(Solved): Consider a scale model of the entire Milky Way galaxy shown in the figure below with additional ...

Consider a scale model of the entire Milky Way galaxy - shown in the figure below with additional information and labels not relevant to this problem. At such a scale, the disk of the Milky Way Galaxy fits on a football field \\( (91.4 \\mathrm{~m}) \\). At this scale, how big would the planet Earth be? The actually diameters of the galaxy and Earth are \\( D_{\\text {MilkyWay }}=9.590 \\times 10^{4} \\) light-years and \\( D_{\\text {Earth }}=1.2742 \\times 10^{4} \\mathrm{~km} \\), respectively - and 1 light-year is \\( 9.461 \\times 10^{12} \\mathrm{~km} \\). Give your answer in picometers (one picometer is one trillionth of a meter, i.e. \\( 1 \\mathrm{pm}=10^{-12} \\mathrm{~m} \\). HINT: you should expect the Earth to be very small (unbelievable small) since the galaxy is so vast for context, the galaxy has approximately 100 billion stars with average interstellar distances that are more than a hundred million planet Earths lined up!