Vernal Equinox and True Anomaly point on earth's orbit

[shalevy]

Hi All,

I'm new to the forum and it's my first question. I'm trying to build a solar system simulation with Unity and currently having problem with marking Vernal Equinox on top of the earth orbit. The position I calculate falls around 16/April/2000 on the orbit, which I know is wrong (should be around March 20).

Below is how I tried calculating this point, but I might have gotten this all wrong... would appreciate any help.

The way I calculated this point is as follows:
Mean Anomaly of the vernal equinox = longitude of the ascending node Ω, and the argument of perihelion ω = 114.20783 + -11.26064 = 102.94719 (also called Longitude of the Perihelion).
Convert Mean to True anomaly and plot the point on the orbit.

What am I doing wrong?

Thanks,
Shay

 

[BrianJ]

Hi,
welcome to the forum

I'm not entirely sure what you are trying to do, but if you are following convention and using J2000 Ecliptic as your reference frame to measure the LAN Ω and ArgP ω, then the Earth's vernal equinox is the 0deg axis.
The point you need to plot is where the Earth's orbit crosses this axis.

If you are trying to find the True Anomaly of the vernal equinox point, surely it must be -(Longitude of Perihelion).
Or (360-Longitude of Perihelion) if you want a positive angle.
(Ignoring any inclination of the Earth's orbit)

NOTE: Not sure if you can use True Anomaly or Mean Anomaly to describe a point that doesn't move with time, though.

Any good?
Apologies if I misunderstood your question
BrianJ

---------- Post added at 08:25 PM ---------- Previous post was at 10:07 AM ----------

Actually, I think I'm 180 degrees out! The autumnal equinox lies on the 0deg longitude line(J2000 frame) - so the vernal equinox must be on 180deg. Sorry!

 

[MontBlanc2012]

I always have to do these by reverting to the basic Euler angle transformations between ecliptic and equatorial coordinates and then grinding methodically through the algebra.

But having just done that I find that the equinox corresponding to the 0 degree axis is indeed (as per 'BrianJ') just the negative of the Longitude of Perihelion (~102.947 degrees according to the Nasa Earth Fact Sheet).

So, assuming BrianJ's correction that the vernal equinox points along the 180 degree axis, then the true anomaly is 180 degrees - Longitude of Perihelion = 77.053 degrees.

Now, Earth perihelion is around 4th January and if (albeit a little crudely) we ignore Earth's orbital eccentricity of around 0.0167, Earth will pass through the Vernal equinox about 76 days later - or roughly March 21. That seems about right to me.