I played around at the NASA site and discovered:
* With the orbit viewer I used earlier "The position of the small body is computed using so-called two-body equations: only the gravitational force of the Sun is considered in the viewer. "
* A 'Horizons' page does more detailed calculations
* Using the Horizons App, I asked for about 5000 days of results for 2024 YR4 and it responded in less than 2 seconds. (I suppose this means it accessed precomputed data. Could this still be less accurate than the software used for collision warnings?)
Three different output options are possible: Observer Table, Vector Table, Osculating Orbital Elements. (Below is shown Observer Table, with Observer on Earth).
Almost all of this was meaningless to me. I'm not sure how best to locate a near-approach from this data.
I did see that 'delta' became very small in December of 2024, 2028, 2032 and that 'RelVel-Ang' changed dramatically at about the same date. But these did not occur again, though I asked for data until 2041.
I'm attaching data for the recent near approach to 2024 YR4. The approach -- just like the mythical Star of Bethlehem!! -- was on Christmas Day 2024!
Code:
*******************************************************************************
Initial IAU76/J2000 heliocentric ecliptic osculating elements (au, days, deg.):
EPOCH= 2460695.5 ! 2025-Jan-20.00 (TDB) Residual RMS= .057989
EC= .6616164102004315 QR= .8515161099862746 TP= 2460636.9244826701
OM= 271.3679794495887 W= 134.3642503445431 IN= 3.408321749645021
Equivalent ICRF heliocentric cartesian coordinates (au, au/d):
X=-5.932501620613568E-01 Y= 9.668449181317200E-01 Z= 3.822901210499166E-01
VX=-1.937102285403371E-02 VY= 3.768670993505030E-07 VZ=-1.257688187524957E-03
Asteroid physical parameters (km, seconds, rotational period in hours):
GM= n.a. RAD= n.a. ROTPER= n.a.
H= 23.96 G= .150 B-V= n.a.
ALBEDO= n.a. STYP= n.a.
******************************************************************************************************************************************************************************
Date__(UT)__HR:MN R.A._____(ICRF)_____DEC APmag S-brt delta deldot S-O-T /r S-T-O Sky_motion Sky_mot_PA RelVel-ANG Lun_Sky_Brt sky_SNR
******************************************************************************************************************************************************************************
$$SOE
2024-Nov-01 00:00 19 02 47.84 -15 33 08.1 25.034 n.a. 0.43889015279490 -11.9113116 66.7048 /T 87.0870 0.9464332 78.255300 -67.14314 n.a. n.a.
2024-Nov-02 00:00 19 04 20.38 -15 28 31.3 25.028 n.a. 0.43195130055931 -12.1133907 66.0919 /T 88.1168 0.9502921 78.087589 -67.72562 n.a. n.a.
2024-Nov-03 00:00 19 05 53.15 -15 23 49.6 25.023 n.a. 0.42489716436977 -12.3104077 65.4801 /T 89.1612 0.9529876 77.916268 -68.31750 n.a. n.a.
2024-Nov-04 00:00 19 07 26.03 -15 19 03.2 25.018 n.a. 0.41773078112157 -12.5019709 64.8688 /T 90.2201 0.9544738 77.741709 -68.91837 n.a. n.a.
2024-Nov-05 00:00 19 08 58.89 -15 14 12.5 25.013 n.a. 0.41045541626027 -12.6876809 64.2576 /T 91.2935 0.9547048 77.564325 -69.52781 n.a. n.a.
2024-Nov-06 00:00 19 10 31.61 -15 09 17.6 25.010 n.a. 0.40307456773947 -12.8671324 63.6460 /T 92.3817 0.9536348 77.384594 -70.14534 n.a. n.a.
2024-Nov-07 00:00 19 12 04.07 -15 04 19.1 25.007 n.a. 0.39559196892918 -13.0399159 63.0335 /T 93.4845 0.9512190 77.203063 -70.77046 n.a. n.a.
2024-Nov-08 00:00 19 13 36.12 -14 59 17.3 25.004 n.a. 0.38801159045521 -13.2056199 62.4196 /T 94.6019 0.9474143 77.020376 -71.40259 n.a. n.a.
2024-Nov-09 00:00 19 15 07.63 -14 54 12.7 25.003 n.a. 0.38033764094865 -13.3638324 61.8037 /T 95.7339 0.9421810 76.837292 -72.04110 n.a. n.a.
2024-Nov-10 00:00 19 16 38.45 -14 49 05.8 25.002 n.a. 0.37257456629759 -13.5141446 61.1852 /T 96.8803 0.9354847 76.654716 -72.68523 n.a. n.a.
2024-Nov-11 00:00 19 18 08.46 -14 43 57.2 25.002 n.a. 0.36472704607797 -13.6561578 60.5637 /T 98.0412 0.9272988 76.473727 -73.33411 n.a. n.a.
2024-Nov-12 00:00 19 19 37.50 -14 38 47.4 25.003 n.a. 0.35679998447519 -13.7894958 59.9384 /T 99.2163 0.9176086 76.295597 -73.98670 n.a. n.a.
2024-Nov-13 00:00 19 21 05.44 -14 33 37.3 25.005 n.a. 0.34879849171700 -13.9138254 59.3088 /T 100.4054 0.9064139 76.121785 -74.64179 n.a. n.a.
2024-Nov-14 00:00 19 22 32.12 -14 28 27.4 25.008 n.a. 0.34072785191818 -14.0288825 58.6744 /T 101.6083 0.8937307 75.953892 -75.29801 n.a. n.a.
2024-Nov-15 00:00 19 23 57.42 -14 23 18.6 25.013 n.a. 0.33259347555049 -14.1344974 58.0345 /T 102.8247 0.8795892 75.793598 -75.95393 n.a. n.a.
2024-Nov-16 00:00 19 25 21.20 -14 18 11.7 25.018 n.a. 0.32440083969878 -14.2306103 57.3885 /T 104.0544 0.8640279 75.642589 -76.60813 n.a. n.a.
2024-Nov-17 00:00 19 26 43.34 -14 13 07.4 25.025 n.a. 0.31615542475318 -14.3172674 56.7359 /T 105.2970 0.8470850 75.502525 -77.25934 n.a. n.a.
2024-Nov-18 00:00 19 28 03.71 -14 08 06.7 25.032 n.a. 0.30786265853623 -14.3945998 56.0761 /T 106.5520 0.8287912 75.375075 -77.90651 n.a. n.a.
2024-Nov-19 00:00 19 29 22.18 -14 03 10.3 25.041 n.a. 0.29952787590332 -14.4627932 55.4085 /T 107.8190 0.8091645 75.262040 -78.54879 n.a. n.a.
2024-Nov-20 00:00 19 30 38.65 -13 58 19.3 25.052 n.a. 0.29115629535310 -14.5220611 54.7328 /T 109.0976 0.7882099 75.165506 -79.18551 n.a. n.a.
2024-Nov-21 00:00 19 31 52.99 -13 53 34.5 25.064 n.a. 0.28275300832539 -14.5726284 54.0482 /T 110.3873 0.7659212 75.088040 -79.81613 n.a. n.a.
2024-Nov-22 00:00 19 33 05.09 -13 48 56.8 25.077 n.a. 0.27432297450467 -14.6147263 53.3544 /T 111.6876 0.7422842 75.032885 -80.44012 n.a. n.a.
2024-Nov-23 00:00 19 34 14.83 -13 44 27.4 25.092 n.a. 0.26587101743276 -14.6485958 52.6507 /T 112.9979 0.7172790 75.004178 -81.05699 n.a. n.a.
2024-Nov-24 00:00 19 35 22.09 -13 40 07.2 25.108 n.a. 0.25740181721426 -14.6744938 51.9367 /T 114.3179 0.6908808 75.007228 -81.66623 n.a. n.a.
2024-Nov-25 00:00 19 36 26.75 -13 35 57.4 25.126 n.a. 0.24891989943747 -14.6926993 51.2118 /T 115.6471 0.6630592 75.048879 -82.26732 n.a. n.a.
2024-Nov-26 00:00 19 37 28.68 -13 31 59.1 25.145 n.a. 0.24042962096106 -14.7035180 50.4754 /T 116.9850 0.6337764 75.138035 -82.85973 n.a. n.a.
2024-Nov-27 00:00 19 38 27.76 -13 28 13.6 25.166 n.a. 0.23193515396295 -14.7072837 49.7269 /T 118.3313 0.6029839 75.286455 -83.44298 n.a. n.a.
2024-Nov-28 00:00 19 39 23.85 -13 24 42.3 25.189 n.a. 0.22344046987716 -14.7043571 48.9659 /T 119.6854 0.5706186 75.509958 -84.01661 n.a. n.a.
2024-Nov-29 00:00 19 40 16.82 -13 21 26.5 25. n.a. 0.21494932478587 -14.6951223 48.1915 /T 121.0472 0.5365976 75.830337 -84.58021 n.a. n.a.
2024-Nov-30 00:00 19 41 06.53 -13 18 27.8 25. n.a. 0.20646524758910 -14.6799808 47.4033 /T 122.4164 0.5008143 76.278482 -85.13345 n.a. n.a.
2024-Dec-01 00:00 19 41 52.82 -13 15 48.1 25. n.a. 0.19799153188013 -14.6593446 46.6003 /T 123.7927 0.4631337 76.899660 -85.67603 n.a. n.a.
2024-Dec-02 00:00 19 42 35.50 -13 13 29.1 25. n.a. 0.18953123192031 -14.6336292 45.7819 /T 125.1762 0.4233911 77.762893 -86.20768 n.a. n.a.
2024-Dec-03 00:00 19 43 14.40 -13 11 33.0 25. n.a. 0.18108716250101 -14.6032473 44.9471 /T 126.5670 0.3813955 78.978556 -86.72802 n.a. n.a.
2024-Dec-04 00:00 19 43 49.29 -13 10 02.4 25. n.a. 0.17266190193330 -14.5686044 44.0949 /T 127.9651 0.3369481 80.733778 -87.23640 n.a. n.a.
2024-Dec-05 00:00 19 44 19.91 -13 08 59.9 25. n.a. 0.16425779707674 -14.5300961 43.2240 /T 129.3712 0.2898983 83.370129 -87.73146 n.a. n.a.
2024-Dec-06 00:00 19 44 45.97 -13 08 29.0 25. n.a. 0.15587696929650 -14.4881076 42.3332 /T 130.7859 0.2403116 87.572905 -88.20991 n.a. n.a.
2024-Dec-07 00:00 19 45 07.13 -13 08 33.6 25. n.a. 0.14752132046773 -14.4430137 41.4206 /T 132.2101 0.1890169 94.889966 -88.66313 n.a. n.a.
2024-Dec-08 00:00 19 45 22.95 -13 09 18.4 25. n.a. 0.13919253842599 -14.3951811 40.4842 /T 133.6454 0.1396418 109.24646 -89.06492 n.a. n.a.
2024-Dec-09 00:00 19 45 32.91 -13 10 49.1 26. n.a. 0.13089210137524 -14.3449695 39.5216 /T 135.0936 0.1063096 139.14632 -89.32820 n.a. n.a.
2024-Dec-10 00:00 19 45 36.38 -13 13 13.1 26. n.a. 0.12262128064201 -14.2927362 38.5295 /T 136.5572 0.1203634 180.00259 -89.28485 n.a. n.a.
2024-Dec-11 00:00 19 45 32.55 -13 16 39.2 26. n.a. 0.11438114107672 -14.2388397 37.5041 /T 138.0398 0.1849998 205.19879 -88.97086 n.a. n.a.
2024-Dec-12 00:00 19 45 20.38 -13 21 19.1 26. n.a. 0.10617253901074 -14.1836438 36.4402 /T 139.5460 0.2805602 217.16200 -88.54578 n.a. n.a.
2024-Dec-13 00:00 19 44 58.49 -13 27 27.8 26. n.a. 0.09799611989029 -14.1275135 35.3312 /T 141.0820 0.4017598 223.40326 -88.07062 n.a. n.a.
2024-Dec-14 00:00 19 44 25.03 -13 35 25.8 26. n.a. 0.08985232225794 -14.0707949 34.1679 /T 142.6565 0.5525259 227.02982 -87.55785 n.a. n.a.
2024-Dec-15 00:00 19 43 37.45 -13 45 40.8 26. n.a. 0.08174140178760 -14.0137634 32.9378 /T 144.2816 0.7425527 229.30058 -87.00297 n.a. n.a.
2024-Dec-16 00:00 19 42 32.06 -13 58 52.4 26. n.a. 0.07366349867414 -13.9565215 31.6231 /T 145.9750 0.9884898 230.79704 -86.39134 n.a. n.a.
2024-Dec-17 00:00 19 41 03.37 -14 15 58.8 26. n.a. 0.06561878639715 -13.8988109 30.1970 /T 147.7631 1.3183358 231.82428 -85.69738 n.a. n.a.
2024-Dec-18 00:00 19 39 02.81 -14 38 29.4 26. n.a. 0.05760777050674 -13.8396611 28.6185 /T 149.6867 1.7809507 232.56272 -84.87937 n.a. n.a.
2024-Dec-19 00:00 19 36 16.21 -15 08 49.0 26. n.a. 0.04963188448266 -13.7766564 26.8201 /T 151.8132 2.4670440 233.13479 -83.86794 n.a. n.a.
2024-Dec-20 00:00 19 32 18.43 -15 51 08.8 26. n.a. 0.04169474990405 -13.7041993 24.6836 /T 154.2605 3.5599088 233.64232 -82.54102 n.a. n.a.
2024-Dec-21 00:00 19 26 20.33 -16 53 24.2 27. n.a. 0.03380515289861 -13.6087167 21.9832 /T 157.2542 5.4750044 234.20208 -80.66402 n.a. n.a.
2024-Dec-22 00:00 19 16 31.79 -18 32 27.8 27. n.a. 0.02598529673598 -13.4526565 18.2309 /T 161.2821 9.3186485 235.01798 -77.72461 n.a. n.a.
2024-Dec-23 00:00 18 57 47.94 -21 30 47.3 30. n.a. 0.01829964959795 -13.1043898 12.1930 /T 167.5764 18.829537 236.64732 -72.36697 n.a. n.a.
2024-Dec-24 00:00 18 09 57.04 -27 59 14.6 42. n.a. 0.01100016802592 -11.8683491 4.5717 /L 175.3771 52.115390 241.67392 -59.71887 n.a. n.a.
2024-Dec-25 00:00 14 42 37.18 -38 50 35.1 19. n.a. 0.00575801537682 -3.7465923 47.1986 /L 132.5555 190.09506 271.80504 -15.80707 n.a. n.a.
2024-Dec-26 00:00 10 07 08.82 -14 03 06.4 15.913 n.a. 0.00843316417841 10.3502870 112.8331 /L 66.7167 88.625945 306.70026 48.882553 n.a. n.a.
2024-Dec-27 00:00 09 03 38.72 -01 46 56.3 16.615 n.a. 0.01532164109864 12.7980240 133.6345 /L 45.7275 26.897465 308.92902 68.731330 n.a. n.a.
2024-Dec-28 00:00 08 41 06.45 +02 45 07.9 17.271 n.a. 0.02289446567090 13.3270922 141.7767 /L 37.4141 12.099584 308.86736 75.895867 n.a. n.a.
2024-Dec-29 00:00 08 29 44.81 +05 01 07.9 17.789 n.a. 0.03065533088115 13.5257874 146.3242 /L 32.7118 6.8009762 308.64810 79.445428 n.a. n.a.
2024-Dec-30 00:00 08 22 53.43 +06 22 21.3 18.208 n.a. 0.03849989988518 13.6337280 149.4215 /L 29.4760 4.3619310 308.44780 81.531208 n.a. n.a.
2024-Dec-31 00:00 08 18 16.64 +07 16 31.4 18.557 n.a. 0.04639645314824 13.7109697 151.7964 /L 26.9785 3.0509129 308.28802 82.886508 n.a. n.a.
2025-Jan-01 00:00 08 14 56.29 +07 55 28.1 18.855 n.a. 0.05433407527075 13.7779015 153.7593 /L 24.9086 2.2691968 308.17492 83.826216 n.a. n.a.
2025-Jan-02 00:00 08 12 23.41 +08 25 02.9 19.115 n.a. 0.06230954795476 13.8428814 155.4636 /L 23.1125 1.7672009 308.11516 84.507678 n.a. n.a.
2025-Jan-03 00:00 08 10 22.02 +08 48 29.1 19.345 n.a. 0.07032299219339 13.9097760 156.9930 /L 21.5061 1.4263227 308.11668 85.018347 n.a. n.a.
2025-Jan-04 00:00 08 08 42.58 +09 07 41.2 19.551 n.a. 0.07837613059137 13.9805126 158.3964 /L 20.0399 1.1844921 308.18750 85.410796 n.a. n.a.
2025-Jan-05 00:00 08 07 19.09 +09 23 51.5 19.738 n.a. 0.08647150098570 14.0560928 159.7039 /L 18.6834 1.0067366 308.33470 85.718566 n.a. n.a.
2025-Jan-06 00:00 08 06 07.57 +09 37 47.5 19.909 n.a. 0.09461206876726 14.1370459 160.9341 /L 17.4171 0.8721703 308.56387 85.964064 n.a. n.a.
2025-Jan-07 00:00 08 05 05.31 +09 50 02.0 20.066 n.a. 0.10280102607491 14.2236536 162.0989 /L 16.2284 0.7677183 308.87909 86.162818 n.a. n.a.
2025-Jan-08 00:00 08 04 10.38 +10 00 58.1 20.212 n.a. 0.11104168656915 14.3160691 163.2053 /L 15.1095 0.6848703 309.28320 86.325918 n.a. n.a.
2025-Jan-09 00:00 08 03 21.38 +10 10 52.3 20.348 n.a. 0.11933743244786 14.4143846 164.2568 /L 14.0558 0.6178998 309.77830 86.461494 n.a. n.a.
2025-Jan-10 00:00 08 02 37.28 +10 19 57.2 20.477 n.a. 0.12769169122530 14.5186693 165.2542 /L 13.0653 0.5628407 310.36633 86.575654 n.a. n.a.
2025-Jan-11 00:00 08 01 57.31 +10 28 22.2 20.598 n.a. 0.13610792922179 14.6289904 166.1959 /L 12.1380 0.5168725 311.04978 86.673114 n.a. n.a.
2025-Jan-12 00:00 08 01 20.86 +10 36 14.4 20.713 n.a. 0.14458965287551 14.7454198 167.0782 /L 11.2760 0.4779401 311.83232 86.757624 n.a. n.a.
2025-Jan-13 00:00 08 00 47.48 +10 43 39