Question

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).

Answer 1

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.

Answer 2

Beautiful !  What a great exercise !  I won't even check to verify
that 1:10⁻¹⁹ is an appropriate scale to map the Milky Way onto a
football field.  I'll just accept it and go from there.

(4.4 light years) x (10⁻¹⁹) = (2.5848 x 10¹³ miles) x (10⁻¹⁹)

                                       =  2.5848 x 10⁻⁶ mile

                                       =    0.164 inch .

(1,391,400 kilometers) x (10⁻¹⁹) = 1.3914 x 10⁻¹⁰ meter


Research Conclusions:

If the Milky Way shrinks to fit on a football field, then

-- Alpha Centauri is  0.164 inch from us.

-- The sun's diameter is about 1.39 times that of a Hydrogen atom. 

Playing with this same fun concept a little more:

-- The Earth is sailing around in its orbit, once a year,
    about 0.000015 millimeter from the sun. 

-- It takes light almost 27 years to travel 1 inch !

wow  !