#### Zack Bimmel

• 9
##### Erathostenes and the North Star
« on: May 28, 2018, 01:11:34 AM »
Most of you are familiar with Erathostenes' shadow experiments in which he thought that he would measure the diameter of Earth. Alternatively, one can derive from his measurements (7.12 deg shadow with 500 miles distance between measurement points) the diameter of the flat earth to be 25000 miles ( https://wiki.tfes.org/Erathostenes_on_Diameter ) and also the height of the sun above earth ( 500 miles * tan(90-7.12)) to be some 4000 miles. So who is right ?  Well, I am not going to travel to repeat and expand on his experiment, somebody else might do that.

Here is an alternative : let's measure the height of Polaris, the North Star, above earth. We all can do that without having to travel. Don't believe me ? So, here it goes.

If you were at the North pole the North Star would be vertically above you and the angle between the horizontal and the line from you to the North Star would be 90 degrees. Of course you couldn't see the North Star right now - it's daylight there right now, 24 hours a day.
Anyway, lets say you live at 70 deg northern latitude - the angle between the horizontal and the line to the North Star would be 70 deg. And similar for other latitudes. Nice thing is, everybody can check that out if you live not too far North. If you do, you will have yo wait for the winter to do the checking.
Now, we can do the calculations using the radius of earth, the number of degree latitude from north to south and trigonometry :

(12250miles*((90-70)/180)*tan(70) = 3740 miles above flat earth.

And now we can go beyond Erathostenes !!!   I am calling up my friend who lives a little bit north of San Antonia, Texas, at 30 deg latitude.

(12250miles*((90-30)/180)*tan(30) = 2357 miles above flat earth.

So, who is right ?  My challenge to everybody : do the calculations for the latitude where you live.

#### Max_Almond

##### Re: Erathostenes and the North Star
« Reply #1 on: May 28, 2018, 03:19:42 AM »
Yep. Trying to figure the altitude of the north star is one of the best ways to show the impossibility of the flat Earth.

That's why not a single one of them will attempt it.

#### LersmenThe3

• 9
##### Re: Erathostenes and the North Star
« Reply #2 on: May 29, 2018, 08:21:53 PM »
Yep. Trying to figure the altitude of the north star is one of the best ways to show the impossibility of the flat Earth.

That's why not a single one of them will attempt it.

My personal favorite is this: