Pro Calculation and Solar Wobble

[Geometrian]

Hi,

I'm building a solar system simulator, designing it to be as accurate as possible. Visualization is done through OpenGL (although I may be forced to use a software renderer for higher precision).

I have set up all the planets and their orbits, tilts, and made them update according to the best models I have available. The model can, for instance, show Earth's solstices hundreds of years in the future.

I'm trying to show the upcoming transit of Venus, and unfortunately my model predicts the transit about a day too early!

Explanations:

-The sun is currently modeled as not moving, yet the sun wobbles significantly (like up to a solar width). I believe this accounts for at least part of the difference. Where can I find data to model this?
-I am not accounting for the moon's effect on the Earth either. I can work out how to fix this myself.
-The orbits of the planets evolve over time. My model is based on the evolving equations given on this site, and the computation is much the same. The model uses J2000 as a basis, so perhaps errors accrued over the following 12 years? Is this model correct?
-Relativistic effects​

All of these I know figure into the model, but I'm not sure which are most important (though I suspect the sun's wobble and Earth/moon most), nor if I'm omitting something significant.

Finally, how was this transit predicted anyway? There must be some simulation or calculation somewhere. How was it predicted? Ideally, I could base my work on that instead . . .

Thanks,
Ian

 

[AndyW]

Dear Ian,

It is great to hear that you are building a solar system simulator and striving for accuracy. There are a few factors that could be contributing to the discrepancy in your transit prediction.

Firstly, as you mentioned, the sun does have a slight wobble due to the gravitational pull of the planets. This can be accounted for by using data from NASA's Solar Dynamics Observatory (SDO) or the Solar and Heliospheric Observatory (SOHO). These satellites constantly monitor the sun's position and can provide precise data for your model.

Secondly, the moon's effect on Earth's orbit can also play a role in the accuracy of your simulation. You can incorporate this by using data from the Jet Propulsion Laboratory's DE430 ephemeris, which includes the moon's gravitational influence on Earth.

Thirdly, as you noted, the orbits of the planets do evolve over time. It is important to use accurate data for the initial conditions of your simulation, such as the J2000 epoch. However, it is also important to regularly update the data to account for any changes that may occur over time.

In terms of relativistic effects, they can have a small impact on the accuracy of your simulation. However, for a transit prediction, they are not likely to be a significant factor.

As for how the transit was predicted, it was done using a combination of observations and calculations. Astronomers use data from previous transits and known orbital mechanics to make predictions for future transits. These predictions are constantly updated and refined as more data becomes available.

In summary, to improve the accuracy of your transit prediction, you can incorporate data from SDO, SOHO, and the DE430 ephemeris. Regularly updating your data and accounting for the moon's gravitational influence can also help. Keep in mind that there may still be small discrepancies due to factors such as the sun's wobble and relativistic effects. However, by using precise and regularly updated data, you can minimize these discrepancies and create a more accurate simulation.

Best of luck with your project!