
print "compare to: ", 364857
"""
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Format
1
Color
20160113
AAAAMMJJ
1524194526250
HHMMSSsssssss
24340653926601
2sssssssssssss times 0.1 ps
3
Reflector code (3 = Apollo 15)
01910
Station Code (01910 = Grasse)
034
Number of Echoes
002705
Uncertainty (0.1 ps)
017
S/N ratio (0.1 ps)
"""
below: Moon landing sites, from Bob the Alien!
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The measurements are of distance from one particular place on Earth, to one particular place on the Moon. But these places move around relative to the center of the Earth or moon ... the Earth surface "flexes" due to various tidal forces from the Moon, sun, and other planets, and so does the moon to a lesser degree. In addition, the moon doesn't orbit the Earth in a nice perfect circle. Then you need to consider that the speed of light through the atmosphere is not constant (varies with weather). Also, the measurement instruments have a lot of noise and jitter (it's a lot compared to the precision & accuracy of the measurements).
