3 The predictions

We computed eclipses of J5 Amalthea by the Galileans moons from November 2002 to June 2003, since these events could give access to the best signal/noise ratio that geometric circumstances would allow, for an apparent distance of the eclipsing satellite which was large enough to measure photometric variation of Amalthea alone. The signal to detect during occultations, when both satellites are measured, is too faint. We iteratively calculated the first and last contacts of the eclipsed satellite with the umbra cone (when an eclipse is detected) and its minimum distance to the axis of this cone. The relative positions of the cone and the satellites are calculated by taking into account the aberration effects and the date of prediction includes the light-time delay.

   

Table 1: Mutual events between Amalthea and Io during the 2002-2003 period.

Julian Day	Date Greg.	$\Delta X~$a	$\Delta Y~$b	$\Delta_{\rm Io}$	$\Delta_{\rm J}$	$\rho$	${\rm d}t$	${\rm d}m$	${\rm d}p$
UT	UT	arcsec	arcsec	arcsec	arcsec	arcsec	second	arcsec	arcsec
2452595.672984954	2002/11/17 04:09:05.89	-18.494	6.756	19.68	48.94	18.99	0.	0.76	0.57
2452627.498471065	2002/12/18 23:57:47.90	-10.767	3.678	11.37	36.45	20.85	1450.	0.40	0.55
2452630.844881944	2002/12/22 08:16:37.79	-10.952	3.914	11.63	46.93	21.03	487.	0.54	0.55
2452631.060819444	2002/12/22 13:27:34.79	-16.678	6.130	17.76	54.20	21.04	0.	0.81	0.58
2452646.991589121	2003/01/07 11:47:53.30	-10.754	4.110	11.51	56.41	21.77	0.	0.80	0.57
2452655.634476852	2003/01/16 03:13:38.79	-10.602	3.870	11.28	35.09	22.05	0.	0.81	0.60
2452687.507636574	2003/02/17 00:10:59.80	8.383	-2.678	8.80	32.50	22.09	113.	0.19	0.61
2452691.019006944	2003/02/20 12:27:22.19	9.608	-3.100	10.09	45.17	21.99	136.	0.07	0.60
2452694.535236111	2003/02/24 00:50:44.39	10.044	-3.195	10.54	54.47	21.88	181.	0.02	0.58
2452698.070984954	2003/02/27 13:42:13.09	9.063	-2.700	9.45	53.46	21.76	465.	0.10	0.56
2452698.314288194	2003/02/27 19:32:34.49	10.902	-2.873	11.27	54.63	21.75	152.	0.40	0.57
2452701.834429398	2003/03/03 08:01:34.70	14.239	-4.023	14.79	43.92	21.60	134.	0.25	0.59
2452706.955986111	2003/03/08 10:56:37.19	17.460	-5.213	18.22	42.34	21.37	131.	0.01	0.60
2452710.470355324	2003/03/11 23:17:18.69	16.782	-4.880	17.47	51.50	21.20	163.	0.03	0.59
2452713.995875000	2003/03/15 11:54:03.60	14.672	-4.056	15.22	54.03	21.02	272.	0.15	0.57
2452714.245583334	2003/03/15 17:53:38.40	14.709	-4.107	15.27	54.10	21.01	272.	0.10	0.57
2452717.770649306	2003/03/19 06:29:44.09	18.841	-5.448	19.61	44.39	20.81	161.	0.06	0.59
2452722.893640046	2003/03/24 09:26:50.50	23.133	-6.541	24.04	38.82	20.53	126.	0.01	0.60
2452726.406620370	2003/03/27 21:45:31.99	21.646	-5.966	22.45	47.86	20.32	149.	0.08	0.59
2452729.927077546	2003/03/31 10:14:59.49	18.836	-5.015	19.49	52.08	20.11	208.	0.19	0.57
2452730.171966435	2003/03/31 16:07:37.90	15.725	-4.523	16.36	52.15	20.10	419.	0.14	0.56
2452737.222520833	2003/04/07 17:20:25.80	24.083	-6.968	25.07	32.45	19.68	116.	0.31	0.60
2452738.831780093	2003/04/09 07:57:45.80	26.264	-7.211	27.23	34.83	19.58	122.	0.01	0.61
2452742.343684028	2003/04/12 20:14:54.30	24.301	-6.563	25.17	43.84	19.37	139.	0.09	0.59
2452745.860995370	2003/04/16 08:39:50.00	21.179	-5.635	21.91	49.17	19.16	182.	0.15	0.58
2452749.406243056	2003/04/19 21:44:59.40	15.543	-4.125	16.08	40.68	18.95	841.	0.12	0.55
2452749.641084491	2003/04/20 03:23:09.70	20.300	-5.963	21.15	45.08	18.93	149.	0.38	0.58
2452753.159864584	2003/04/23 15:50:12.30	23.741	-6.859	24.71	33.83	18.73	117.	0.34	0.59
2452754.770166667	2003/04/25 06:29:02.40	27.027	-7.419	28.02	30.57	18.63	118.	0.00	0.61
2452758.281230324	2003/04/28 18:44:58.29	24.877	-6.813	25.79	39.62	18.43	134.	0.02	0.60
2452761.796299769	2003/05/02 07:06:40.30	21.722	-5.980	22.53	45.80	18.24	169.	0.02	0.58
2452765.324815972	2003/05/05 19:47:44.10	17.157	-4.839	17.82	45.21	18.05	323.	0.08	0.56
2452765.574181713	2003/05/06 01:46:49.30	18.321	-5.445	19.11	45.16	18.03	180.	0.38	0.57
2452769.096738426	2003/05/09 14:19:18.20	21.723	-6.323	22.62	35.37	17.85	133.	0.29	0.59
2452774.219069445	2003/05/14 17:15:27.60	23.718	-6.807	24.67	35.32	17.58	122.	0.17	0.60
2452777.732592592	2003/05/18 05:34:55.99	20.792	-6.106	21.67	42.21	17.41	138.	0.25	0.59
2452781.254724537	2003/05/21 18:06:48.19	16.874	-5.155	17.64	44.70	17.24	176.	0.38	0.57
2452781.503969907	2003/05/22 00:05:42.99	15.302	-4.628	15.98	44.58	17.23	276.	0.31	0.56
2452785.033035879	2003/05/25 12:47:34.29	18.682	-5.549	19.48	36.93	17.07	153.	0.25	0.58
2452790.157081019	2003/05/30 15:46:11.80	21.271	-6.580	22.26	30.99	16.85	72.	0.48	0.60
2452793.669351852	2003/06/03 04:03:52.00	18.646	-5.974	19.57	38.47	16.70	0.	0.60	0.59
2452797.187765046	2003/06/06 16:30:22.90	15.360	-5.149	16.20	42.83	16.56	0.	0.70	0.57
2452797.385594907	2003/06/06 21:15:15.39	9.919	-3.204	10.42	31.37	16.56	836.	0.33	0.54
2452800.968388889	2003/06/10 11:14:28.80	15.077	-4.654	15.77	38.40	16.42	170.	0.25	0.58
2452804.485777778	2003/06/13 23:39:31.19	16.651	-5.267	17.46	29.05	16.30	106.	0.38	0.59

^a

$\Delta X = \Delta \alpha \cos(\delta)$ is Differential coordinate of Amalthea relative to Io.

^b

$\Delta Y = \Delta \delta$ is Differential coordinate of Amalthea relative to Io.

A large set of predictions has been obtained and will be made available on the web server that we have set up, dedicated to the international campaign PHEMU03 for the observation of the Galilean satellites' mutual events (http://www.bdl.fr/Phemu03/phemu03_eng.html).

In this paper we only give a selection of the most interesting phenomena, i.e. only the eclipses of J5 Amalthea by J1 Io, when elongation to Jupiter is large enough.

This is why these predictions are given from November 17, 2002 to June 13, 2003, when the elongation of Jupiter to the Sun is greater than 50 degrees. During this period, all events are observable all around the world depending on the date of the event and the local circumstances of elevation above the horizon.

We give in Table 1:

• the dates of the events in Julian day UT (Col. 1);
• and in Gregorian date UT (Col. 2);
• $\Delta X$ and $\Delta Y$, the differential coordinates of the satellite with respect to the center of Io (Cols. 3 and 4);
• $\Delta_{\rm Io}$, the apparent distance from Io (Col. 5);
• $\Delta_{\rm J}$, the apparent distance from Jupiter (Col. 6);
• $\rho$, the apparent radius of Jupiter (Col. 7);
• dt, the duration of the event in seconds of time, this value is 0. when it concerns close approaches and grazing phenomena (Col. 8);
• dm, the minimal apparent distance from the center of the umbra cone (Col. 9);
• dp, the minimal apparent distance for an event to take place (Col. 10) which corresponds to the sum of the apparent radius of the satellite and to the apparent radius of the section of the umbra cone.

According to the accuracy of our model and considering a mean radius of J5 Amalthea (120 km) instead of a triaxial model (125 km, 73 km, 64 km) (Thomas 1998), we include in this table only the phenomena or the grazing phenomena with ${\rm d}m-{\rm d}p$ smaller than 0.23 arcsec.