Well, when I consider if a lie is before me, then I ask myself what purpose would they have to try and deceive me. If there is no reason, they the nest question is whether or not their information is accurate to the level they claim.
Since, as you note, there are resources that abound, then you have a means to test one model against several others. I think I recently mentioned that the Shuttle flights had 5 computers and they compared their calculations with one another, then if one or two were different, the majority result would be used as the odds favored that result.
Orbital equations have the advantage of being retrodictive. You can reverse the time clock and see if these equations are accurate in either time direction, as they would have to be accurate in both directions to claim any accuracy.
"But what if they are lying? How can I determine what that information is for myself??" from post #3.
Helio is correct in post #4, this is easy to test. I use Stellarium 0.20.3 and Starry Night Pro Plus 8. This morning I was out viewing the waning crescent Moon (plenty of earthshine visible too) and Venus. The Moon in Virgo along with the bright star, Spica. Venus in Libra. The software provides a sky view for my location and time, 0617 EST. I could see the stars of Virgo and Libra as well, e.g. Zubenelgenbui in Libra That is a simple visual test that shows the software sky view is accurate for my location, date, and time. Sunrise local time for me near 0715 EST. The Sun is in Ophiuchus, you can see stars in that constellation too rising before the Sun like the position of Venus and the Moon this morning. Simple visual tests of the software like this is easy to do. Before the Sun came up in Ophiuchus, the brighter star Ras Alhague is visible in the east.
The issue raised here and question in post #3, does the concern of *lying software* used that supports the heliocentric solar system, is this because of flat earth videos teaching astronomy on the Internet?
One of the great evidences that shows the Earth is round and spinning, is the ability of modern software to accurately predict rise, transit, and set times for various objects in the sky and show the position of the Sun in various constellations along the ecliptic throughout the year that shows the heliocentric solar system is modeled accurately too.
First, I’m not sure who is doing the lying or why. Star charts are made by kazillions of people, from many countries independently. What would any deception get us? But, at any rate, try this. Set up a small post in the ground. One day, measure the length of the shadow from the stake, when it’s the shortest, that will be noon according to the sun, not the clock. It varies by a few minutes because of earth’s elliptical orbit. We just make the clock 24 even hours per day for convenience. From the tip of the shadow to the stake is true south. Mark that direction. The next day set up a piece of tube and fix it at sun noon again so the sunlight shines through to the ground. Now, you know where the sun was at sun noon. Wait exactly 12 hours and look through the tube and note the star field and any star you see. Find that on any star chart, try several, the sun was exactly 180 degrees within a few seconds of arc as the sun constantly moves. You can even determine its declination, how far south it was from the chart. This is kinda how they do it. But, with millions of observations over years, they’ve gotten pretty exact with their positions. Just don’t look at the sun, it’s not a good thing.