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Table A.5.

Orbital elements from certain combined dynamical and LTTE solutions for systems.

KIC No. P1 P2 a2 e2 ω2 τ2 f(mC) m C m ABC $ \frac{m_{\mathrm{C}}}{m_{\mathrm{ABC}}} $ mAB mC A dyn meas A LTTE $ \frac{{\cal{A}}^{\mathrm{meas}}_{\mathrm{dyn}}}{{\cal{A}}_{\mathrm{LTTE}}} $
(day) (day) (R) (deg) (MBJD) (M) (M) (M)
3544694 3.84572314(8) 80.92(3) 97(4) 0.113(4) 327(2) 55723.9(4) 0.043(8) 0.29(1) 1.34(20) 0.54(8) 4.13
4079530 17.727144(1) 141.7(9) 130(5) 0.52(2) 22(7) 54987(8) 0.000000004(1) 0.0013(2) 1.48(16) 0.0020(3) 475
4909707 2.30236795(4) 515.0(3) 489(23) 0.59(2) 175(3) 54848(5) 0.349(124) 0.39(06) 3.60(77) 2.31(35) 0.52
4940201 8.8165585(3) 364.6(2) 303(4) 0.227(5) 258(3) 54868(3) 0.10(1) 0.33(1) 1.88(9) 0.94(6) 3.06
5095269 18.6118308(1) 235.89(2) 219.32(2) 0.072(3) 328.4(6) 55004.2(5) 0.000000016(1) 0.00192(7) 2.28 0.0049(2) 133
5255552a 32.46529(7) 860.1(6) 574(7) 0.372(2) 40.2(4) 54868(1) 0.20(1) 0.390(5) 2.10(10) 1.34(7) 35
5384802 6.08309218(9) 256.08(5) 297(9) 0.371(4) 9(2) 54998(2) 0.42(6) 0.43(1) 3.06(39) 2.31(32) 4.4
5650317 2.14054699(2) 118.38(2) 182(6) 0.20(2) 228(7) 55238(3) 0.22(5) 0.34(2) 3.81(48) 1.94(31) 0.83
5653126 38.49130(2) 969.4(4) 687(5) 0.170(3) 322.2(8) 54514(3) 0.127(9) 0.303(7) 3.22(9) 1.40(6) 30
5731312 7.94638807(8) 919.7(8) 458(2) 0.598(2) 19(1) 54830(1) 0.00192(5) 0.1082(8) 1.36(2) 0.165(3) 4.69
5771589 10.738237(2) 113.20(2) 168(2) 0.088(2) 105(2) 54974.8(4) 1.25(7) 0.634(4) 1.81(9) 3.14(17) 16.8
5952403 0.90567813(1) 45.468(7) 86(2) 0.0007(5) 131(20) 55506(3) 0.75(12) 0.57(3) 1.81(9) 2.35(30) 0.036
6525196 3.42059731(1) 418.90(8) 330(5) 0.27(1) 92(4) 55063(5) 0.075(6) 0.301(7) 1.93(11) 0.83(6) 0.41
6531485b 0.676990690(7) 48.324(7) 60(5) 0.63(1) 47(10) 54982(2) 0.025(8) 0.276(8) 0.88(28) 0.34(11) 4.23
6545018 3.99145675(2) 90.586(3) 106.3(8) 0.247(5) 233(1) 54970.3(4) 0.023(1) 0.228(5) 1.52(4) 0.45(2) 8.33
6546508 6.1071013(2) 1235(27) 722(35) 0.32(3) 318(8) 55088(28) 0.23(7) 0.41(4) 1.94(34) 1.37(31) 0.29
7177553 17.9964523(4) 526.5(4) 343(4) 0.47(2) 213(2) 54714(2) 0.00000012(2) 0.0039(3) 1.95(6) 0.0077(6) 39
7289157 5.2665486(2) 244.1(1) 241(6) 0.31(1) 163(2) 54941(2) 0.17(2) 0.38(2) 1.96(18) 1.18(14) 4.08
6950(424) 426(42)c 0.26(6) 137(18) 53338(409) 0.021(6) 0.66c 3:
7668648 27.82517(4) 202.9(1) 180(4) 0.112(7) 188(6) 54931(2) 0.018(2) 0.213(1) 1.51(13) 0.41(4) 78
7690843d 0.78625579(4) 74.21(3) 157(13) 0.48(3) 358(2) 54990(1) 4.7(16) 0.81(5) 1.84(9) 7.6(24) 0.77
7812175 17.793579(1) 582.0(3) 358(14) 0.023(2) 220(6) 54799(10) 0.061(1) 0.323(4) 1.23(19) 0.59(9) 6.27
7821010 24.23821642(9) 990(1) 572(1) 0.343(7) 128(2) 55122(5) 0.000000002(0) 0.00090(2) 2.56(1) 0.00229(6) 35.3
8023317 16.5789557(3) 609.9(1) 385(11) 0.24(2) 165(2) 55010(4) 0.0006(1) 0.067(6) 1.92(17) 0.14(2) 8.31
8143170e 28.78582(1) 1580.5(6) 995(9) 0.690(6) 107.3(4) 54541.1(6) 0.0081(6) 0.123(4) 4.64(13) 0.65(3) 22.2
8210721 22.673093(2) 789.1(2) 480(5) 0.236(2) 218.1(5) 54634(1) 0.082(4) 0.325(4) 1.61(6) 0.78(3) 9.90
8719897 3.15142051(1) 333.30(4) 269(8) 0.251(4) 130(1) 54997.1(8) 0.13(2) 0.384(8) 1.46(19) 0.91(12) 0.56
9007918 1.387206538(2) 471.3(3) 328(7) 0.65(1) 286(2) 54818(1) 0.00034(3) 0.054(2) 2.10(13) 0.121(8) 0.34
9451096 1.250390741(3) 106.89(2) 144(5) 0.10(1) 163(6) 54994(2) 0.046(7) 0.24(1) 2.65(32) 0.84(11) 0.19
9714358 6.4742284(2) 103.76(1) 101(1) 0.28(1) 119(1) 54977.6(2) 0.008(1) 0.185(9) 1.03(5) 0.23(2) 26.2
9850387 2.74849803(3) 670.6(8) 479(1) 0.42(3) 112(4) 54690(9) 0.019(1) 0.180(5) 2.72 0.59(2) 0.24
10095512 6.0172058(1) 472.8(2) 334(23) 0.18(1) 232(6) 54861(9) 0.16(5) 0.42(2) 1.31(36) 0.93(27) 0.79
10223616 29.12926(8) 541.9(6) 395(14) 0.29(3) 239(3) 55299.0(7) 0.13(6) 0.36(7) 1.81(8) 1.00(31) 33
10483644 5.11077040(5) 372.8(6) 299(14) 0.03(3) 320(9) 55314(7) 0.0019(8) 0.09(2) 2.36(37) 0.24(6) 0.14
10549576 9.0895323(8) 1486(4) 1002(25) 0.48(4) 158(7) 54970(32) 0.35(7) 0.42(3) 3.54(25) 2.58(38) 0.60
10613718 1.17587798(2) 88.18(5) 129(4) 0.11(3) 35(17) 54989(4) 0.24(6) 0.40(3) 2.23(23) 1.49(25) 0.25
10979716 10.6840969(4) 1046.0(6) 602(16) 0.470(8) 58(2) 54513(7) 0.15(2) 0.41(1) 1.59(17) 1.09(13) 2.29
11519226 22.161754(1) 1434(1) 873(13) 0.339(3) 321.9(6) 55010(2) 0.33(3) 0.43(1) 2.50(13) 1.84(13) 4.90

Notes. (a)Quadratic and cubic ephemeris: ΔP = −5.5(2)×10−5 d/c2, c3 = 1.15(5)×10−7 d/c3. These non-linear polynomial coefficients are for the mathematical representations of additional perturbations, not considered in the analytic ETV three-body model (see Appendix B for details); (b)Quadratic ephemeris: ΔP = −1.02(2)×10−10 c/d; (c)The ‘fourth-body orbit’ is a pure LTTE solution, hence, the given value is aABCsin i3 instead of a3 and, similarly, instead of mD, what is given is its minimum mass (for i3 = 90°); (d)Quadratic and cubic ephemeris: ΔP = 53.8(3)×10−10 d/c2, c3 = −1.49(2)×10−13 d/c3; (e)Quadratic and cubic ephemeris: ΔP = 2.4(4)×10−6 d/c2, c3 = 1.16(8)×10−8 d/c3. These non-linear polynomial coefficients are for the mathematical representations of additional perturbations, not considered in the analytic ETV three-body model (see Appendix B for details).

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