**Publication date:** Sep 2011

**Abstract:**

Using the pseudo-Newtonian (PN) potential reflecting properties of the

Schwarz-schild-de Sitter spacetime, we estimate the influence of the

repulsive cosmological constant Λ ~ 1.3 ×

10^{-56}cm^{-2} implied by recent cosmological tests

onto the motion of both Small and Large Magellanic Clouds (SMC and LMC)

in the gravitational field of the Milky Way. Considering detailed

modelling of the gravitational field of the Galaxy disc, bulge and cold

dark matter halo, the trajectories of SMC and LMC constructed for the PN

potential with the cosmological constant are confronted to those given

for Λ = 0. In the realistic model of the extended cold dark matter halo

its edge and related total mass are taken at typical values reflecting

recent diversity in the total Galaxy mass estimates. In all cases,

strong influence of the cosmological constant, on 10% level or higher,

has been found for motion of both SMC and LMC. Inside the halo, the

Newtonian part of the PN potential is exact enough, while outside the

halo the PN potential can give relevant relativistic corrections. The

role of the cosmological constant is most conspicuous when binding mass

is estimated for the satellite galaxies. We have found a strong

influence of cosmic repulsion on the total binding mass for both

galaxies. For SMC there is the binding mass M_{SMC}^{Λ =
0} = 7.07 × 10^{11}M_{⨀} and M_{SMC}^{Λ
> 0} = 8.61 × 10^{11}M_{⨀}, while even much

higher increase is found for LMC, where M_{LMC}^{Λ = 0}

= 1.50 × 10^{12}M_{⨀} and M_{LMC}^{Λ >
0} = 2.21 × 10^{12}M_{⨀}, putting serious doubts on

the possibility that the LMC is bounded by the Milky Way. However, the

estimates of binding masses are strongly influenced by initial velocity

of SMC and LMC; we took the values inferred for the IAU MW rotation

velocity ~ 220 km/s. Our results indicate very important role of the

cosmic repulsion in the motion of interacting galaxies, clearly

demonstrated in the case of the satellite SMC and LMC galaxies moving in

the field of Milky Way. In some cases, the effect of the cosmic

repulsion can be even comparable to the effects of the dynamical

friction and the Andromeda Galaxy.

**Authors:**

Stuchlík, Zdeněk; Schee, Jan;