On top of the sitaution Mystery Cache
-
Difficulty:
-
-
Terrain:
-
Size: 
(small)
Please note Use of geocaching.com services is subject to the terms and conditions
in our disclaimer.
A unit of length now defined as exactly 149,597,870,700 m or roughly the average Earth-Sun distance. Originally defined as the length of the semi-major axis of the Earth's elliptical orbit around the Sun.
An equivalent definition is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with an angular frequency of 0.01720209895 radians per day.
In numerical standards, the speed of light in a vacuum is defined as c0 = 299,792,458 m/s, in accordance with the SI units. The time to traverse one unit is found to be τA = 499.0047838061±0.00000001 s, resulting in a measurement in metres as cτ = 149,597,870,700±3 m.
In other words....approximately equal to the distance from the earth to the sun!
Precise measurements of relative positions of inner planets can be made by radar and by telemetry. As with all radar measurements, these rely on measuring the time taken for photons to be reflected from an object. These positions are then compared with those calculated by the laws of celestial mechanics: an assembly of calculated positions is often referred to as an ephemeris.
The comparison of the ephemeris with the measured positions leads to a value for the speed of light which is 173.132 632 6852(69). As the speed of light in meters per second is fixed in the International System of Units, this measurement of the speed of light determines the value of the units in meters.
The best current (2009) estimate of the International Astronomical Union (IAU) for the value of units in meters is A = 149 597 870 723(3) m, based on a comparison of JPL and IAA–RAS ephemerides.
With definitions used before 2012 measurements were dependent on the heliocentric gravitational constant, that is the product of the gravitational constant G and the solar mass M☉. Neither G nor M☉ can be measured to high accuracy in SI units, but the value of their product is known very precisely from observing the relative positions of planets (Kepler's Third Law expressed in terms of Newtonian gravitation). Only the product is required to calculate planetary positions for an ephemeris, which explains why ephemerides are calculated in astronomical units and not in SI units.
The calculation of ephemerides also requires a consideration of the effects of general relativity. In particular, time intervals measured on the surface of the Earth (terrestrial time, TT) are not constant when compared to the motions of the planets: the terrestrial second (TT) appears to be longer in Northern Hemisphere winter and shorter in Northern Hemisphere summer when compared to the "planetary second". This is because the distance between the Earth and the Sun is not fixed and when the Earth is closer to the Sun (perihelion), the Sun's gravitational field is stronger and the Earth is moving faster along its orbital path. As the meter is defined in terms of the second, and the speed of light is constant for all observers, the terrestrial meter appears to change in length compared to the "planetary meter" on a periodic basis.
The meter is defined to be a unit of proper length, but the SI definition does not specify the metric tensor to be used in determining it. Indeed, the International Committee for Weights and Measures notes that "its definition applies only within a spatial extent sufficiently small that the effects of the non-uniformity of the gravitational field can be ignored." As such, the meter is undefined for the purposes of measuring distances within the Solar System.
The parsec is used for interstellar distances. The light year is often used in popular works, but is not an approved non-SI unit.
According to Archimedes in the Sandreckoner, Aristarchus of Samos estimated the distance to the Sun to be 10,000 times the Earth's radius (the true value is about 23,000). However, the book On the Sizes and Distances of the Sun and Moon, which has long been ascribed to Aristarchus, says that he calculated the distance to the sun to be between 18 and 20 times the distance to the Moon, whereas the true ratio is about 389.174
According to Eusebius of Caesarea the distance to the sun was literally "of stadia myriads 400 and 80000". This has been translated either as 4,080,000 stadia or as 804,000,000 stadia. Using the Greek stadium of 185 to 190 meters the former translation comes to a far too low 755,000 km whereas the second translation comes to 148.7 to 152.8 million km (accurate within 2%).
A Chinese mathematical treatise, the Zhoubi suanjing, shows how the distance to the Sun can be computed geometrically, using the different lengths of the noontime shadows observed at three places 1000 li apart and the assumption that the Earth is flat.
In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as 1,210 times the Earth radius. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few percent can make the solar distance infinite.
Johannes Kepler was the first to realize that Ptolemy's estimate must be significantly too low (according to Kepler, at least by a factor of three) in his Rudolphine Tables (1627). Kepler's laws of planetary motion allowed astronomers to calculate the relative distances of the planets from the Sun, and rekindled interest in measuring the absolute value for the Earth. The invention of the telescope allowed far more accurate measurements of angles than is possible with the naked eye.
A somewhat more accurate estimate can be obtained by observing the transit of Venus. By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of the Earth and Venus from the Sun, the solar parallax α. Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15 arcseconds. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by;
The smaller the solar parallax, the greater the distance between the Sun and the Earth: a solar parallax of 15" is equivalent to an Earth–Sun distance of 13,750 Earth radii.
Christiaan Huygens believed the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24,000 Earth radii.
Jean Richer and Giovanni Domenico Cassini measured the parallax of Mars between Paris and Cayenne in French Guiana when Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of 9½", equivalent to an Earth–Sun distance of about 22,000 Earth radii. They were also the first astronomers to have access to an accurate and reliable value for the radius of the Earth, which had been measured by their colleague Jean Picard in 1669 as 3,269 thousand toises. Another colleague, Ole Rømer, discovered the finite speed of light in 1676.
Another method involved determining the constant of aberration, and Simon Newcomb gave great weight to this method when deriving his widely accepted value of 8.80″ for the solar parallax although Newcomb also used data from the transits of Venus.
The unit distance A (value in meters) can be expressed in terms of other astronomical constants:
where G is the Newtonian gravitational constant, M☉ is the solar mass, k is the numerical value of Gaussian gravitational constant and D is the time period of one day.
As the speed of light has an exact defined value in SI units and the Gaussian gravitational constant k is fixed in the astronomical system of units, measuring the light time per unit distance is exactly equivalent to measuring the product GM☉ in SI units. Hence, it is possible to construct ephemerides entirely in SI units, which is increasingly becoming the norm.
A 2004 analysis of radiometric measurements in the inner Solar System suggested that the secular increase in the unit distance was much larger than can be accounted for by solar radiation, +15±4 meters per century.
The measurements of the secular variations of are not confirmed by other authors and are quite controversial. Furthermore, since 2010, the unit is not yet estimated by the planetary ephemerides.
| Date |
Method |
A/Gm |
Uncertainty |
| 1895 |
aberration |
149.25 |
0.12 |
| 1941 |
parallax |
149.674 |
0.016 |
| 1964 |
radar |
149.5981 |
0.001 |
| 1976 |
telemetry |
149.597 870 |
0.000 001 |
| 2009 |
telemetry |
149.597 870 700 |
0.000 000 003 |
Assume N 50° and W 004° ....
You can validate your puzzle solution with certitude.
Additional Hints
(Decrypt)
Haqre n ebpx
Treasures
You'll collect a digital Treasure from one of these collections when you find and log this geocache:
Loading Treasures