The diameter of our disk-shaped galaxy, the Milky Way, is about 1.7E+5 light-years (ly). The distance to the Andromeda galaxy, which is the spiral galaxy nearest to the Milky Way, is about 1.9E+6 ly. If a scale model represents the Milky Way and Andromeda galaxies as dinner plates 26 cm in diameter, determine the distance between the centers of the two plates.
19/1.7 = 11.2
11.2 * 26 = 290 cm = 2.9 meters
Hi Damon
Can you please explain how you got 19 ? and why is it being divided by 1.7 ?
Thanks!
Sarah
1.9 * 10^6 = 19 * 10^5
divide that by 1.7 * 10^5
the 10^5 cancels and the ratio of distance between to diameter is
19/1.7
To determine the distance between the centers of the two dinner plates that represent the Milky Way and Andromeda galaxies, we need to scale down the actual distances to the size of the plates.
Given:
- Diameter of the Milky Way (d_mw) = 1.7E+5 light-years
- Diameter of the Andromeda galaxy (d_andromeda) = 1.9E+6 light-years
- Diameter of the dinner plates (d_plate) = 26 cm
To begin, we need to establish a ratio between the actual distances and the scaled-down distances.
Ratio = (scaled distance) / (actual distance)
For the Milky Way:
Ratio_mw = d_plate / d_mw
For Andromeda:
Ratio_andromeda = d_plate / d_andromeda
Now, we can use the ratio to calculate the distance between the centers of the two plates.
Distance = Ratio_andromeda * actual distance
Distance = Ratio_andromeda * (d_mw + d_andromeda)
Note that adding the diameters together accounts for the distance between the centers of both galaxies.
Let's calculate the values:
Ratio_mw = 26 cm / 1.7E+5 ly
≈ 1.529E-12 cm/ly
Ratio_andromeda = 26 cm / 1.9E+6 ly
≈ 1.368E-8 cm/ly
Distance = (1.368E-8 cm/ly) * (1.7E+5 ly + 1.9E+6 ly)
= 1.368E-8 cm/ly * 2.07E+6 ly
≈ 2.841 cm
Therefore, the distance between the centers of the two dinner plates, representing the Milky Way and Andromeda galaxies, is approximately 2.841 cm.