Question

Suppose you could fit 100 dimes, end to end, between your card with the pinhole and your dime-sized sunball. how many suns could it fit between earth and the sun?

Answer 1

Answer: 100 suns

Step-by-step explanation:

We can solve this with the following relation:

`(d)/(x_(sunball-pinhole))=(D)/(x_(sun-pinhole))`

Where:

`d=17.91 mm =17.91(10)^(-3)  m` is the diameter of a dime

`D` is the diameter of the Sun

`x_(sun-pinhole)=150,000,000 km=1.5(10)^(11)  m` is the distance between the Sun and the pinhole

`x_(sunball-pinhole)=100 d=1.791 m` is the amount of dimes that fit in a distance between the sunball and the pinhole

Finding
`D`:

`D=(d)/(x_(sunball-pinhole))x_(sun-pinhole)`

`D=(17.91(10)^(-3)  m)/(1.791 m) 1.5(10)^(11)  m`

`D=1.5(10)^(9)  m` This is roughly the diameter of the Sun

Now, the distance between the Earth and the Sun is one astronomical unit (1 AU), which is equal to:

`1 AU=149,597,870,700 m`

So, we have to divide this distance between
`D` in order to find how many suns could it fit in this distance:

`(149,597,870,700 m)/(1.5(10)^(9)  m)=99.73 suns \approx 100 suns`