Consider the 1-to10^19 scale on which the disk of the Milky Way Galaxy fits on a football field. On this scale, how far is it from the sun to the alpa centauri (real distance:4.4 light-years) How big is the sun itself on this scale? Compare the sun's size on this scale to the actual size of a typical atom (about 10^-10 m in diameter).

Verified Answer :

Limosa

Answer:

Sun is \(0.4162708\) cm away from alpha century.

Sun is \(1.391016\times10^{-10}\)m.

Sun is 1.391016 time the size of an atom at this scale.

Step-by-step explanation:

Light year is a measure of distance. It is the distance light travels in an year.

Light year = \(9.4607\times10^{12}\) km

So 4.4 light years = \(4.4\times9.4607\times10^{12}\) km

                                \(41.62708\times10^{12}\) km

Lets scale this down to the level of \(1\times10^{-19}\)

\(41.62708\times10^{12}\times1\times10^{-19}\) km

=\(41.62708\times10^{-7}\) km

Change the units to centimeters:

\(41.62708\times10^{-7}\times1\times10^{5}\) cm

=\(41.62708\times10^{-2}\) cm

=\(0.4162708\) cm

Therefore on the new scale sun is \(0.4162708\) cm away from alpha century.

Diameter of the sun is 1.391016 million km

Lets change Sun's diameter to the new scale:

\(1.391016\times10^{6} \times10^{-19}\)km

=\(1.391016\times10^{-13}\)km

Lets change kilometers in to meters:

\(1.391016\times10^{-13}\times10^{3}\)m

=\(1.391016\times10^{-10}\)m

Therefore, sun is \(1.391016\times10^{-10}\)m

and an atom is \(1\times10^{-10}\)

Therefore the sun is 1.391016 time the size of an atom at this scale.