The issues flat earthers have with the heliocentric model are:

1. You cannot see the curve of the earth (sideways)
2. You cannot prove the curve of the earth over the horizon (sinking ships)
3. You cannot prove gravity
4. Nobody has ever been across the south pole
5. You cannot feel the motion of movement on the earth, and we cannot prove we are speeding across the galaxy at impossible speeds
6. The distance to the celestial objects have never been measured.

All examples provided are based on these 5 concepts.

The examples used to show the flatness of earth

1. If you turn 360o on the surface of the earth, the horizon is always level and flat.
2. Aircraft do not have to dip to fly, so there is no curve
3. People do not fall of the earth in southern hemisphere
4. People have seen things over the horizon, or tested with lasers
5. Clouds are seen behind the sun
6. Pictures from outside the earth are always composites of several 'flat' pictures
7. Pictures from weather balloons and aircraft do no show a curve.
8. Water is always level, so how can it curve
9. Aircraft, birds can fly, but the oceans are pulled to the earth.
10. Super zoom camera's show a whole boat.

The examples to show the distance to the moon/sun

1. Crepuscular sun rays prove the sun is close
2. The sun gets smaller when setting
3. The sun is exactly as big as the moon

To disprove a spinning globe, or moving globe

1. Aircraft take the same time to traverse the from east to west as west to east
2. If you throw a ball up, it will come down on the same spot
3. The same star patterns have been visible for centuries
4. We do not feel the earth moving

And what do they use to provide explanations:

1. Sun and moon movements are just perspective
2. Seasons are formed because of the distance to the sun
3. Gravity is explained through buoyancy and density