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Table A.1

Summary of our star, planet, and moon parameter grid.

Case ID
1a 1b 1c 1 d 1e 1f 1g 1h 1i 1j 1k 1l 1m 1n 1o 1p
Parameter

R [R] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
M [M] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
q1 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
q2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

Rp RJ RJ RJ RJ RJ RJ RJ RJ RJ RJ RJ RJ RJ RJ RJ RJ
Mp MJ MJ MJ MJ MJ MJ MJ MJ MJ MJ MJ MJ MJ MJ MJ MJ
Pb [d] 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30
bb 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
φb 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Rs 0 0 0 0 R R R R 0 0 0 0 R R R R
Ms 0 0 M M 0 0 M M 0 0 M M 0 0 M M
Ps PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu
φs 0-1 0-1 0-1 0-1 0-1 0-1 0-1 0-1 0-1 0-1 0-1 0-1 0-1 0-1 0-1 0-1
is 0 0 0 0 0 0 0 0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2


Case ID
2a 2b 2c 2d 3a 3b 3c 3d 4a 4b 4c 4d 5a 5b 5c 5d 6a 6b 6c 6d 7a 7b 7c 7d 8a 8b 8c 8d 9a 9b 9c 9d

Parameter

R [R] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85
M [M] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84
q1 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45
q2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

Rp RJ RJ RJ RJ RS RS RS RS RN RN RN RN R R R R RJ RJ RJ RJ RS RS RS RS RN RN RN RN R R R R
Mp MJ MJ MJ MJ MS MS MS MS MN MN MN MN M M M M MJ MJ MJ MJ MS MS MS MS MN MN MN MN M M M M
Pb [d] 30 30 58.31 58.41 30 30 58.31 58.41 30 30 58.31 58.41 30 30 58.31 58.41 30 30 58.31 58.41 30 30 58.31 58.41 30 30 58.31 58.41 30 30 58.31 58.41
bb 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
φb 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Rs RN RN RN RN 2 R 2 R 2 R 2 R R R R R R R R R RN RN RN RN 2 R 2 R 2 R 2 R R R R R R R R R
Ms MN MN MN MN 8 M 8 M 8 M 8 M M M M M M M M M MN MN MN MN 8 M 8 M 8 M 8 M M M M M M M M M
Ps PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu PIo PEu
φs 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
is 0.233 0.149 0.233 0.149 0.255 0.163 0.255 0.163 0.201 0.130 0.201 0.130 0.141 0.092 0.141 0.092 0.233 0.149 0.233 0.149 0.255 0.163 0.255 0.163 0.201 0.130 0.201 0.130 0.141 0.092 0.141 0.092

Notes. To preserve the orbital advancement per transit we changed the long planet orbit period from 60 d to the given values depending on the orbital period of the moon. The inclinations (is) tested in cases 1a–1p are 0 and 0.2 radians. For the other cases, the inclination is calculated as the smallest value needed to prevent occultations. The mass and radius of the Earth’s moon are referred to as M and R, respectively.Subscripts S and N refer to Saturn and Neptune, respectively.

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