How is Heliocentric Earth Longitude Measured?

[spossatamente]

Hello,
in heliocentric coordinates the longitude of the Earth on april 15, 2010 is 204.91°... well I know that the longitude in ecliptic system (centered on the Earth ) is measured from the vernal equinox... if i started measure from V.E. in heliocentric system too I would find the Earth in Autumn!
So I'm wondering...is the longitude measured from libra point?

 

[D H]

Heliocentric ecliptic longitude is measured with respect to the vernal point. The position of the Sun as seen from the Earth is more-or-less in the direction of the vernal point on the vernal equinox. This means the position of the Earth as seen from the Sun is more-or-less in the direction of the autumnal point on the vernal equinox.

 

[spossatamente]

what's wrong with my picture?

 

[D H]

What is that picture supposed to show, in your mind?

Turning the question right back at ya, what was wrong with my explanation?

 

[Philosophaie]

The equatorial plane differs from the ellipical plane by the obliquity angle which for the Earth is about 23.45deg. The equatorial and elliptical are equal to each other at the equinoxes: Spring or Vernal, and Autumnal as the above drawing is trying to show.

 

[spossatamente]

Well, if you measure 204° from Aries point along the orbit you find the Earth quite near to the Libra point, I mean the Earth is very far from 21 March... it sounds weird since the 204° angle corresponds to 15 April!
Look at any terrestrial seasons figure as http://www.ilfaromag.com/wp-content/uploads/2009/05/orbita-terrestre.gif
it is a heliocentric system, isn't? Start from 21 March and walk on the orbit for 204°... you arrive in November.

 

[D H]

I hope you two are not astrologers. If not, accept my apology for even accusing you of such.

Look at any terrestrial seasons figure as http://www.ilfaromag.com/wp-content/uploads/2009/05/orbita-terrestre.gif
it is a heliocentric system, isn't? Start from 21 March and walk on the orbit for 204°... you arrive in November.

Where is the zero point in that figure, spossatamente?


Look at it this way. On March 21, 2010 00:00 CT, the cartesian coordinates of the Sun with respect to the Earth were (0.996018, 0.002179, -0.000001) AU in the ecliptic and mean equinox of J2000 frame. In other words, just about (1,0,0) AU. Where was the Earth respect to the Sun? Simple: Negate this vector, or (-0.996018, -0.002179, 0.000001) AU. Converting that to polar coordinates yields an ecliptic longitude and latitude of 180.1204° and 0.0001°.

How about April 15, 2010? Using the same coordinate system, the coordinates of the Sun with respect to the Earth were (0.910778, 0.420501, -0.000010) AU. The coordinates of the Earth with respect to the Sun were the additive inverse of this vector, or (-0.910778, -0.420501, 0.000010) AU. Converting to polar coordinates yields an ecliptic longitude and latitude of 204.7776° and 0.0006°.

 

[spossatamente]

That is clear but you still don't understand what is my problem.
Since Aries+180°= Libra ==> in heliocentric coordinates system you start measure longitude from Libra point...

 

[D H]

No! You start measuring from the vernal point. Let's look at the state of things on the vernal equinox. The Sun as viewed from the perspective of the Earth is in the direction of the vernal point on the vernal equinox. Where is the Earth as viewed from the perspective of the Sun?

 

[spossatamente]

...mmmh so on 15 april...if i am on the sun i see the Earth in Autumn but i am on the Earth so when i look at the sun it is ascending ( http://www.astro.virginia.edu/class/oconnell/astr121/im/CS-ecliptic-2-CK.jpg ) and that means we are on spring.
But how can you explain that in the picture i posted before ? http://www.ilfaromag.com/wp-content/uploads/2009/05/orbita-terrestre.gif

 

[D H]

What is the direction of the vernal point in that picture, spossatamente?

 

[spossatamente]

Vernal point is called in this picture <<equinozio 21-3 >>
the other names are
primavera= spring
estate= summer
autunno=autumn
inverno= winter
solstizio= solstice

 

[D H]

No! The vernal point is a point at infinity. Think of it this way: The vernal point points in the direction of the Sun as seen from the Earth on the vernal equinox.

 

[spossatamente]

if i am on the sun on spring equinox and i look at the Earth this one is aligned with libra point..
can we say that the vernal point is rotated of 180° in heliocentric system with respect to geocentric system?

 

[D H]

No! The vernal point is a point at infinity.

 

[spossatamente]

you mean that it lies at an infinite distance because the radius of the celestial sphere is infinite...but you usually take its projection on the orbit of the Earth to measure the longitude... but this is not the point.
Vernal point (put it into Hyperuranium or any else place i don't mind it) has a sense (as a vector) on the line which joins libra and aries. Passing from a heliocentric reference of frame to geocentric one you rotate 180° this sense. So the sense of the vector now points to libra

 

[D H]

you mean that it lies at an infinite distance because the radius of the celestial sphere is infinite

Correct.

...but you usually take its projection on the orbit of the Earth to measure the longitude...

Incorrect.Please answer the raised question in post #7. Are you pursuing this from the point of view of astrology?

 

[spossatamente]

Astrology? It is absurd.
I collected some data (one of these is longitude of earth) to work out the declination and R.A. of Mars on April 15,2010. This is an exercise I did during a lesson of << misure astrofische>> (i'm attending the university of Ferrara) . Anyway... from the book Fundamental Astronomy by H. Karttunen

>> The other coordinate is the ecliptic longitude λ, measured
counterclockwise from the vernal equinox.

 

[D H]

OK. Sorry I even accused you of such.

It appears you have a misunderstanding of celestial coordinate systems. This discussion needs to back up a bit.

Two orthogonal unit vectors are needed to define a coordinate system in three dimensional space. (The third unit vector is fixed once those first two are defined.) One way to do this is to define a fundamental plane. A normal to the plane defines one of the unit vectors, a line on the plane defines another, and the cross product of these defines the third.

Two widely-used fundamental planes in astronomy are the Earth's equatorial plane and the Earth's orbital plane.

These planes intersect along a line. That line defines one of the unit vectors. This is the x-hat vector and is common to both the equatorial and ecliptic based systems. At the vernal equinox (a point in time), the Sun as viewed from the Earth lies more or less in the direction of the x-hat axis. The equatorial z-hat unit vector points from the center of the Earth to the North Pole (more or less). The ecliptic z-hat unit vector is normal to the ecliptic plane with sign defined so that the projection onto the equatorial z-hat unit vector is positive. The y-axis completes the right-handed coordinate system.

Thus we have two sets of right-handed orthogonal unit vectors, the equatorial and ecliptic axes. Now a reference frame needs an origin and a set of axes. For geocentric references, the origin is the center of the Earth. Another reference frame can be defined by choosing a different origin. The heliocentric ecliptic frame shares the same set of unit vectors as does the geocentric ecliptic frame, but the origin is now the center of the Sun rather than the center of the Earth.

Note that at any time, if the geocentric position of the Sun is \vec r_{\text{Sun}}(t), then the heliocentric position of the Earth is \vec r_{\text{Earth}}(t) = -r_{\text{Sun}}(t). Now think of what this means the vernal equinox. From the perspective of the Earth, the Sun will be at 1 AU in the x-hat direction. From the perspective of the Sun, the Earth will thus be at -1 AU in the x-hat direction.

Spherical coordinate are another way to express a vector. Ecliptic latitude and longitude (along with radial distance) are spherical coordinates. The Earth's heliocentric longitude at the vernal equinox is 180 degrees.