April / 2010 UFOOrbitV2 1 UFOOrbitV2 (UO2) A Tool for Simultaneous Observers

April / 2010 UFOOrbitV2 2 General orbit determination processes 1)Observed radiant computation 2)Trajectory determination 3)Diurnal aberration compensation 4)Zenith attraction compensation 5)Heliocentric state vector computation 6)Heliocentric orbit element computation

April / 2010 UFOOrbitV2 3 Problems UO2 has faced on automated orbit computation - Quality control - Quality elements - Simultaneously happened meteors - Start time problem - Delayed report problem - How to deal with a meteor that is observed by more than 2 cameras - Handling of encrypted locations - Key Values - Leap seconds - Solar longitude - Sun distance - Earth ’ s orbit velocity - GST - Earth shape model - Earth gravity model - Escape velocity

April / 2010 UFOOrbitV2 4 Quality control Quality control is necessary for automated orbit computation. Because : 1)Automated process makes many fictional results, because computation can be done on any combination of observations, even they are the observations of different meteors. 2)Even only from 1 pair of simultaneous observations, we get 2 trajectories from both stations. In case of 10 cameras capture one meteor, we will get 900 orbits for one meteor. They are similar with each other, but different. So we should do something for them to get only 1 result. Simple averaging might involve big errors, so we should use some quality measures there. 3)Observation quality differs on each meteor very much. While, required orbit accuracy is depending on the purpose. So, observation DB should include all observations regardless of their accuracy. And quality selection should be done at orbit computation stage.

April / 2010 UFOOrbitV2 5 Actual distribution of Qo Observed trajectory angular length ( Qo ) is the major factor of accuracy. It dominates both accuracy of radiant and velocity on each meteor. Ex. Typical pole determination accuracy (Ep = atan ( 0.05 / Qo / N^0.5 ) : simple estimation) Qo = 1 deg, 2 fields  4 deg Qo = 10 deg, 10 fields  0.06 deg The result of our observation Qo < 3 deg : 50% Qo > 10 deg : 7% Short meteors were the major ! So we cannot reject them.

April / 2010 UFOOrbitV2 6 Quality Control sample Q0 Q1 Quality levels preset on UO2 Q0: Compute all possible pairs within assigned start time difference (DT) Q1 : Rejection of fictional meteors for general purpose Q2 : Rejection of poor radiant accuracy for radiant research Q3: Rejection of poor velocity accuracy for orbit research Note: different quality threshold makes different result set!

April / 2010 UFOOrbitV2 7 Fictional meteors Fictional meteors often have abnormal Vo, H1, H2 and not matched ground trajectories. Limiting of Vo might cause rejection of interstellar meteors. UO2 uses H1,H2,dGP,Gm for Q1

April / 2010 UFOOrbitV2 8 QUA 2009

April / 2010 UFOOrbitV2 9 Quality elements for quality control UO2 original values Ed = (Dc/sqrt(N) + Dd)/Qo*Qr2/sin(Qc) (radiant accuracy proportional value) Ex = Ed / sin(Qd) (trajectory accuracy proportional value) QA : experimental combination of drop, inout, tme, leap, Qo, Vo, e, Ex Dc: linearity, Dd: FOV accuracy N: number of samples How about using Ed as accuracy value of radiant in DB? It is more useful than σRA and σDEC, also clear and easier than covariance.

April / 2010 UFOOrbitV2 10 Preset Quality levels

April / 2010 UFOOrbitV2 11 Simultaneously happened meteors …. a difficult problem !! 3 actual meteors in two seconds Miss-combined fictional trajectory UO2 procedure 1.Computes all pair of observations in 2 to 30 (dt) seconds. (when 3 meteors happened simultaneously, and they were observed by 10 stations, 435 combinations should be tried) 2. Reject low quality pair 3. Combine pairs that have almost same radiant and geocentric plane pole (dD), and make a set for one meteor. Yet, there happens miss-combined set or miss- rejection of true observations.

April / 2010 UFOOrbitV2 12 Start time problem dt cannot be too small !! because each station captures different part of the trajectory

April / 2010 UFOOrbitV2 13 Delayed report problem computation time 12:30 21:00 next week Reported obs obs1 met1 obs1 met1 ’ obs1 met1 ’’ obs2 obs2 obs2 obs3 obs3 met2 obs3 obs4 obs4 obs5 Problem We cannot decide permanent ID for each meteor We cannot fix the meteor set Same situation occurs by changing the quality conditions or updates of each observation.  Meteor ID should be temporal number of each computation at one time.  Meteor set will be updated frequently except annual summary.

April / 2010 UFOOrbitV2 14 How to deal with a meteor that is observed by more than 2 cameras  We should develop a method that utilize all information from more than 2 cameras. for - more precise observed radiant and velocity computation. - accuracy confirmation or correction of each observations. Problem of traditional pair computation - Computation from different pairs on one meteor produces many different orbits. ( Especially when the cross angle (Qc) is not enough or radiant distance (Qr) is big.)

April / 2010 UFOOrbitV2 15 Unified Radiant Computation UO2 uses least square method to minimize the total orthogonal error among the pole directions of multiple observations.

April / 2010 UFOOrbitV2 16 Unified Radiant

April / 2010 UFOOrbitV2 17 Unification of Trajectory Time unification : forcing using single time to compute trajectory. – fix the Earth ’ s orientation. (Time correction of each station was tried but it failed. It did over correction, caused by direction measurement errors). Trail unification : unification of trajectory geocentric plane.

April / 2010 UFOOrbitV2 18 Unified radiant computation process 1. All pair computation 2. Quality check of each pair -- rejection of fictional pairs 3. Simultaneous observation set determination (grouping of pairs) the logic is “ Friend of a friend is a friend ”. 4. Unified radiant computation 5. Observed plane pole, begin/end direction, time correction 6. Find best pairing observation for each 7. Each trajectory computation using unified radiant 8. Trajectory unification (optional) 9. Observed velocity computation

April / 2010 UFOOrbitV2 19 Handling of encrypted locations on UA2-UO2 UA2 encodes the location. UO2 decodes the location and uses only for internal computation. (coder and decoder uses original same secret procedure.) Thus, the server became free from privacy issues. Someone who wants to know locations of other people, asks directory to the observer and network does not concern it at all. It seems everything is going well. Encryption of station ’ s location was introduced to protect home observer ’ s privacy.

April / 2010 UFOOrbitV2 20 Key Values on UO2 (v2.23) Note: Pole direction accuracy( Ep) of current video observation may reach to a few degrees for short meteors. Ep is amplified by Qc, Qd, and Qr. This dominates the overall orbit accuracy. Other factors seems concerning only small number of long meteors. 1) Leap seconds TT = UTC - leap_seconds : definition TT ’ = UTC - leap_seconds – dsec : UFOseries UO2 UFOx_LSec.csv

April / 2010 UFOOrbitV2 21 2) Planets position, Solar longitude, Distance from Sun Same as freeware XYZ2000.C by Munehiro Umeda considering 6 planets and moon perturbation, based on TDT ’ : 1) accuracy : solar ecliptic longitude : 0.12 arcsec ( deg), latitude 0.14 arcsec. << 1 sec ! ex. Sol-long at UTC _ > deg (SPICE ) 3) Earth ’ s orbit velocity vector compute from difference of Earth ’ s position 2) in ±0.001 day 4) Greenwich Sidereal Time JD0: JD of 0H hour,min,sec : UTC double T = (JD ) / ; double GST = *(hour + min/ sec/3600.0) *T *T*T; 5) Earth shape model Lc : geocentric latitude, Ld : geographic latitude, Rl : radius at the geocentric latitude Ld = Lc *sin(2*Lc) – *sin(4*Lc) Rl = *( *cos(2*Lc) *cos(4*Lc)) 6) Earth gravity model not used. 7) Escape velocity Vlim = ; // km/s, Escape velocity at H=100km

April / 2010 UFOOrbitV2 22 Conclusion / Comment Simultaneous observation brings us far more information of the object, compared with single station observation. Simultaneous observation by more than 2 cameras brings much more information. We should utilize them. Automated orbit computation faces many problems. Most of them are practical issues, but unless the solution of those problems, we cannot go further. Measurement accuracy on video field dominates total orbit accuracy at present. Especially, the accuracy of velocity is poor for most of the meteors. Over 10% error is often. Standing on this, the difference of heliocentric orbit computation methods seems not so important now. Comparing with velocity, as is shown in the radiant map, the radiant position seems to have fair accuracy for most of the meteors. It is usable for shower discussions.