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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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
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.
altitude: 37.6454136245 azimuth: 193.116013331 distance (to center of Moon): 366418.551453 distance to closest point on moon: 364652.0 compare to: 364857
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 """ 5 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!
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).