Date: Wed, 26 May 1999 17:29:34 -1000 (Hawaiian Standard Time) From: Justin Greenhalgh To: ndo@ecgs.lu Subject: Earth tides Dear Nicolas, I hope you don't mind me bothering you with a question from a newcomer to the earth tides field. Here in Hawaii we have been using inclinometers to measure the way that our telescope moves, and some of the results we cannot understand. It occurred to us that maybe the influence of the sun's or moon's gravity was playing a role and so we did some very simple calculations to see if that made sense. We do not understand the answers. As we see it, gravity from a nearby body (the Earth, the Sun, etc) is proportional to the mass, and inversely proprtional to the square of the distance. So the sun, for example, should exert about 1/1000th of the gravity the Earth does, on me (more accurately 6E-4). So the gravitational force I see will be the vector sum of 1g towards the centre of mass of the Earth plus a component about 1000 times smaller in a direction towards the Sun. So as the Earth rotates, my local gravity vector will swing very slightly as the small sun vector rotates. This means, looking at it simply, that our inclinometer should give us a diurnal variation of about 120 arc seconds (inverse tan of 6e-4) give or take a factor of two. It doesn't. Is this because the ground to which my inclinometer is indirectly attached, also tilts and by nearly the same amount? I hope you will be able to answer what is probably a very basic question in Earth tides. Thanks in advance - Justin Greenhalgh Joint Astronomy Centre ------------------------------------- Date: Thu, 27 May 1999 12:36:42 +0100 From: Nicolas d'Oreye To: Justin Greenhalgh Subject: Re: Earth tides Dear Justin, Your question is not boring at all. Also, I should say that probably nothing is really basic in ET, even if it looks so... Indeed, your explanation is a good start. However you should, in a second stage, take into account the influence of the moon's attraction and the centrifugal forces. The theoretical earth tide can be computed very accurately for any location at any time thanks to well known models. But in a third stage, you should also take into account the influence of the ocean tides which is exerting additional varying direct attraction (but this plays a role only for the gravimetric earth tides) + a loading effect that will again tilt the crust. Because the oceanic tides are caused by the same phenomenon, their frequencies are similar to the earth tides of course. Those oceanic effects can be very large near the coast and can still be visible up to more than 300 km inland for instance. Because Hawaii is an Island (yes I red that somewhere...), those effects are expected to be even worst. But there is something else (I told you: nothing is really simple when dealing with Earth Tides...). In order to enable good records of those Earth Tides, we are obliged to install our instruments in underground stations while the room temperature or humidity variations or human perturbations would jeopardize the tidal signal (those perturbations can be much larger than the tidal signal itself). Also, atmospheric pressure changes (again by attraction and loading effect), thermoelastic stress or cavity effects can perturb strongly the Earth Tides records. But alls this should be far from your question. In conclusion, I have computed for you a one month tidal tilt (May 1999) based on the potential exerted mainly by the sun and the moon. Results are given for the EW and NS azimuths, without taking into account any perturbing effect. The data are in ascii format at a one hour sampling rate. The data are given in milli arc second, i.e. 4.848 nanoradian. This should allow you to have a better idea of the spectrum you could expect. If you need additional information, you can consult the bible: "The Tides of the Planet Earth, 2nd ed.", by P. Melchior, Pergamon Press, 1983. It is unfortunately out of press but it can maybe be found at the volcanological institute of Hawaii (?). If you don't find that book and if you need such a kind of reference, I can give you additional information later. If you need additional theoretical tide computations (other time windows or other azimuths), please feel free to ask. I hope this will help. Best regards Nicolas PS just for curiosity, may I ask you how you got my references? Luxembourg is rather far from Hawaii (unfortunately..) * * Nicolas d'Oreye de Lantremange * * European Center for Geodynamics and Seismology * ECGS * 19, rue J. Welter, L-7256 Walferdange, Gd Duchy of Luxembourg * * Tel: (+ 352) 33.14.87 /\ Fax: (+ 352) 33.61.29 * * E-mail: ndo@ecgs.lu __/ \ /\ ___ Web Page: www.ecgs.lu \/ \/YYYY MM DD hh mm ss EW thero. Tilt NS theor. Tilt 1999 5 1 0 0 0 1.5000000e+001 4.0000000e+000 1999 5 1 1 0 0 2.1000000e+001 2.0000000e+000 1999 5 1 2 0 0 2.2000000e+001 0.0000000e+000 1999 5 1 3 0 0 1.8000000e+001 -2.0000000e+000 1999 5 1 4 0 0 1.0000000e+001 -2.0000000e+000 1999 5 1 5 0 0 0.0000000e+000 0.0000000e+000 1999 5 1 6 0 0 -1.0000000e+001 4.0000000e+000 1999 5 1 7 0 0 -1.6000000e+001 8.0000000e+000 1999 5 1 8 0 0 -1.8000000e+001 1.3000000e+001 1999 5 1 9 0 0 -1.4000000e+001 1.7000000e+001 1999 5 1 10 0 0 -7.0000000e+000 2.0000000e+001 1999 5 1 11 0 0 2.0000000e+000 2.1000000e+001 1999 5 1 12 0 0 1.1000000e+001 1.9000000e+001 1999 5 1 13 0 0 1.6000000e+001 1.5000000e+001 1999 5 1 14 0 0 1.7000000e+001 1.1000000e+001 1999 5 1 15 0 0 1.3000000e+001 6.0000000e+000 1999 5 1 16 0 0 5.0000000e+000 2.0000000e+000 1999 5 1 17 0 0 -5.0000000e+000 -1.0000000e+000 1999 5 1 18 0 0 -1.4000000e+001 -2.0000000e+000 1999 5 1 19 0 0 -2.0000000e+001 -2.0000000e+000 1999 5 1 20 0 0 -2.2000000e+001 0.0000000e+000 1999 5 1 21 0 0 -1.8000000e+001 1.0000000e+000 1999 5 1 22 0 0 -1.0000000e+001 3.0000000e+000 1999 5 1 23 0 0 0.0000000e+000 3.0000000e+000 1999 5 2 0 0 0 1.0000000e+001 3.0000000e+000 1999 5 2 1 0 0 1.8000000e+001 1.0000000e+000 1999 5 2 2 0 0 2.1000000e+001 -1.0000000e+000 1999 5 2 3 0 0 2.0000000e+001 -2.0000000e+000 1999 5 2 4 0 0 1.4000000e+001 -2.0000000e+000 1999 5 2 5 0 0 5.0000000e+000 -1.0000000e+000 1999 5 2 6 0 0 -5.0000000e+000 2.0000000e+000 1999 5 2 7 0 0 -1.2000000e+001 6.0000000e+000 1999 5 2 8 0 0 -1.6000000e+001 1.1000000e+001 1999 5 2 9 0 0 -1.5000000e+001 1.6000000e+001 1999 5 2 10 0 0 -1.0000000e+001 1.9000000e+001 1999 5 2 11 0 0 -2.0000000e+000 2.1000000e+001 1999 5 2 12 0 0 6.0000000e+000 2.0000000e+001 1999 5 2 13 0 0 1.3000000e+001 1.8000000e+001 1999 5 2 14 0 0 1.6000000e+001 1.3000000e+001 1999 5 2 15 0 0 1.4000000e+001 9.0000000e+000 1999 5 2 16 0 0 8.0000000e+000 4.0000000e+000 1999 5 2 17 0 0 -1.0000000e+000 0.0000000e+000 1999 5 2 18 0 0 -1.0000000e+001 -2.0000000e+000 1999 5 2 19 0 0 -1.7000000e+001 -2.0000000e+000 1999 5 2 20 0 0 -2.0000000e+001 -2.0000000e+000 1999 5 2 21 0 0 -1.9000000e+001 0.0000000e+000 1999 5 2 22 0 0 -1.3000000e+001 1.0000000e+000 1999 5 2 23 0 0 -5.0000000e+000 1.0000000e+000 1999 5 3 0 0 0 5.0000000e+000 1.0000000e+000 1999 5 3 1 0 0 1.4000000e+001 0.0000000e+000 1999 5 3 2 0 0 1.9000000e+001 -1.0000000e+000 1999 5 3 3 0 0 2.0000000e+001 -2.0000000e+000 1999 5 3 4 0 0 1.6000000e+001 -3.0000000e+000 1999 5 3 5 0 0 9.0000000e+000 -2.0000000e+000 1999 5 3 6 0 0 1.0000000e+000 0.0000000e+000 1999 5 3 7 0 0 -7.0000000e+000 4.0000000e+000 1999 5 3 8 0 0 -1.3000000e+001 9.0000000e+000 1999 5 3 9 0 0 -1.4000000e+001 1.3000000e+001 1999 5 3 10 0 0 -1.1000000e+001 1.7000000e+001 1999 5 3 11 0 0 -6.0000000e+000 2.0000000e+001 1999 5 3 12 0 0 2.0000000e+000 2.0000000e+001 1999 5 3 13 0 0 9.0000000e+000 1.9000000e+001 1999 5 3 14 0 0 1.3000000e+001 1.6000000e+001 1999 5 3 15 0 0 1.3000000e+001 1.1000000e+001 1999 5 3 16 0 0 1.0000000e+001 7.0000000e+000 1999 5 3 17 0 0 3.0000000e+000 3.0000000e+000 1999 5 3 18 0 0 -5.0000000e+000 0.0000000e+000 1999 5 3 19 0 0 -1.3000000e+001 -2.0000000e+000 1999 5 3 20 0 0 -1.8000000e+001 -2.0000000e+000 1999 5 3 21 0 0 -1.9000000e+001 -2.0000000e+000 1999 5 3 22 0 0 -1.5000000e+001 -1.0000000e+000 1999 5 3 23 0 0 -9.0000000e+000 0.0000000e+000 1999 5 4 0 0 0 0.0000000e+000 0.0000000e+000 1999 5 4 1 0 0 8.0000000e+000 0.0000000e+000 1999 5 4 2 0 0 1.5000000e+001 -1.0000000e+000 1999 5 4 3 0 0 1.8000000e+001 -2.0000000e+000 1999 5 4 4 0 0 1.7000000e+001 -3.0000000e+000 1999 5 4 5 0 0 1.2000000e+001 -2.0000000e+000 1999 5 4 6 0 0 5.0000000e+000 -1.0000000e+000 1999 5 4 7 0 0 -2.0000000e+000 2.0000000e+000 1999 5 4 8 0 0 -8.0000000e+000 6.0000000e+000 1999 5 4 9 0 0 -1.1000000e+001 1.1000000e+001 1999 5 4 10 0 0 -1.1000000e+001 1.5000000e+001 1999 5 4 11 0 0 -8.0000000e+000 1.8000000e+001 1999 5 4 12 0 0 -2.0000000e+000 2.0000000e+001 1999 5 4 13 0 0 4.0000000e+000 1.9000000e+001 1999 5 4 14 0 0 9.0000000e+000 1.7000000e+001 1999 5 4 15 0 0 1.1000000e+001 1.4000000e+001 1999 5 4 16 0 0 1.0000000e+001 1.0000000e+001 1999 5 4 17 0 0 6.0000000e+000 5.0000000e+000 1999 5 4 18 0 0 -1.0000000e+000 2.0000000e+000 1999 5 4 19 0 0 -8.0000000e+000 -1.0000000e+000 1999 5 4 20 0 0 -1.3000000e+001 -2.0000000e+000 1999 5 4 21 0 0 -1.6000000e+001 -2.0000000e+000 1999 5 4 22 0 0 -1.5000000e+001 -2.0000000e+000 1999 5 4 23 0 0 -1.1000000e+001 -1.0000000e+000 1999 5 5 0 0 0 -5.0000000e+000 -1.0000000e+000 1999 5 5 1 0 0 3.0000000e+000 -1.0000000e+000 1999 5 5 2 0 0 1.0000000e+001 -1.0000000e+000 1999 5 5 3 0 0 1.4000000e+001 -2.0000000e+000 1999 5 5 4 0 0 1.5000000e+001 -2.0000000e+000 1999 5 5 5 0 0 1.3000000e+001 -2.0000000e+000 1999 5 5 6 0 0 9.0000000e+000 -1.0000000e+000 1999 5 5 7 0 0 3.0000000e+000 1.0000000e+000 1999 5 5 8 0 0 -3.0000000e+000 4.0000000e+000 1999 5 5 9 0 0 -7.0000000e+000 8.0000000e+000 1999 5 5 10 0 0 -9.0000000e+000 1.2000000e+001 1999 5 5 11 0 0 -8.0000000e+000 1.6000000e+001 1999 5 5 12 0 0 -5.0000000e+000 1.8000000e+001 1999 5 5 13 0 0 0.0000000e+000 1.9000000e+001 1999 5 5 14 0 0 5.0000000e+000 1.8000000e+001 1999 5 5 15 0 0 8.0000000e+000 1.6000000e+001 1999 5 5 16 0 0 9.0000000e+000 1.2000000e+001 1999 5 5 17 0 0 7.0000000e+000 8.0000000e+000 1999 5 5 18 0 0 2.0000000e+000 5.0000000e+000 1999 5 5 19 0 0 -3.0000000e+000 2.0000000e+000 1999 5 5 20 0 0 -8.0000000e+000 -1.0000000e+000 1999 5 5 21 0 0 -1.2000000e+001 -2.0000000e+000 1999 5 5 22 0 0 -1.4000000e+001 -2.0000000e+000 1999 5 5 23 0 0 -1.2000000e+001 -2.0000000e+000 1999 5 6 0 0 0 -8.0000000e+000 -2.0000000e+000 1999 5 6 1 0 0 -2.0000000e+000 -1.0000000e+000 1999 5 6 2 0 0 4.0000000e+000 -1.0000000e+000 1999 5 6 3 0 0 9.0000000e+000 -2.0000000e+000 1999 5 6 4 0 0 1.2000000e+001 -2.0000000e+000 1999 5 6 5 0 0 1.3000000e+001 -1.0000000e+000 1999 5 6 6 0 0 1.1000000e+001 -1.0000000e+000 1999 5 6 7 0 0 7.0000000e+000 1.0000000e+000 1999 5 6 8 0 0 2.0000000e+000 3.0000000e+000 1999 5 6 9 0 0 -2.0000000e+000 6.0000000e+000 1999 5 6 10 0 0 -6.0000000e+000 9.0000000e+000 1999 5 6 11 0 0 -7.0000000e+000 1.3000000e+001 1999 5 6 12 0 0 -6.0000000e+000 1.6000000e+001 1999 5 6 13 0 0 -4.0000000e+000 1.7000000e+001 1999 5 6 14 0 0 0.0000000e+000 1.8000000e+001 1999 5 6 15 0 0 3.0000000e+000 1.7000000e+001 1999 5 6 16 0 0 6.0000000e+000 1.4000000e+001 1999 5 6 17 0 0 6.0000000e+000 1.1000000e+001 1999 5 6 18 0 0 4.0000000e+000 8.0000000e+000 1999 5 6 19 0 0 1.0000000e+000 4.0000000e+000 1999 5 6 20 0 0 -3.0000000e+000 2.0000000e+000 1999 5 6 21 0 0 -7.0000000e+000 -1.0000000e+000 1999 5 6 22 0 0 -1.0000000e+001 -2.0000000e+000 1999 5 6 23 0 0 -1.1000000e+001 -2.0000000e+000 1999 5 7 0 0 0 -9.0000000e+000 -2.0000000e+000 1999 5 7 1 0 0 -6.0000000e+000 -2.0000000e+000 1999 5 7 2 0 0 -2.0000000e+000 -1.0000000e+000 1999 5 7 3 0 0 3.0000000e+000 -1.0000000e+000 1999 5 7 4 0 0 7.0000000e+000 -1.0000000e+000 1999 5 7 5 0 0 1.0000000e+001 0.0000000e+000 1999 5 7 6 0 0 1.1000000e+001 0.0000000e+000 1999 5 7 7 0 0 1.0000000e+001 1.0000000e+000 1999 5 7 8 0 0 7.0000000e+000 3.0000000e+000 1999 5 7 9 0 0 3.0000000e+000 5.0000000e+000 1999 5 7 10 0 0 -1.0000000e+000 7.0000000e+000 1999 5 7 11 0 0 -4.0000000e+000 1.0000000e+001 1999 5 7 12 0 0 -6.0000000e+000 1.3000000e+001 1999 5 7 13 0 0 -6.0000000e+000 1.5000000e+001 1999 5 7 14 0 0 -4.0000000e+000 1.6000000e+001 1999 5 7 15 0 0 -2.0000000e+000 1.7000000e+001 1999 5 7 16 0 0 1.0000000e+000 1.6000000e+001 1999 5 7 17 0 0 4.0000000e+000 1.4000000e+001 1999 5 7 18 0 0 5.0000000e+000 1.1000000e+001 1999 5 7 19 0 0 4.0000000e+000 8.0000000e+000 1999 5 7 20 0 0 2.0000000e+000 4.0000000e+000 1999 5 7 21 0 0 -1.0000000e+000 2.0000000e+000 1999 5 7 22 0 0 -5.0000000e+000 -1.0000000e+000 1999 5 7 23 0 0 -7.0000000e+000 -2.0000000e+000 1999 5 8 0 0 0 -9.0000000e+000 -2.0000000e+000 1999 5 8 1 0 0 -8.0000000e+000 -2.0000000e+000 1999 5 8 2 0 0 -6.0000000e+000 -1.0000000e+000 1999 5 8 3 0 0 -3.0000000e+000 0.0000000e+000 1999 5 8 4 0 0 1.0000000e+000 0.0000000e+000 1999 5 8 5 0 0 5.0000000e+000 1.0000000e+000 1999 5 8 6 0 0 8.0000000e+000 2.0000000e+000 1999 5 8 7 0 0 1.0000000e+001 3.0000000e+000 1999 5 8 8 0 0 1.0000000e+001 4.0000000e+000 1999 5 8 9 0 0 8.0000000e+000 5.0000000e+000 1999 5 8 10 0 0 5.0000000e+000 6.0000000e+000 1999 5 8 11 0 0 1.0000000e+000 8.0000000e+000 1999 5 8 12 0 0 -3.0000000e+000 1.0000000e+001 1999 5 8 13 0 0 -6.0000000e+000 1.2000000e+001 1999 5 8 14 0 0 -7.0000000e+000 1.4000000e+001 1999 5 8 15 0 0 -7.0000000e+000 1.5000000e+001 1999 5 8 16 0 0 -4.0000000e+000 1.6000000e+001 1999 5 8 17 0 0 -1.0000000e+000 1.5000000e+001 1999 5 8 18 0 0 2.0000000e+000 1.3000000e+001 1999 5 8 19 0 0 5.0000000e+000 1.1000000e+001 1999 5 8 20 0 0 6.0000000e+000 7.0000000e+000 1999 5 8 21 0 0 4.0000000e+000 4.0000000e+000 1999 5 8 22 0 0 2.0000000e+000 1.0000000e+000 1999 5 8 23 0 0 -2.0000000e+000 -1.0000000e+000 1999 5 9 0 0 0 -6.0000000e+000 -2.0000000e+000 1999 5 9 1 0 0 -8.0000000e+000 -2.0000000e+000 1999 5 9 2 0 0 -9.0000000e+000 -1.0000000e+000 1999 5 9 3 0 0 -8.0000000e+000 0.0000000e+000 1999 5 9 4 0 0 -5.0000000e+000 2.0000000e+000 1999 5 9 5 0 0 -1.0000000e+000 3.0000000e+000 1999 5 9 6 0 0 4.0000000e+000 4.0000000e+000 1999 5 9 7 0 0 8.0000000e+000 5.0000000e+000 1999 5 9 8 0 0 1.1000000e+001 6.0000000e+000 1999 5 9 9 0 0 1.2000000e+001 6.0000000e+000 1999 5 9 10 0 0 1.1000000e+001 6.0000000e+000 1999 5 9 11 0 0 7.0000000e+000 6.0000000e+000 1999 5 9 12 0 0 1.0000000e+000 7.0000000e+000 1999 5 9 13 0 0 -4.0000000e+000 9.0000000e+000 1999 5 9 14 0 0 -9.0000000e+000 1.1000000e+001 1999 5 9 15 0 0 -1.1000000e+001 1.3000000e+001 1999 5 9 16 0 0 -1.0000000e+001 1.4000000e+001 1999 5 9 17 0 0 -7.0000000e+000 1.5000000e+001 1999 5 9 18 0 0 -2.0000000e+000 1.5000000e+001 1999 5 9 19 0 0 3.0000000e+000 1.3000000e+001 1999 5 9 20 0 0 7.0000000e+000 1.0000000e+001 1999 5 9 21 0 0 9.0000000e+000 7.0000000e+000 1999 5 9 22 0 0 8.0000000e+000 4.0000000e+000 1999 5 9 23 0 0 5.0000000e+000 1.0000000e+000 1999 5 10 0 0 0 0.0000000e+000 -1.0000000e+000 1999 5 10 1 0 0 -5.0000000e+000 -2.0000000e+000 1999 5 10 2 0 0 -1.0000000e+001 -1.0000000e+000 1999 5 10 3 0 0 -1.2000000e+001 1.0000000e+000 1999 5 10 4 0 0 -1.1000000e+001 3.0000000e+000 1999 5 10 5 0 0 -8.0000000e+000 5.0000000e+000 1999 5 10 6 0 0 -2.0000000e+000 7.0000000e+000 1999 5 10 7 0 0 4.0000000e+000 8.0000000e+000 1999 5 10 8 0 0 1.0000000e+001 9.0000000e+000 1999 5 10 9 0 0 1.4000000e+001 8.0000000e+000 1999 5 10 10 0 0 1.5000000e+001 7.0000000e+000 1999 5 10 11 0 0 1.3000000e+001 6.0000000e+000 1999 5 10 12 0 0 7.0000000e+000 6.0000000e+000 1999 5 10 13 0 0 0.0000000e+000 6.0000000e+000 1999 5 10 14 0 0 -8.0000000e+000 7.0000000e+000 1999 5 10 15 0 0 -1.3000000e+001 9.0000000e+000 1999 5 10 16 0 0 -1.5000000e+001 1.1000000e+001 1999 5 10 17 0 0 -1.4000000e+001 1.3000000e+001 1999 5 10 18 0 0 -9.0000000e+000 1.4000000e+001 1999 5 10 19 0 0 -1.0000000e+000 1.4000000e+001 1999 5 10 20 0 0 6.0000000e+000 1.2000000e+001 1999 5 10 21 0 0 1.2000000e+001 1.0000000e+001 1999 5 10 22 0 0 1.4000000e+001 6.0000000e+000 1999 5 10 23 0 0 1.3000000e+001 3.0000000e+000 1999 5 11 0 0 0 8.0000000e+000 0.0000000e+000 1999 5 11 1 0 0 1.0000000e+000 -1.0000000e+000 1999 5 11 2 0 0 -6.0000000e+000 -1.0000000e+000 1999 5 11 3 0 0 -1.2000000e+001 1.0000000e+000 1999 5 11 4 0 0 -1.5000000e+001 3.0000000e+000 1999 5 11 5 0 0 -1.4000000e+001 7.0000000e+000 1999 5 11 6 0 0 -1.0000000e+001 1.0000000e+001 1999 5 11 7 0 0 -2.0000000e+000 1.2000000e+001 1999 5 11 8 0 0 6.0000000e+000 1.3000000e+001 1999 5 11 9 0 0 1.3000000e+001 1.2000000e+001 1999 5 11 10 0 0 1.8000000e+001 1.1000000e+001 1999 5 11 11 0 0 1.8000000e+001 8.0000000e+000 1999 5 11 12 0 0 1.4000000e+001 6.0000000e+000 1999 5 11 13 0 0 6.0000000e+000 5.0000000e+000 1999 5 11 14 0 0 -4.0000000e+000 4.0000000e+000 1999 5 11 15 0 0 -1.3000000e+001 5.0000000e+000 1999 5 11 16 0 0 -1.8000000e+001 7.0000000e+000 1999 5 11 17 0 0 -2.0000000e+001 1.0000000e+001 1999 5 11 18 0 0 -1.6000000e+001 1.2000000e+001 1999 5 11 19 0 0 -8.0000000e+000 1.3000000e+001 1999 5 11 20 0 0 1.0000000e+000 1.3000000e+001 1999 5 11 21 0 0 1.1000000e+001 1.1000000e+001 1999 5 11 22 0 0 1.7000000e+001 8.0000000e+000 1999 5 11 23 0 0 1.9000000e+001 5.0000000e+000 1999 5 12 0 0 0 1.6000000e+001 1.0000000e+000 1999 5 12 1 0 0 9.0000000e+000 -1.0000000e+000 1999 5 12 2 0 0 0.0000000e+000 -1.0000000e+000 1999 5 12 3 0 0 -9.0000000e+000 0.0000000e+000 1999 5 12 4 0 0 -1.6000000e+001 3.0000000e+000 1999 5 12 5 0 0 -1.9000000e+001 7.0000000e+000 1999 5 12 6 0 0 -1.7000000e+001 1.2000000e+001 1999 5 12 7 0 0 -1.0000000e+001 1.5000000e+001 1999 5 12 8 0 0 -1.0000000e+000 1.7000000e+001 1999 5 12 9 0 0 9.0000000e+000 1.7000000e+001 1999 5 12 10 0 0 1.7000000e+001 1.5000000e+001 1999 5 12 11 0 0 2.1000000e+001 1.2000000e+001 1999 5 12 12 0 0 1.9000000e+001 8.0000000e+000 1999 5 12 13 0 0 1.3000000e+001 5.0000000e+000 1999 5 12 14 0 0 3.0000000e+000 3.0000000e+000 1999 5 12 15 0 0 -9.0000000e+000 2.0000000e+000 1999 5 12 16 0 0 -1.8000000e+001 3.0000000e+000 1999 5 12 17 0 0 -2.4000000e+001 5.0000000e+000 1999 5 12 18 0 0 -2.3000000e+001 8.0000000e+000 1999 5 12 19 0 0 -1.7000000e+001 1.0000000e+001 1999 5 12 20 0 0 -6.0000000e+000 1.1000000e+001 1999 5 12 21 0 0 6.0000000e+000 1.1000000e+001 1999 5 12 22 0 0 1.6000000e+001 9.0000000e+000 1999 5 12 23 0 0 2.3000000e+001 6.0000000e+000 1999 5 13 0 0 0 2.4000000e+001 2.0000000e+000 1999 5 13 1 0 0 1.9000000e+001 0.0000000e+000 1999 5 13 2 0 0 9.0000000e+000 -1.0000000e+000 1999 5 13 3 0 0 -2.0000000e+000 0.0000000e+000 1999 5 13 4 0 0 -1.3000000e+001 3.0000000e+000 1999 5 13 5 0 0 -1.9000000e+001 7.0000000e+000 1999 5 13 6 0 0 -2.1000000e+001 1.2000000e+001 1999 5 13 7 0 0 -1.7000000e+001 1.7000000e+001 1999 5 13 8 0 0 -9.0000000e+000 2.0000000e+001 1999 5 13 9 0 0 2.0000000e+000 2.1000000e+001 1999 5 13 10 0 0 1.3000000e+001 2.0000000e+001 1999 5 13 11 0 0 2.0000000e+001 1.7000000e+001 1999 5 13 12 0 0 2.2000000e+001 1.3000000e+001 1999 5 13 13 0 0 1.9000000e+001 8.0000000e+000 1999 5 13 14 0 0 1.0000000e+001 4.0000000e+000 1999 5 13 15 0 0 -2.0000000e+000 1.0000000e+000 1999 5 13 16 0 0 -1.4000000e+001 0.0000000e+000 1999 5 13 17 0 0 -2.4000000e+001 1.0000000e+000 1999 5 13 18 0 0 -2.7000000e+001 3.0000000e+000 1999 5 13 19 0 0 -2.5000000e+001 6.0000000e+000 1999 5 13 20 0 0 -1.6000000e+001 8.0000000e+000 1999 5 13 21 0 0 -3.0000000e+000 9.0000000e+000 1999 5 13 22 0 0 1.1000000e+001 8.0000000e+000 1999 5 13 23 0 0 2.2000000e+001 6.0000000e+000 1999 5 14 0 0 0 2.7000000e+001 3.0000000e+000 1999 5 14 1 0 0 2.6000000e+001 0.0000000e+000 1999 5 14 2 0 0 1.9000000e+001 -2.0000000e+000 1999 5 14 3 0 0 8.0000000e+000 -2.0000000e+000 1999 5 14 4 0 0 -5.0000000e+000 1.0000000e+000 1999 5 14 5 0 0 -1.6000000e+001 5.0000000e+000 1999 5 14 6 0 0 -2.2000000e+001 1.1000000e+001 1999 5 14 7 0 0 -2.2000000e+001 1.6000000e+001 1999 5 14 8 0 0 -1.6000000e+001 2.1000000e+001 1999 5 14 9 0 0 -6.0000000e+000 2.4000000e+001 1999 5 14 10 0 0 5.0000000e+000 2.4000000e+001 1999 5 14 11 0 0 1.6000000e+001 2.2000000e+001 1999 5 14 12 0 0 2.2000000e+001 1.8000000e+001 1999 5 14 13 0 0 2.2000000e+001 1.2000000e+001 1999 5 14 14 0 0 1.7000000e+001 7.0000000e+000 1999 5 14 15 0 0 6.0000000e+000 2.0000000e+000 1999 5 14 16 0 0 -7.0000000e+000 -1.0000000e+000 1999 5 14 17 0 0 -1.9000000e+001 -2.0000000e+000 1999 5 14 18 0 0 -2.7000000e+001 -1.0000000e+000 1999 5 14 19 0 0 -2.9000000e+001 1.0000000e+000 1999 5 14 20 0 0 -2.4000000e+001 3.0000000e+000 1999 5 14 21 0 0 -1.3000000e+001 5.0000000e+000 1999 5 14 22 0 0 1.0000000e+000 6.0000000e+000 1999 5 14 23 0 0 1.5000000e+001 5.0000000e+000 1999 5 15 0 0 0 2.5000000e+001 2.0000000e+000 1999 5 15 1 0 0 2.9000000e+001 0.0000000e+000 1999 5 15 2 0 0 2.7000000e+001 -2.0000000e+000 1999 5 15 3 0 0 1.8000000e+001 -3.0000000e+000 1999 5 15 4 0 0 5.0000000e+000 -1.0000000e+000 1999 5 15 5 0 0 -7.0000000e+000 2.0000000e+000 1999 5 15 6 0 0 -1.7000000e+001 8.0000000e+000 1999 5 15 7 0 0 -2.2000000e+001 1.4000000e+001 1999 5 15 8 0 0 -2.1000000e+001 2.0000000e+001 1999 5 15 9 0 0 -1.4000000e+001 2.4000000e+001 1999 5 15 10 0 0 -3.0000000e+000 2.7000000e+001 1999 5 15 11 0 0 8.0000000e+000 2.6000000e+001 1999 5 15 12 0 0 1.7000000e+001 2.3000000e+001 1999 5 15 13 0 0 2.2000000e+001 1.8000000e+001 1999 5 15 14 0 0 2.0000000e+001 1.1000000e+001 1999 5 15 15 0 0 1.3000000e+001 5.0000000e+000 1999 5 15 16 0 0 1.0000000e+000 0.0000000e+000 1999 5 15 17 0 0 -1.2000000e+001 -3.0000000e+000 1999 5 15 18 0 0 -2.3000000e+001 -4.0000000e+000 1999 5 15 19 0 0 -2.9000000e+001 -3.0000000e+000 1999 5 15 20 0 0 -2.8000000e+001 -1.0000000e+000 1999 5 15 21 0 0 -2.1000000e+001 1.0000000e+000 1999 5 15 22 0 0 -9.0000000e+000 2.0000000e+000 1999 5 15 23 0 0 5.0000000e+000 2.0000000e+000 1999 5 16 0 0 0 1.8000000e+001 1.0000000e+000 1999 5 16 1 0 0 2.7000000e+001 -1.0000000e+000 1999 5 16 2 0 0 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4.0000000e+000 -1.0000000e+000 1999 5 31 0 0 0 1.3000000e+001 -1.0000000e+000 1999 5 31 1 0 0 2.0000000e+001 -2.0000000e+000 1999 5 31 2 0 0 2.2000000e+001 -4.0000000e+000 1999 5 31 3 0 0 1.9000000e+001 -4.0000000e+000 1999 5 31 4 0 0 1.2000000e+001 -3.0000000e+000 1999 5 31 5 0 0 3.0000000e+000 -1.0000000e+000 1999 5 31 6 0 0 -6.0000000e+000 3.0000000e+000 1999 5 31 7 0 0 -1.3000000e+001 8.0000000e+000 1999 5 31 8 0 0 -1.5000000e+001 1.3000000e+001 1999 5 31 9 0 0 -1.3000000e+001 1.8000000e+001 1999 5 31 10 0 0 -7.0000000e+000 2.1000000e+001 1999 5 31 11 0 0 1.0000000e+000 2.2000000e+001 1999 5 31 12 0 0 8.0000000e+000 2.1000000e+001 1999 5 31 13 0 0 1.4000000e+001 1.7000000e+001 1999 5 31 14 0 0 1.5000000e+001 1.2000000e+001 1999 5 31 15 0 0 1.2000000e+001 7.0000000e+000 1999 5 31 16 0 0 5.0000000e+000 2.0000000e+000 1999 5 31 17 0 0 -4.0000000e+000 -1.0000000e+000 1999 5 31 18 0 0 -1.3000000e+001 -4.0000000e+000 1999 5 31 19 0 0 -1.9000000e+001 -4.0000000e+000 1999 5 31 20 0 0 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