The Milky Way ( MW ) and M31 both harbor massive satellite galaxies , the Large Magellanic Cloud ( LMC ) and M33 , which may comprise up to 10 per cent of their host ’ s total mass .
Massive satellites can change the orbital barycentre of the host-satellite system by tens of kiloparsecs and are cosmologically expected to harbor dwarf satellite galaxies of their own .
Assessing the impact of these effects depends crucially on the orbital histories of the LMC and M33 .
Here , we revisit the dynamics of the MW-LMC system and present the first detailed analysis of the M31-M33 system utilizing high precision proper motions and statistics from the dark matter-only Illustris cosmological simulation .
With the latest Hubble Space Telescope proper motion measurements of M31 , we reliably constrain M33 ’ s interaction history with its host .
In particular , like the LMC , M33 is either on its first passage ( t _ { inf } < 2 Gyr ago ) or if M31 is massive ( \geq 2 \times 10 ^ { 12 } M _ { \odot } ) , it is on a long period orbit of about 6 Gyr .
Cosmological analogs of the LMC and M33 identified in Illustris support this picture and provide further insight about their host masses .
We conclude that , cosmologically , massive satellites like the LMC and M33 are likely completing their first orbits about their hosts .
We also find that the orbital energies of such analogs prefer a MW halo mass \sim 1.5 \times 10 ^ { 12 } M _ { \odot } and an M31 halo mass \geq 1.5 \times 10 ^ { 12 } M _ { \odot } .
Despite conventional wisdom , we conclude it is highly improbable that M33 made a close ( < 100 kpc ) approach to M31 recently ( t _ { peri } < 3 Gyr ago ) .
Such orbits are rare ( < 1 per cent ) within the 4 \sigma error space allowed by observations .
This conclusion can not be explained by perturbative effects through four body encounters between the MW , M31 , M33 , and the LMC .
This surprising result implies that we must search for a new explanation for M33 ’ s strongly warped gas and stellar discs .