Christ's Birthday is June 17th 2 BC. ( It's important to note, "BC" stands for = Before Christ )
How do we know ? Astronomy software.
We have software that can calculate the positions of the planets in the solar system.
On a side note, planets are also considered stars in biblical terms due to their resemblance to the naked eye.
The 4 brightest objects in the sky from Earth's perspective..
1. The Sun
2. The Moon
3. Jupiter
4. Venus
But we're looking for the Star of Bethlehem right ?
First you need to look at what the Star of Bethlehem actually is, and.... It is a conjunction of Jupiter and Venus lining up with one another. If you ever saw Jupiter and Venus in the night sky, you might have wondered "What the hell is that bright star ?" It's one of those 2 and they are quite spectacular ( Last time I saw them from here was maybe in 2013-2014. It depends on their orbit. Jupiter in particular as far as I know is covered in daylight these days.
For an idea of how bright Jupiter and Venus are compared to the moon, skim through this, but nothing beats seeing it for yourself.
Using the software, we can see the planets positions, see solar eclipses etc... And we roll back to that day when Jupiter and Venus cross paths... And on that day.... Jupiter and Venus did indeed come together. I'm telling you these two objects are very bright. When they are in our night sky, they both stand out nice and sharp even with the light pollution. If we can see them connect, it will appear as a very bright star.
This event also happened in 1 BC, so some speculate that is the correct year.
The last time there was a conjunction between Venus and Jupiter was in 2015, but they never overlapped like it did in 1 BC and 2 BC.