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Context: I'm looking for some authority on a particular idea that I brought up in regards to a new update brought out for a space travel sim game, Elite Dangerous

The vessels in that game can travel between star systems, requiring fuel- they can only jump between star systems, and have a limit on how many light years they can travel in one jump.

The latest update added a vessel that can jump up to 500 light years.

Vessels can't travel continuously to a location, it has to be point to point, i.e. teleportation (sort of)

The question:

Given the context above, can it be estimated that there are enough high orbiting, or orphaned star systems between the edge of the milky way, and the edge of the Canis Major dwarf galaxy for one of these vessels to traverse a 'corridor' of 500ly (or closer) intervals of star systems between the two galaxies?

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The Canis Major dwarf galaxy is about 8 kpc from the Sun, but is only 8 degrees below the Galactic plane (and further out than the Sun). So it is about 42,000 light years from the Galactic centre and about 1150 light years below the plane.

This almost within the disc of the Galaxy itself. The Galactic disc has a density that varies pseudo-exponentially in both radial distance from the centre and with height above the plane: $$ n \propto \exp(-r/R_0)\exp(-z/Z_0),$$ where $R_0$ and $Z_0$ are appropriate numbers for the radial scale length and the height scale length respectively, and $r$ and $z$ are the radial and vertical coordinates with respect to the Galactic centre.

In this coordinate system, the position of the Sun is about $r=25,000$ light years and $z \sim 0$ light years. The appropriate numbers for the scale-lengths/heights are $R_0 \sim 10,000$ light years and $Z_0 \sim 1000$ light years.

The density of stars in the solar neighbourhood is about 0.1 pc$^{-3}$ or about $3\times 10^{-3}$ stars per cubic light year. We can now scale this number according to the equation above, to work out the approximate density in the vicinity of the Canis Major dwarf galaxy, which will be loer than the solar neighbourhood. $$ \frac{n_{\rm CM}}{n_{\rm Sun}} \simeq \exp[(r_{\rm Sun} - r_{\rm CM})/R_0]\exp[(z_{\rm Sun}-z_{\rm CM})/Z_0],$$ from which we get $n_{\rm CM} \simeq 0.06 n_{\rm Sun} = 2\times 10^{-4}$ stars per cubic light year.

To work out the average distance between stars we take the reciprocal of the cube root, $$n_{\rm CM}^{-1/3} = 18\ {\rm light\ years}.$$

So, if you have a range of 500 light years per "jump" you have no problem skipping all the way to the Canis Major dwarf galaxy.

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