Table B.5.

Orbital parameters for the case of the 2 isolated MW potentials as described in Section 7): ’Light MW’ (light) and ’Heavy MW’ (heavy). For both of these models, are given: the pericentre (peri), apocentre (apo), eccentricity (ecc), period (T), time since last pericentre (T_last, peri) and fraction of orbit reaching there apocentre in the last 8 Gyr (ℱ_apo). The values correspond to the median of these parameters calculated fro 100 Monte-Carlo realisations, and the uncertainties correspond to the 16^th and 84^th quantiles. When the majority of there orbits do not reach the apocentre, the uncertainties on the apocentre, eccentricity and period cannot be computed. Thus, for those galaxies, we rather give the values of the 16^th quantile. These values are marked by a ⋆. Galaxies with name in italics indicate those for which the uncertainty on the total Galactocentric velocity is > 70 km s⁻¹ (see Sect. 7). The systemic PM from the run with the spectroscopic information were used for Pisces II and Tucana V. Pegasus III is omitted due to the lack of a trustworthy systemic PM.

Galaxy	Peri(light)	Apo(light)	ecc(light)	T(light)	Tlast, peri(light)	ℱapo(light)	Peri(heavy)	Apo(heavy)	ecc(heavy)	T(heavy)	Tlast, peri(heavy)	ℱapo(heavy)
	[kpc]	[kpc]		[Gyr]	[Gyr]		[kpc]	[kpc]		[Gyr]	[Gyr]
Antlia II						1.00						1.00
Aquarius II						0.86						0.99
Bootes I						1.00						1.00
Bootes II		−	−	−	−	0.11						0.98
Bootes III						1.00						1.00
Canes Venatici I						0.75						1.00
Canes Venatici II						0.80						0.97
Carina						0.71						1.00
Carina II		−	−	−		0.01						1.00
Carina III		−	−	−		0.05						0.99
Columba I		−	−	−	−	0.11		≥206⋆	≥0.38⋆	≥5.23⋆	≥ − 2.17⋆	0.45
Coma Berenices						0.91						1.00
Crater I						0.79						0.95
Crater II						1.00						1.00
Draco						1.00						1.00
Draco II						0.94						1.00
Eridanus II		−	−	−	−	0.00		−	−	−	−	0.09
Fornax						0.98						1.00
Grus I		≥434⋆	≥0.97⋆	≥11.02⋆	−	0.22						1.00
Grus II						0.99						1.00
Hercules		≥342⋆	≥0.87⋆	≥8.40⋆		0.33						1.00
Horologium I						0.87						1.00
Horologium II		≥304⋆	≥0.71⋆	≥8.33⋆		0.18						0.70
Hydra II		≥325⋆	≥0.88⋆	≥8.09⋆		0.23						0.71
Hydrus I		≥229⋆	≥0.90⋆	≥4.64⋆	≥ − 2.98⋆	0.31						1.00
Leo I		−	−	−		0.00						0.57
Leo II						0.77						1.00
Leo IV						0.60						0.86
Leo V		−	−	−		0.12		≥246⋆	≥0.50⋆	≥5.81⋆		0.31
Leo T		−	−	−	−	0.00		−	−	−	−	0.02
Phoenix		−	−	−	−	0.00		≥668⋆	0.93⋆	≥14.04⋆	−	0.23
Phoenix II		≥422⋆	≥0.83⋆	≥11.96⋆	−	0.16						0.80
Pisces II		−	−	−	−	0.00		−	−	−	−	0.00
Reticulum II						1.00						1.00
Reticulum III		≥138⋆	≥0.67⋆	≥3.03⋆		0.41						0.77
Sagittarius II						0.72						1.00
Sculptor						1.00						1.00
Segue 1						0.99						1.00
Segue 2						1.00						1.00
Sextans						0.96						1.00
Triangulum II						1.00						1.00
Tucana II		≥254⋆	≥0.87⋆	≥5.48⋆	≥ − 3.23⋆	0.27						0.95
Tucana III						1.00						1.00
Tucana IV						0.95						1.00
Tucana V						1.00						1.00
Ursa Major I						0.98						1.00
Ursa Major II					≥ − 3.79⋆	0.64						1.00
Ursa Minor						1.00						1.00
Willman 1						1.00						1.00
NGC 6822		−	−	−		0.01		≥521⋆	≥0.58⋆	≥12.91⋆		0.37