Some simple questions

So here are my questions and I will try to keep with in what I have personally experienced:

1. Why can some from a higher vantage point see things I can not?  When sailing someone up on the mast can see islands other boats, etc when on person on deck can not.

2. How was Erastosthenes able to calculate the circumference of the Earth in 300 BC?  Simply by measuring shadows at different locations, the method he used would not have been accurate if the Earth was not round. 

3. Why when sailing do I see objects rise from the horizon and not just appear?

4.  How can I or sailors in the past successfully navigate with celestial navigation when it is based on a round Earth?  The math does not work with a FE model.

5. What causes  lunar eclipses and phases? What is casting a shadow on the moon?  With a Flat Earth model I do not see how the Earth would end up between the Moon and Sun.

6. Why can I see different constellations depending on my distance from the equator?  With a flat earth model this would not change.  I can measure the distance from the horizon using a sextant.  Depending on my direction of travel they will either move closer or further away from the horizon. 

7. Why is it dark in one location of the planet and light in another?

8. Why do I see the moon and sun set on the horizon? 

I asked these questions on tfes.org and the response I got was to read th FAQ forum.
I read the forum searched the topics on their site on none answered the questions I was asking except for number 5 above.  The answer to that was it was either hollow with 1/2 being opaque and the other 1/2 being transparent that rotated. The other answer was it is either a projection or hologram.  With nothing backing up the claims except that is how the person thinks it is.

To give an example of what I am looking for:

Eratosthenes was able to calculate the circumference of the Earth around 300 BC,

Please do not comment on the 1st part when she talks about pictures from space, voyager etc if you want to skip to the meat with out hearing about space travel skip to 1:10. I did not create this thread to debate about Space agencies being part of a conspiracy.

Here is how he did it:

" class="bbc_link" target="_blank" rel="noopener noreferrer">

It is reproducible and gives evidence that supports the Earth is round.

I am looking for math, reproducible experiments, observable evidence, science that answers the above questions and how the above things work within a FE model.

2) Erastosthenes experiment is flawed. He had to PRESUPPOSE the shape of the Earth. If you believe it is flat, you will get different answers (that are wrong if you use more than just 2 points) (http://www.theflatearthsociety.org/forum/index.php?topic=64777.msg1729335#msg1729335). Aligning an equatorially mounted telescope to the N/S Celestial Pole (done hundreds/thousands of times daily) to the latitude of the observer to within minutes and seconds of arc, demonstrates the Earth is spherical. It is the only shape that can be aligned this way and be parallel to the axis of rotation of the Earth and sky so one motor can track the sky.

5) Per the FE fantasy, since the Sun's light is a "spotlight", it does not illuminate the Moon. The Moon is self-illuminating and flat (so everyone can see the same face everywhere on Earth). Some mechanism behind it makes the correct phases and eclipse (Keebler elves with hand puppets I wager - FE is a FANTASY after all). THE question is how does Lunar Libration happen. How does the "skin" of the Moon shift on a round surface?

6) First, the arcs/circles of stars get larger as you go farther and farther south away from the N.Pole. Why would they converge after the equator if the Earth is getting bigger? The S. Celestial Pole (SCP) would be on the ground somewhere beyond the Antarctica "wall". Why does it get higher and higher in the sky as you go south? How can you see the stars below the SCP as they are on the other side of the Earth BEHIND you? In truth, it is impossible to actually see the SCP at all on a disk because it is in the sky above the true S.Pole under the N.Pole under the Earth.

7) Sun "spotlight":


8 ) Given the "spotlight" above, I would like FEers to explain sunsets. Also, why does the sun set at all:
(http://www.theflatearthsociety.org/forum/index.php?topic=65498.msg1748939#msg1748939)

I'd really like to see someone explain why the spotlight changes its shape (difference between June and Mar/Sep), and i'd really love to see someone explain how on Earth the spotlight can do what it supposedly does in December.

Also what accounts for the tides? Without the gravity from the sun and the moon? And what accounts for the difference in tide amplitude (difference between low and high tide) in different places around the world? Someplaces it can have a maximum tide amplitude of 12 meters, while in others just 4m, during the course of a year. That's perfectly explained by a round earth and gravity, but i'd love to hear what FE theorists think.