The speed of light is not constant as such but the classically quoted speed of light in vacuum is the maximum speed in the medium. The medium in this case being vacuum aether or whatever fills the volume of space. The key property of the medium is that it is an electromagnetic medium and its density can change. This could be the local minimum density affecting light propagating through an electrical wire at about 0.7 of the speed in vacuum, or bending around a star in space where the gravitational influence of the star is causing a slight vacuum density gradient in the vicinity of its gravitational influence. When you look at the structure of the planet we have structure of the earth subdividing itself into a whole variety of regions that seems to be defined by temperature and pressure. Regions of the domain of an energy density with different characteristic speeds of propagation for pressure waves and for light waves. Media such as water or glass have their characteristic veleocities of propagation for energy at different frequencies. Once you get into EM spectrum frequencies the local speed of light is the defining factor. Other than being less dense why should vacuum be anything other than a very low density medium so that "empty" space is just another medium like every other medium that occupies a volume anywhere else. The medium has electrical and magnetic properties that combine to give its characteristic property of vacuum impedance Z0. The ratio of this impedance to the magnetic property is the maximum velocity of propagation (movement) of energy through the medium. This maximum velocity is the speed of light in vacuum.
Just out of interest you can calculate the speed of light as 1.00003^.25*sqrt(3)^11*1.03^.25/(1.03^4*4*pi*1e-7). This looks a lot nicer as a properly written equation which you can see on my website http://www.abstractinventions.uk
on the page titled the speed of light from geometry. The number you get from this equation is 299792456.98 which is about 3ppb less than the value a comitttee decided to define for the speed of light in vacuum. Interestingly it is almost exactly what the best measurement of the speed of light recorded.