[Spheres]

So what is gravity? If you answer that the earth is moving forward rapidly and giving us the sense of gravity, why to we have an atmosphere, why do we have planets that move around in our sky. Why, does the southern hemisphere see different stars then the people in the northern hemisphere, What is Day and night? What is the Moon?

[Macarios]

First of all, I have to remind that every measurement has error margin.
Whatever we measure we do it with limited number of decimals.
Deeper accuracy would not make much difference for our purposes.

For example, movement of object of five centimeters in size is enough with accuracy of 1 mm, or in precision mechanics 0,001 mm (1 micron).
Accuracy of 1 nanometer is required in VERY RARE occasions.
Most of the time such accuracy is required for objects much smaller than said five centimeters.

So, in practical applications, we just have to know what accuracy is enough.
For closer accuracy, beyond our measuring abilities, we developed mathematics that helps us calculate exact values.

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Gravitation is property of mass.
Everthing that has mass attracts everything else that has mass.
Force of attraction depends directly on gravitational constant G, both masses M1 and M2, and inversely on distance between centers of mass squared.

Here is one of mainstream definitions:

Gravity, or gravitation, is a natural phenomenon by which all things with mass are brought toward (or gravitate toward) one another, including objects ranging from atoms and photons, to planets and stars.

Objects with electric properties interact with each other, objects with magnetic properties interact with each other, object with mass interact with each other.
Fundamental nature of gravitation is no more known than fundamental nature of electricity or magnetism.
What we have is observed and measured interaction, enough to give us tools to use forces and fields.

Before Einstein, science was trying to explain it through force fields.
Newton noticed and Cavendish measured behavior of gravitational forces analog to electrostatic and magnetic forces.
Methodology of calculating gravitation force vectors worked well.
Interaction between electric and magnetic phenomena was observed. Flow of electric current creates magnetic field.
Scientists were trying to achieve opposite as well, and Michael Faraday finally found the way.
Permanent magnetic field couldn't create electric current, but change in magnetic field could.
Field equations to predict behavior in gravitational field worked, but interaction between electromagnetism and gravity couldn't be reached.

Set of gravitational tools, named Newton's laws, worked with good enough accuracy to help Johannes Kepler establish another set of tools.
Set that will help astronomers predict positions of celestial bodies with greater accuracy, known as Kepler's laws.

It worked and still works within our needs in Solar system.
Except for one "detail": Mercury trajectory.

Einstein allowed time and space not to be considered absolutes, which allowed him formulate new, more accurate set of tools, named General Relativity.
It works with better accuracy than Newton's laws.
It also explains (maybe) why there's no interaction between gravitation and electromagnetism.
Gravitation still can be treated as force field, but it isn't.
It is distortion in space-time continuum, caused by mass.

It wasn't too long after Newton published his laws of motion that people noticed something was off about them. To be specific, they were off by the orbit of an entire planet. And they remained off until Einstein, and general relativity, explained why Mercury moves the way it does.

(from: https://io9.gizmodo.com/the-200-year-old-mystery-of-mercurys-orbit-solved-1458642219)

[6or1/2Dozen]

Macarios - Excellent post. It seems like Spheres might also be looking for the flat earth model explanation.

 TFES 'official' explanations can be found in the wiki. However, it has been noted on several occasions to be out of date.

There is also a FAQ section and the forums have a search feature.

In most flat earth models, the force perceived as gravity, is the disc of the planet being accelerated upwards by force know as the Universal Accelerator (UA). The Universal Accelerator, as the name might imply, accelerates universally, so that the Sun, Moon and planets accelerate at the same rate as the disc of the earth. [There is also an infinite plane model in which gravity is gravity, but requires the Earth to be an infinite plane with infinite mass].

Please note that although it is called the Universal Accelerator, it does not actually accelerate things universally, objects like people, trees, small rocks and cheese are exempt.

Based of the fact that the air has a measurable weight (about 15 pound per square inch @ people altitude), I'd assume UA doesn't work on it either. I'm not sure is any explanation has been provided as to what holds the air on the disc. If I had to place a bet, I'd go with 'Celestial Gravitation', which is not to be confused with actual gravitation, as most FE proponents as careful to point out that their is no such thing as attraction between massive objects. What causes celestial gravitation is not well explained. [The other choice would probably be the 'Firmament'.]

Note 'Celestial Gravitation' is often attributed as the cause of local variances in the measured force of acceleration of the disc and the possibly tides. [Other models attribute tides to the bobbing of the floating continents in a great ocean]

Day and night is caused by the periodic rotation of a solar object over the disc. This solar object is 32 miles wide at a height of 3000 miles, with an rotational period of 24 hours. A second rotation, with a period of (about) 365.25 days causes it to transition along a path contained between the Tropics, which causes the seasons. It cast a directional beam of light as to only illuminate (about) half the disc at a time.

The Moon follows a similar rotational mechanic, also being 32 miles wide at an altitude of 3000 miles. I haven't seen a good FE description of the Moons motion, but I would assume it has a period of (about) 24 hours and 50 minutes. Some FE models claim it to be self illuminating and possessing a 'cold-light' (i.e. some sort of anti-photon that causes objects it falls upon on to get colder).

Finally, the stars differ between hemispheres either because:

a) there is a Bi-polar FE model (which you'll need to get someone else to explain because it's a level of [something] beyond my comprehension)
b) I've never come across a reasonable FE model explanation of the southern star field. My bet here would by, 'something to do with perspective'.