Answer: [tex]1 pc > 1 ly > 1 AU > 1 km > 1 m[/tex]
Explanation:
Firstly, we need to work with the same units in order to compare among the given distances. So, let's work with kilometers ([tex]km[/tex]) with the following information:
[tex]1pc=206265AU[/tex]
[tex]1AU=1.5(10)^{8} km[/tex]
[tex]1 ly=63000 AU[/tex]
[tex]1 km=1000 m[/tex]
For the Astronomical Unit (AU):
[tex]1AU=1.5(10)^{8} km[/tex]
For Light years (ly):
[tex]1 ly=63000 AU \frac{1.5(10)^{8} km}{1 AU}=9.45(10)^{12} km[/tex]
For Parsecs (Pc):
[tex]1pc=206265AU \frac{1.5(10)^{8} km}{1 AU}=3.09(10)^{13} km[/tex]
For Kilometers (Km):
[tex]1 km[/tex]
For Meters (m):
[tex]1 m \frac{1 km}{1000 m}=0.001 km[/tex]
Now that we have all the distances in kilometers we can compare and arrange them in order from largest to smallest:
[tex]1 pc=3.09(10)^{13} km[/tex]
[tex]1 ly=9.45(10)^{12} km[/tex]
[tex]1AU=1.5(10)^{8} km[/tex]
[tex]1 km[/tex]
[tex]1 m=0.001 km[/tex]
Therefore:
[tex]1 pc > 1 ly > 1 AU > 1 km > 1 m[/tex]
