Sun's Position in Our Solar System

[wolram]

I had a thought about the possition of the sun in our SS, and wondered if
the suns possition varied by any significant amount due to the gravitational
pull of the planets, all the simulations i can find have the sun static.

 

[Garth]

The Sun orbits around the Centre of Mass of the Solar system, just as all the planets do.

However, in the two body Newtonian problem you can transform the orbital motion around the CoM into an orbital motion, to a non-inertial frame of reference, around either of the masses. Normally the Sun is taken as the origin of the coordinate system, and the planet performs a Keplerian ellipse around it.

Garth

 

[wolram]

The Sun orbits around the Centre of Mass of the Solar system, just as all the planets do.

However, in the two body Newtonian problem you can transform the orbital motion around the CoM into an orbital motion, in a non-inertial frame of reference, around either of the masses, normally the Sun is taken as the origin of the coordinate system, and the planet performs a Keplerian ellipse around it.

Garth

Hi Garth, i imagine the center of mass is not far from the sun, so the sun would wobble , rather than actually orbit, but is this a chaotic wobble, due
to having so many planets to pull on it. or is it more than a wobble.

 

[mubashirmansoor]

Wolram, your imagination is abseloutely correct and its just a wobble and not more.

 

[Labguy]

Wolram, your imagination is abseloutely correct and its just a wobble and not more.

With the Sun being 99.8% of the mass of the entire solar system and Jupiter being most of the rest, the center of mass would be very near the core and well below the photosphere, It might even be in the core (however defined) and the wobble would be very small. Even that small wobble effected by Jupiter would often be offset some by any other solar system masses opposite Jupiter at the time and I don't know if the wobble would even be detectable...

 

[Kurdt]

The wobble of stars is one of the main tools used in detecting extra solar planets. This can be done by astrometry (carefully measuring the position of a star over a long period of time) or by doppler shifting of the stars spectra. I did see a website a while back that demonstrated the suns wobble with a video and it is rather erratic and mainly due to Jupiter. I can't find it at the minute but if i do I'll post it.

 

[Labguy]

The wobble of stars is one of the main tools used in detecting extra solar planets. This can be done by astrometry (carefully measuring the position of a star over a long period of time) or by doppler shifting of the stars spectra. I did see a website a while back that demonstrated the suns wobble with a video and it is rather erratic and mainly due to Jupiter. I can't find it at the minute but if i do I'll post it.

I was going to mention that (extra solar planets) but I think I remember that most found by this method are much larger than Jupiter and quite a few are much closer to their primary than Jupiter is to the Sun.

But, a quick search shows me that I was wrong and that the barycenter of the Earth-Jupiter system is a bit outside the Sun's photosphere as described by the heretical "Wikepedia" source:

Sun-Jupiter system: put Sun in position 0, mass = 333,000 Earths. Jupiter in position 778,000,000 km, mass=318 Earths. Center of mass is 742,000 km from the Sun center, 96,000 km outside its surface. As Jupiter does its 11 year orbit, the Sun does a 1.5 million km orbit around the center of mass.

and more, including the animations, at:
http://en.wikipedia.org/wiki/Center_of_mass

In the case of a planet the size of Jupiter, which is 318 times as massive as Earth, the barycenter of Jupiter and the sun is a bit further from the sun's center. So, as Jupiter revolves around the sun, the sun itself is actually revolving around this slightly off-center point, located just outside its surface. Thus, a planet the size of Jupiter will make the sun (or any star) appear to wobble a tiny bit.

and more stuff at:
http://www.madsci.org/posts/archives/oct99/940428154.As.r.html
http://sprott.physics.wisc.edu/lectures/seasons/sld016.htm

Guess I better stick to stellar stuff and leave the solar system stuff to Janus..

 

[Garth]

You might find the following discussion interesting:The barycentric motion of the Sun and the test of general relativity using radio links with the Cassini spacecraft , as it tests the question under GR.

Garth

 

[tony873004]

The solar system barycenter is often outside the photosphere of the Sun, but not outside the corona.

Here is an image of the Sun locked to the center of the screen:
http://orbitsimulator.com/BA/sbc1.GIF

Unlocking the Sun exposes the solar system barycenter which is now locked to the center of the screen. The Sun spends nearly a decade in this image circling the solar system barycenter:
http://orbitsimulator.com/BA/sbc2.GIF

Editing the Sun and setting its size to 0 while retaining its mass allows me to zoom in on the solar system barycenter and observe the Sun's path around it:
http://orbitsimulator.com/BA/sbc4.GIF

The center of the Sun strays near its maximum barycenter distance of about 1.3 million kilometers on Dec. 3, 2022.This can be corroborated by querying the JPL Ephemeris system which gives the following data for Dec. 3, 2022.
$$SOE
2459916.500000000 = A.D. 2022-Dec-03 00:00:00.0000 (CT)
1.357796530286104E+06 -5.340761458326381E+04 -3.117957726829686E+04
-9.802716335062548E-04 1.565705785929941E-02 -1.077297045285839E-04
4.533817068543462E+00 1.359204163100999E+06 -1.592002604514373E-03
$$EOE

The boldfaced, italicized number represents the Sun / solar system barycenter distance (km) on that date.


In the simulation, editing Jupiter, and setting its mass to 0 demonstrates that Jupiter is responsible for the majority of wobble.
http://orbitsimulator.com/BA/sbc5.GIF

Saturn is the next strongest perturber. Additionally, setting its mass to 0 shows:
http://orbitsimulator.com/BA/sbc6.GIF

The next strongest perturber is Neptune. Additionally, setting its mass to 0 causes the Sun's motion around the solar system barycenter to trace a circle around its barycenter. Uranus is responsible for this circle. The Sun's period around the barycenter and Uranus' period around the barycenter match.
http://orbitsimulator.com/BA/sbc7.GIF

Zooming in exposes the effects of the smaller planets on the Uranus-induced circle.
http://orbitsimulator.com/BA/sbc8.GIF

Setting Uranus' mass to 0 eliminates the Uranus-induced wobble. The Sun's center now appears to rest on the solar system barycenter.
http://orbitsimulator.com/BA/sbc9.GIF

But zooming in further exposes the influences of the remaining planets on the solar system barycenter: The Earth/Moon system is responsible for the majority of the wobble
http://orbitsimulator.com/BA/sbc10.GIF

Setting the Earth/Moon mass to 0 leaves Venus as the most significant perturber. It has the following influence:
http://orbitsimulator.com/BA/sbc11.GIF

Setting Venus' mass to 0 leaves Mercury, Mars, and Pluto as the sole perturbers. They cause the center of the Sun to trace the following path around the solar system barycenter:
http://orbitsimulator.com/BA/sbc12.GIF

Zooming in for a clearer view, the effects of Mercury and Mars are seen. Pluto's effects is simply pulling this pattern off-center. If left to run for a quarter century of sim time, the entire pattern would trace a circle around the center of the screen:
http://orbitsimulator.com/BA/sbc13.GIF

Setting Mars, which is now the most significant perturber, to 0 shows Mercury's influence causing the center of the Sun to trace circles around the solar system barycenter:
http://orbitsimulator.com/BA/sbc14.GIF

Letting this simulation run for half of a Pluto orbit exposes Pluto's influence on the solar system barycenter.
http://orbitsimulator.com/BA/sbc15.GIF

 

[wolram]

Thankyou everyone, the links you provided etc have been most interesting,
i imagine the seasoned space pilot would have to know his orbits.