How can I find angle of mars relatvie to Vernal point in this diagram?

ncc1701d

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Looking at this diagram found here:

http://www.nakedeyeplanets.com/mars-seasons.htm

I would like to find out the angle between the Mars WS (winter solstice) location shown and the vernal point (0 deg) which is also shown between Pisces and Aquarius
in the diagram.
does anyone know how to find that angle?
if so how?
Thanks
 

Keithth G

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I would like to find out the angle between the Mars WS (winter solstice) location shown and the vernal point (0 deg) which is also shown between Pisces and Aquarius
in the diagram.
does anyone know how to find that angle?

It seems to me that the discussion in your previous post http://www.orbiter-forum.com/showthread.php?t=37135 and the various papers there - particularly your link to the Mars24 calculations - give you enough information to be able to calculate this.

But before diving into the details, it may be worthwhile thinking about the definitions of the vernal equinox and winter solstice. To do that, we need to have in mind the concept of Mars-centric planes. The first of these is Mars' orbital plane around the Sun. This is Mars' version of the ecliptic. From a Mars-centric point of view, the Sun is always constrained to lie on its orbital plane - just as the Sun always lies on the ecliptic plane when seen from Earth. The second relevant Mars-centric plane is Mars' equatorial plane - a plane which is defined by Mars' rotation axis which is always perpendicular to the equatorial plane in exactly the same way as Earth's rotation axis is perpendicular to its equatorial plane.

These two Mars-centric planes - the orbital plane and the equatorial plane intersect along a line (the line of nodes). During the course of the Martian year, as the Sun moves along a path on the orbital plane, it will periodically pass through the line of nodes and cross Mars' equatorial plane. This will happen twice a year - once when the Sun crosses from below the equatorial plane to above it (the Vernal (Spring) Equinox); and once when the Sun crosses from above the equatorial plane to below it (the Autumnal/Fall Equinox). Between the Vernal Equinox and the Autumnal Equinox (northern hemisphere summer), the Sun is above the equatorial plane and, at some point in time (the Summer Solstice) its altitude above the equatorial plane is at a maximum. Equally, between the Autumnal Equinox and the Vernal Equinox, the Sun is below the equatorial plane and, again, at some point in time (the Winter solstice) its altitude below the equatorial plane is at a maximum.

Now, as with Earth, it is conventional to describe the position of a celestial body in the equatorial reference frame using right ascension(RA), [MATH]\alpha[/MATH], and declination, [MATH]\delta[/MATH]. These are essentially altitude-azimuth coordinates of the body in a planet-centric non-rotating coordinate system. Because the rotation axis is more or less fixed, and because most stars are very distant from Earth, the right ascension/declination coordinates of a star are essentially fixed. The position of the Sun can also be described in terms of right ascension/declination coordinates - but in this case, the coordinates change with time.

RA and declination are useful in the problem because (by definition), the Vernal Equinox occurs when the right-ascension of the Sun, [MATH]\alpha_S[/MATH], is zero (and the declination of the Sun, [MATH]\delta_S[/MATH], is also zero). And the Winter Solstice occurs when the Sun's delineation is at a minimum with [MATH]\delta_S<0[/MATH]. So, if you have a way of calculating the Mars-centric right ascension and declination of the Sun at any time, you can use numerical procedures to find the dates of the Vernal Equinox and the Winter Equinox. Mars24 and ancillary papers do just that.

An if you know the dates of the Vernal Equinox and the Winter Solstice, you can calculate the solar longitude [MATH]L_S[/MATH] on those dates. The difference in solar longitude between those two dates should, I think, give you your answer.
 
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ncc1701d

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I think the thing that keeps confusing me as I look at diagrams and that science paper is specifically
for example on that link i sent on the right under gray label "2018 July 27"
the diagram says ...SE is spring (vernal) equinox and it also says First point of aries (vernal equinox)
But SE vernal equinox Mars graphic icon points twords the left on orbital diagram and the vernal equinox red line points twords the top in the orbital diagram.
Its like they are using defintion of vernal equinox 2 different ways.

then here comes the the 1997allison pdf file and in their diagram they show V.E. but iam not sure if that has anything to do with the first point of aries

somehow in the diagram they got Ls = 0 and V.E. and the first point of aries i might be tempted to think all together in one spot in time but i dont know if all 3 things can ever come together at one point in time.

this is one thing that is messing with my head.
 
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Keithth G

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I think the thing that keeps confusing me as I look at diagrams and that science paper is specifically
for example on that link i sent on the right under gray label "2018 July 27"
the diagram says ...SE is spring (vernal) equinox and it also says First point of aries (vernal equinox)
But SE vernal equinox Mars graphic icon points twords the left on orbital diagram and the vernal equinox red line points twords the top in the orbital diagram.
Its like they are using definition of vernal equinox 2 different ways.

I don't find the diagram particularly easy to read, but it may be worth pointing out that Mars will have a different set of equinoxes and solstices. So, given that there is an SE, AE, SS and WS for Earth, so too there will be an SE, AE, SS and WS for Mars - making 8 in total for the diagram (since it shows details for both Earth and Mars). And because the orbital plane and rotation axis of the Earth are not the same as those for Mars, there is no reason to suppose that the these equinoxes and solstices for the two planets will align. Indeed, in general they will not (and do not). Since the First Point of Aries is specific to Earth, it need not have any meaning for equinoxes on Mars.

somehow in the diagram they got Ls = 0 and V.E. and the first point of aries i might be tempted to think all together in one spot in time but i don't know if all 3 things can ever come together at one point in time.

As for Ls = 0, one has to measure angles from some starting direction - and the direction that is chosen for doing this on Earth is the Vernal Equinox direction, i.e. in the direction of the Ascending Node of the line of nodes - the intersection of the ecliptic/orbital plane and Earth's rotational plane. This definition is carried over to Mars - albeit with a different orbital plane, rotational plane and hence a different Ascending Node direction. But, by definition, on Earth as on Mars, Ls=0 precisely at the Vernal Equinox. Or, at least, that's my understanding of the matter.

As for the First Point of Aries, on Earth at least, this is just another name for the Vernal Equinox. So, on Earth, the three terms - Ls = 0, Vernal Equinox and FP of A - all refer to the same thing. On Mars, the FP of A has no particular meaning.

Does that help?
 
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