Difficulty: Easy
Cost: $ (No gear actually needed, but a cellphone camera or another digital camera can help)
Watch a well-known star constellation at night and notice its geometrical shape. Take a picture with a camera if needed.
Good candidate constellations: The Big Dipper, Orion, Crux.
Wait for a couple of hours or for another night. See if the constellation shape has changed.
You can also do one of the following:
Travel to another location and observe from there.
Use Google Image Search to see pictures taken by other observers of the constellation.
If you get clear indications of a varying geometrical shape of the constellation you may have evidence of a sky with local stars. This is a fundamental part of Flat Earth Theory. Any such findings should be reported to your local university or the International Astronomical Union.
Good Luck!
Photo documentation (if you choose to take pictures) should preferably be taken as RAW pictures. This increases the trustability of your images and all accusations of “photoshopped images” can be thwarted.
Better digital cameras and cell phones can capture RAW images. A cell phone might need a dedicated photo app for this.
Depending on the abilities of your camera or cell phone: You may need a tripod for longer exposures. A tracking device is not necessary however unless you decide to take very long exposures or use long focal lengths. (But this is not necessary for getting a clear image of a star constellation).
A Flat Earth cannot exist unless the stars are local (nearby)
Otherwise, if the stars are very distant then the altitude of a particular star constellation would be the same everywhere on Earth.
See the picture below.
We know that the altitude of star constellations is not the same for everyone on Earth at a given moment. It is easy to check up.
Just make a phone call to a friend on another continent. If you live in arctic regions you will see the Big Dipper high in the sky. In Mexico or India, it will be much closer to the horizon.
So the picture above cannot work.
This would need us to lower the Stars to a much lower elevation. Something like this:
Now we can see that this would result in the perceived image of the star constellations changing for different observers, due to perspective.
To prove the Flat Earth Model, we must prove this change in perceived geometrical form.
This observation is necessary proof for the Flat Earth model.
This video shows the effect you should expect:
Stars and constellations have been observed by professional astronomers for centuries and also earlier by humans since prehistoric times. We know that stars do show very slow movements in the skies due to various effects (these are called Precession, Nutation, Stellar Parallax, and Star Proper Motion). But these very slow effects produce visible results only after thousands of years. The experiment described here should produce a significant change in the timespan of hours or a few days, or through just a trip to another country or continent. Can you show this?
CHALLENGE: Get evidence of star constellations being deformed/tweaked like shown above.