Lunar Laser Ranging experiment

When Lunar Laser Ranging (short: LLR) are starting from ground stations on earth, performed time measurements of laser pulses to the moon after the pulse - echo method. LLR measurements provide information about the Earth-Moon system to Earth rotation parameters as well as parameters for checking basic assumptions of gravitational physics. At present, the accuracy of the measurements is a few centimeters in the Earth-Moon distance ( this distance is averaged over time, around 384,400 km ).

Reflectors on the moon

The first laser retroreflector was the Apollo 11 mission installed by astronauts on the lunar surface in July 1969, two additional reflectors in 1971 by the Apollo 14 and 15 as early as 1970 was a reflector with the Soviet Lunokhod - 1 mission placed on the moon be. Since the 1970s, however, this reflector signals could no longer be detected. The reasons for this have not been known for many years. After the American lunar probe Lunar Reconnaissance Orbiter had made 2010 recordings of Lunokhod 1 year and therefore, the position could be determined more accurately, the laser reflector was sighted for the first time successfully again. 1973 was finally deposed by the Lunokhod - 2 mission, another reflector, which can be used for measurements as before. The reflectors have the property of incoming laser light to throw back exactly in the same direction from which the heat is coming. They consist of up to 300 triple prisms of 4 cm in diameter, which are mounted on an aluminum frame.

LLR ground stations

Since the discontinuation of the first reflector on the moon by the Apollo 11 mission measurements at the McDonald Observatory near Fort Davis, Texas to be performed. 1984, another station of Lure Observatory on Haleakala on the island of Maui, Hawaii as well as a laser station of the Observatoire de Calern was put into operation. In 2005, the Apollo system (Apache Point Observatory Lunar Laser - ranging Operation) was placed in service in New Mexico. Occasionally, observations on the geodetic fundamental station Wettzell in the Bavarian Forest, as well as on the Australian station Orroral were performed.

Sequence of measurements and estimation of the number of received photons

When Lunar Laser Ranging working after the pulse - echo method. The transit time between the sending of a pulse is measured up to his return. These short sub -nanosecond laser pulses are radiated by a station on the Earth in the direction of the reflector location on the moon, reflected back there from the reflector in the direction of the received beam and received by the ground station. A measurement consists of several individual pulses with a single pulse energy of 100 mJ each typ ( APOLLO - project: pulse duration 90 ps FWHM, pulse energy 115 mJ ). A one-shot pulse is a radiation disc with a diameter 75 to 350 cm and a thickness of a few centimeters. The illuminated on the moon surface is about 70 km ². A measurement consists of several individual pulses with a total of 1019 photons of which 2,5 seconds on average not even a single photon finds its way back to the receiver ( Wettzell ); also the Observatory of Côte d' Azur could be received only 1019 photons 0125 photons.

Taking the transmission at through the telescope and the atmosphere each to 71%, so come by the 1019 photons half on the moon. Meet the 100 triple prisms, each with a diameter of 3.8 cm in the case of Apollo 11 on average for about 8,109 photons, as can be calculated from the ratio of the areas. The central reflected spot on Earth has a diameter of 10 nautical miles ( 200 km ²), from which a telescope ( Wettzell: diameter 75cm ) receives photons. Adding to an efficiency of 10% of the retroreflector a ( reflection and scattering losses) as result from an average of 0.7 received photons, calculated as the ratio of the telescope area to spot area, with consideration of the 10 - % efficiency and 50 - % - transmission as above:

At a laser distance measurement to the moon photons from the illuminated lunar surface are backscattered. If one takes the illuminated surface as a Lambert radiator and integrates the back -scattered photons on the telescope surface, we obtain

Additionally received photons by scattering on the lunar surface. The factor 0.5 is above the one-way transmission, the 0.1 Mondalbedo, 0,375 m, the radius of the receiving telescope and 380,000,000 m, the distance between earth and moon.

Evaluation of the measurement LLR

The challenge in the evaluation is to find out individual arrived photons from a set of Störphotonen. Window to be set in the frequency and time domain in which the correct photon is expected. While the disturbance events will be distributed more or less evenly over the entire registration interval, the useful signal can be expected in a much narrower range. The registration interval is decomposed into many sub-intervals and formed a histogram. For this, a standard point is constructed that represents a pulse time of arrival, in a sense. Currently, more than 11,500 normal points are available. The analysis of normal points is achieved with the help of extensive program packages. These contain a Ephemeridenteil for the movement of the astronomical body and also a part which is used for parameter estimation.

Results from LLR measurements

Laser distance measurements provide information on various aspects of the Earth- Moon system, such as geocentric coordinates of stationary or mobile laser stations that can be determined to within 3-5 cm exactly. Since the laser stations are partly due to different continental plates can optionally station movements in the form of drift rates with an accuracy of about 0.4 cm can be estimated. Furthermore, can be derived from LLR data important information about the gravitational field ( including the Massenmultipolmomente of the Moon), and derive the tidal deformation of the moon. Because of tidal friction, the rotation of the earth is slowed down, but since the angular momentum in the Earth- Moon system is retained, removed presently the moon by about 3.8 cm per year from the Earth. In addition, can be derived from laser range measurements to the moon relativistic significant sizes and Earth rotation parameters.