VAP Lapping Event Summary June 2016 Produced June 07 2016 Justin Atchison and Fazle Siddique

Terminology The following terms are used: where Δ𝐿𝜙= 𝐿 𝐴 cos 𝜙 𝐴 − 𝐿 𝐵 cos 𝜙 𝐵 2 + 𝐿 𝐴 sin 𝜙 𝐴 − 𝐿 𝐵 sin 𝜙 𝐵 2 𝐿= 𝑟 cos 𝜆 2 𝑟= 𝑥 2 + 𝑦 2 + 𝑧 2 𝜆= atan 𝑧 𝑆𝑀 𝑥 𝑆𝑀 2 + 𝑦 𝑆𝑀 2 𝜙= atan 𝑥 𝑆𝑀 𝑦 𝑆𝑀 and SM denotes a coordinate in the solar magnetic system, and A and B refer to the two spacecraft.

June 2016 Lapping Event (Definitive)

June 2016 Lapping Event (Definitive) #1 03-Jun-2016 02:29:54 Alt at Conj: 30356.8 km Min L-Az Range: 1177.415 km MLT: ( 0.022, 23.903) Hr L: (37856.630, 37885.465) km ZSM: (-6323.339, -6915.178) km Delta MLT: -23.88128 Hr DeltaL: -28.836 km |Delta ZSM|: 591.839 km --------- #2 03-Jun-2016 11:22:17 Alt at Conj: 30320.8 km Min L-Az Range: 546.837 km MLT: ( 0.412, 0.355) Hr L: (36953.240, 36955.156) km ZSM: (3044.176, 2489.518) km Delta MLT: 0.05652 Hr DeltaL: -1.915 km |Delta ZSM|: 554.658 km #3 03-Jun-2016 20:40:03 Alt at Conj: 30356.7 km Min L-Az Range: 58.436 km MLT: ( 23.612, 23.618) Hr L: (38409.656, 38403.965) km ZSM: (-7670.818, -8290.740) km Delta MLT: -0.00578 Hr DeltaL: 5.691 km |Delta ZSM|: 619.922 km #4 04-Jun-2016 05:36:26 Alt at Conj: 30360.3 km Min L-Az Range: 925.810 km MLT: ( 0.018, 0.114) Hr L: (36791.943, 36720.306) km ZSM: (-1400.832, -2058.640) km Delta MLT: -0.09592 Hr DeltaL: 71.637 km |Delta ZSM|: 657.808 km--------- #5 04-Jun-2016 14:44:20 Alt at Conj: 30262.0 km Min L-Az Range: 1324.547 km MLT: ( 23.999, 0.136) Hr L: (36672.217, 36472.653) km ZSM: (1084.470, -35.832) km Delta MLT: 23.86323 Hr DeltaL: 199.565 km |Delta ZSM|: 1120.302 km --------- #6 05-Jun-2016 01:38:11 Alt at Conj: 23500.7 km Min L-Az Range: 1721.716 km MLT: ( 22.141, 22.286) Hr L: (30578.452, 29286.923) km ZSM: (-4519.430, -5010.643) km Delta MLT: -0.14533 Hr DeltaL: 1291.529 km |Delta ZSM|: 491.212 km #7 05-Jun-2016 11:41:33 Alt at Conj: 13948.6 km Min L-Az Range: 1786.741 km MLT: ( 20.892, 20.984) Hr L: (21314.685, 19598.189) km ZSM: (4376.254, 3679.623) km Delta MLT: -0.09271 Hr DeltaL: 1716.496 km |Delta ZSM|: 696.631 km #8 05-Jun-2016 13:39:49 Alt at Conj: 10606.3 km Min L-Az Range: 1761.547 km MLT: ( 4.419, 4.472) Hr L: (17871.561, 19613.703) km ZSM: (-3784.102, -4183.394) km Delta MLT: -0.05320 Hr DeltaL: -1742.142 km |Delta ZSM|: 399.292 km #9 05-Jun-2016 21:37:56 Alt at Conj: 1267.4 km Min L-Az Range: 263.376 km MLT: ( 14.355, 14.276) Hr L: (8438.327, 8239.237) km ZSM: (2343.464, 2336.589) km Delta MLT: 0.07899 Hr DeltaL: 199.091 km |Delta ZSM|: 6.875 km --------- #10 05-Jun-2016 21:49:18 Alt at Conj: 731.1 km Min L-Az Range: 322.041 km MLT: ( 10.817, 10.682) Hr L: (7327.500, 7515.519) km ZSM: (1226.864, 1337.756) km Delta MLT: 0.13458 Hr DeltaL: -188.019 km |Delta ZSM|: 110.892 km

Current Predicted Close Approach Times The predicted time intervals where the spacecraft to spacecraft range is less than 1,000 km:          Start Time (UTCG)           Stop Time (UTCG)    ------------------------      ------------------------     7 Jul 2016 00:46:33.389     7 Jul 2016 01:22:43.829    7 Jul 2016 09:47:10.102     7 Jul 2016 10:26:44.958    9 Jul 2016 10:51:27.934     9 Jul 2016 11:55:42.447    9 Aug 2016 14:21:31.824     9 Aug 2016 15:07:11.410    9 Aug 2016 23:28:12.067    10 Aug 2016 00:06:34.924   12 Aug 2016 00:31:34.875    12 Aug 2016 01:33:00.123   11 Sep 2016 19:03:56.293    11 Sep 2016 19:37:23.900   12 Sep 2016 03:52:17.423    12 Sep 2016 04:52:41.245   12 Sep 2016 13:00:07.859    12 Sep 2016 13:51:05.787   14 Sep 2016 14:11:39.212    14 Sep 2016 15:09:13.327   15 Oct 2016 08:32:47.429    15 Oct 2016 09:21:51.326   15 Oct 2016 17:25:11.119    15 Oct 2016 18:32:33.650   16 Oct 2016 02:37:41.654    16 Oct 2016 03:25:09.458   18 Oct 2016 03:51:20.456    18 Oct 2016 04:44:17.662   17 Nov 2016 22:08:17.110    17 Nov 2016 22:58:03.120   18 Nov 2016 07:05:11.566    18 Nov 2016 08:03:35.244   20 Nov 2016 17:31:06.348    20 Nov 2016 18:17:30.057   21 Dec 2016 11:51:05.213    21 Dec 2016 12:27:36.043   24 Dec 2016 07:12:48.162    24 Dec 2016 07:47:52.482   24 Jan 2017 01:43:08.924    24 Jan 2017 01:50:03.907   26 Jan 2017 21:01:50.360    26 Jan 2017 21:11:07.682 Note: This data is released weekly via the Nav Data Products email.

July 2016 Lapping Event (Predictive)

July 2016 Lapping Event (Predictive) #1 07-Jul-2016 01:09:26 Alt at Conj: 30382.5 km Min L-Az Range: 319.254 km MLT: ( 1.260, 1.227) Hr L: (37033.785, 37041.603) km ZSM: (-3156.875, -3917.965) km Delta MLT: 0.03292 Hr DeltaL: -7.818 km |Delta ZSM|: 761.090 km --------- #2 07-Jul-2016 09:55:06 Alt at Conj: 30296.6 km Min L-Az Range: 229.187 km MLT: ( 1.821, 1.845) Hr L: (37773.850, 37786.019) km ZSM: (6256.024, 5458.153) km Delta MLT: -0.02314 Hr DeltaL: -12.169 km |Delta ZSM|: 797.871 km #3 07-Jul-2016 19:26:47 Alt at Conj: 30270.1 km Min L-Az Range: 817.943 km MLT: ( 0.982, 1.065) Hr L: (37121.400, 37022.728) km ZSM: (-4137.650, -5117.743) km Delta MLT: -0.08366 Hr DeltaL: 98.672 km |Delta ZSM|: 980.093 km #4 08-Jul-2016 04:15:07 Alt at Conj: 30359.2 km Min L-Az Range: 1739.016 km MLT: ( 1.254, 1.435) Hr L: (36822.878, 36736.091) km ZSM: (1770.127, 956.760) km Delta MLT: -0.18040 Hr DeltaL: 86.787 km |Delta ZSM|: 813.367 km #5 08-Jul-2016 11:43:36 Alt at Conj: 28104.1 km Min L-Az Range: 1982.797 km MLT: ( 2.660, 2.842) Hr L: (34741.401, 35794.602) km ZSM: (2977.969, 1784.023) km Delta MLT: -0.18199 Hr DeltaL: -1053.201 km |Delta ZSM|: 1193.947 km --------- #6 09-Jul-2016 01:21:10 Alt at Conj: 13875.5 km Min L-Az Range: 1565.781 km MLT: ( 21.834, 21.938) Hr L: (20258.956, 18786.440) km ZSM: (-327.496, -591.625) km Delta MLT: -0.10423 Hr DeltaL: 1472.516 km |Delta ZSM|: 264.129 km #7 09-Jul-2016 03:21:45 Alt at Conj: 11191.0 km Min L-Az Range: 1676.222 km MLT: ( 5.427, 5.515) Hr L: (17569.208, 19191.157) km ZSM: (-27.007, -242.951) km Delta MLT: -0.08801 Hr DeltaL: -1621.948 km |Delta ZSM|: 215.944 km #8 09-Jul-2016 11:16:46 Alt at Conj: 1306.4 km Min L-Az Range: 282.632 km MLT: ( 16.256, 16.177) Hr L: (7689.056, 7453.712) km ZSM: (186.663, 269.329) km Delta MLT: 0.07897 Hr DeltaL: 235.344 km |Delta ZSM|: 82.666 km #9 09-Jul-2016 11:32:39 Alt at Conj: 1122.0 km Min L-Az Range: 253.319 km MLT: ( 11.535, 11.478) Hr L: (8126.306, 8347.411) km ZSM: (-2081.885, -2040.618) km Delta MLT: 0.05733 Hr DeltaL: -221.105 km |Delta ZSM|: 41.267 km