# Is the gravitational center of the solar-system relative to planetary position?

Discussion in 'Astronomy, Exobiology, & Cosmology' started by JEL, Feb 7, 2023.

1. ### JELRegistered Member

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Is the gravitational center of the solar-system relative to planetary position?

Google did not work for me this time, so I'm trying here instead.

Light-speed is finite and speed-of-gravity is said to be the same as speed-of-light.

So the sun's location is, when observed from Earth, trailing 8 minutes behind it's 'true' location ('True' as meaning the sun's and Earth's location if observed from equal distance to both, such as a triangulated position above or below their orbital-plane)

Given that the light/gravity from the sun takes longer to reach more distant planets, than closer planets, the trailing position of the sun would be greater in time for distant planets than closer ones.

Saturn, for example, is 80 minutes from the sun, or 10 times that of the earth.

So does this mean Saturn is orbiting a center-of-the-solarsystem that is trailing 10 times behind the center the earth is orbiting?

If gravity spreads at the speed-of-light, then logically, the planets must each observe a different center (Location of the sun)

Apparently the orbits work in reality, but if we were to observe the solar-system from above or below the orbital-plane (Think a 90 degrees vertical position above the sun. Similar to if you watch a record on a record-player from exactly above it), then how can Saturn orbit the same center as the earth, if Saturn is 'seeing' this center with an 80 minutes delay?

What don't I get here, since the orbit-aspects of the solar-system clearly appears to work in reality?
Thanks.

A little extra: According to what I can find via google, it seems the solar-system is, as an entirety, moving perpendicular to its plane (So like a record moving up or down the record-player's center-pin) and not side-ways (Like a flying disc you throw)

This would of course make the sun appear as a non-moving center to all planets at all distances along the orbital-plane (And only shift its location 'vertically', compared to the plane)

Does this play a part of some kind in producing orbital stability? Like a table-top spinner.

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3. ### DaveC426913Valued Senior Member

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Where do you think the sun might go in that 80 minutes between reaching Earth and reaching Saturn?
Do you figure it's running away, and might leave Saturn behind?

No, the sun, and the solar system at-large, can be treated as stationary in space.

It is true that other planets (such as Jupiter) will cause tiny perturbations in the sun's position, but ultimately that's still just a small deviation from the sun's centre.

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5. ### sculptorValued Senior Member

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GOOGLE is an idiot.

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7. ### mathmanValued Senior Member

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There is no fixed position for anything. The gravity center is in the interior (?) of the sun, but not exactly at the sun's center.. I presume the planetary motion will affect their relative positions.

8. ### DaveC426913Valued Senior Member

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This stack exchange article covers it pretty nicely. Here's the TL;DR version:

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Y-axis is distance from Sun's centre. Units are AUs. Dotted line is Suns surface.
So, the barycentre moves in and out of the sun's volume over years (x-axis) as the four gas giants in their slow orbits pull it in various directions.

Interesting periodicity of about 40 years. Anyone care to theorize the cause?

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Last edited: Feb 7, 2023
9. ### JELRegistered Member

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Thank you for the replies, but it seems my question was not phrased the best.

I am not talking about a possible barycenter (I'm trying to understand the basics first. How a barycenter works, in a system limited by speed-of-light, is certainly interesting enough, but is a step that comes later)

The sun moves through space at some velocity (Different estimates are given, most seem to be around a velocity of 800 thousand kilometers per hour)

At that speed the sun will have moved about 1 million kilometers in the time it takes for light (And presumably also gravity) to go from the sun to Saturn.

If gravity extends at the speed-of-light, then Saturn will orbit a point that is trailing the sun by about 1 million kilometers (Since the sun will have traveled that distance in 80 minutes)

At the same time earth will orbit a point that is trailing the sun by about 100 thousand kilometers.

Logically this would mean Saturn and earth is not orbiting the same center-of-gravity.

My question is if this is indeed what is happening.

/////////

Maybe the following mental images explain my question better:

When a boat travels through water, a wake (stern wake pattern, the big V shape you see extending behind a boat) is formed that travels outwards perpendicular to the boats direction of travel.

Supposing gravity is behaving like this wake, moving outwards from the sun at the speed-of-light (If you view the solar-system from 'above', like you would view a rotating-disc or a record on a record-player, and the center-pin is the sun (Which is not stationary, but moving through space)), then what effect will this have on the relative planetary orbits between planets close to the sun and far from the sun?

Imagine the disc is moving vertically, such as our solar-system is said to do (The record on the player is being lifted up, or perhaps like a helicopter that takes off vertically and climbs straight up), will the disc then have something like vortices for the outer planetary orbits? (Shifted planes, like a cone-shape with the sun at the 'top', since the observed CoG will trail behind by a greater and greater distance the further out from the sun you go)

And could a solar-system move any other way but along the vertical axis and still remain intact? If the sun was moving in a direction along the disc (Like the turn-table pick-up moves along the record when it plays the music), how would that affect the observed CoG between the points where a planet was ahead of the sun (The sun's velocity-vector) and behind the sun? Would gravity then be 'red-shifted' and 'blue-shifted' like light?

I hope that makes the question slightly more clear (Although text isn't always the best medium to use for subjects such as these)

10. ### James RJust this guy, you know?Staff Member

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JEL:
The theory of relativity tells us that all motion is relative. There is no absolute stationary object in the universe that we can take to be the Standard of Rest. So, yes, the sun moves through space relative to the centre of our galaxy at a certain speed. Our galaxy also moves through space relative to other galaxies. But there's nothing you can point to and say "That thing is not moving at all" (in an absolute sense).

This means that we are free to choose a frame of reference, which means, in effect, arbitrarily choosing an object that we will say is "at rest" and measuring the velocities of all other objects relative to that. The only caveat to that is that things become more difficult to analyse if the "rest" object we choose happens to be accelerating (more accurately, moving non-inertially).

If we're considering the orbits of planets in our solar system, it is convenient to work in a reference frame in which the Sun is considered to be at rest. Or, if we want to make certain calculations easier, we can use the frame in which the barycentre of the solar system is considered to be at rest.

With the Sun fixed in place, the Sun's gravity always pulls the planets directly towards it. The resulting motion is elliptical orbits.

If we want to translate this picture to some other frame of reference (e.g. the one in which the entire solar system is orbiting the centre of the Milky Way), it's more or less just a matter of adding the galactic motion to the calculated motions of the planets. That is: the velocity of, say, Jupiter, relative to the centre of the galaxy is just the velocity of Jupiter relative to the Sun plus the velocity of the Sun relative to the centre of the galaxy.

Isaac Newton described gravity as an instantaneous force. That is, the gravitational force is assumed to cause an attraction between any two masses instantly, such that the force is always directed along the line joining the two masses. If one mass moves relative to the other, gravity is assumed to adjust instantaneously to that motion.

Our best modern theory of gravity is Einstein's theory of general relativity. In that description, there is no "action at a distance". Changes in gravity are predicted to propagate at the speed of light, with "messages" being carried by gravitational waves. That means that there could be a delay in the changing direction of a gravitational "force" (gravity isn't actually a force in GR) when objects move relative to one another.

When it comes to describing the solar system, we are still free to say that the Sun is "stationary", even if we're using GR. The sun has more than 99% of the total mass of our solar system, so in the GR picture all the planets orbit in a sort of curved spacetime "bowl" caused by the sun's mass. As the planets orbit, the shape of that bowl doesn't change very much, because its shape is mostly determined by the Sun. There are small "dents" in the sides of the bowl due to each of the planets, which move around as the planets orbit the Sun.

If you want to extend this picture to the solar system orbiting the centre of the galaxy, it's just a matter of "zooming" out to see the relatively small "bowl" caused by the solar system as being its own relatively small dent in the side of the much larger "bowl" of the galaxy as a whole.

The finite propagation speed of gravity does have some effects on orbits. None of the planets in our solar system actually orbit the Sun in nicely closed ellipses. In fact, we wouldn't expect them to do that even in the Newtonian picture, because each planet also exerts gravitational forces on every other planet, even though the major influence is the Sun's gravity. However, after accounting for those perturbations, we find that there remains an outstanding effect on the orbital trajectories of the planets, which is fundamentally due to the nature of gravity itself. These effects are accurately predicted by GR.

The upshot of this is that, actually, none of the orbits of planets in our solar system are "stable". However, the timescales over which the orbits become observably "chaotic" are very long - much longer than the 4.5 billion years the planets have been there for, so far.

Last edited: Feb 9, 2023
11. ### James RJust this guy, you know?Staff Member

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The observed shape of the oscillations is essentially a combination of the various orbital frequencies of the planets (dominated by the gas giants, which have the most mass). Looking at a 100 year period of time is probably not going to give you a very accurate picture of even one total "cycle" of the orbits. Uranus, for instance, has an orbital period of 84 years.

12. ### JELRegistered Member

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Ah yes, I think a light dawned on me just now

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Let me see if I got this correctly:

The solar-system, the orbital structure and integrity of it, works because it was formed from mass already moving at near zero relative velocity.

Similar to if somebody throws a snow-ball through the air; the components making up that mass of snow (The combined 'stuff' that makes up the entirety of the ball) is all basically moving at zero relative velocity to 'each other' (Every single snow-flake in the ball moves almost identically through space, compared to all the other snow-flakes of the ball)

And this near-zero relative velocity functionally negates the effect of light-speed between inner-circuits and outer-circuits (Mercury vs Saturn, for example), which is why they can all seem to orbit the same reference-point despite light-distance making it impossible for them to observe the same reference-point at the same time.

So orbital stability is basically a result of the combined mass' originating from near-identical properties (In terms of movement)

(Meaning that it doesn't really matter if the snow-ball is hurled through the air or lying still on the curb. What matters is that the mass, comprising the snowball, is initially 'sharing the almost same relative motion')

The effect of the light-distance between center and outer-most orbit, then only becomes relevant when this 'singularity' (The combined mass comprising the solar-system) gets close enough to some other 'singularity' (When, for example, 2 solar-systems collide, or 2 snow-balls collide) so that their respective gravity affects each other.

This means the order of 'break-up' of the solar-system is different for inner-orbits compared to outer-orbits (If the respective suns of the 2 colliding systems where to hit each other 'head to head', for example)

In that case the earth would get thrown off course 8 minutes after the collision, while Saturn would not get thrown off before 80 minutes after the collision.

Kind of like a pudding or gele effect, where, if you tap it on one side, there is a delayed response before the wobble reaches the other side.

Thanks for your time responding, James R, I think you made it clear for me

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jacob.

13. ### exchemistValued Senior Member

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Partly right. You've realised that there is no absolute motion but that it is all relative, which is good. So your boat and water analogy won't work, as there is no objectively static medium, through which astronomical bodies could be said to move.

But I, at least, am still unclear why you think the speed of light comes into the orbits of planets. The gravitational field of the sun is static relative to the sun. A planet moving in orbit about the sun moves relative to this field at its orbital velocity. The speed of light does not enter into this. There are no" waves of gravity" "transmitting" this field in some way: it's just there - a static field.

If the mass of the sun were abruptly to change, there would be an abrupt change in this field, which would propagate outwards at the speed of light of light and would indeed arrive at various planets with a time delay. But that is not what is happening: the field is constant.

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14. ### DaveC426913Valued Senior Member

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Keep in mind though, that the sun's movement and/or mass can't happen abruptly. It is a continuum.

Neither a collision or an explosion will abruptly change the location and/or amount of mass - it will happen at a relatively slow speed. So, for example, a rogue star colliding with the sun will make its influence felt looooong before it even enters the system and the expanding sphere of mass after a collision will continue to pull on the planets. There's no discontinuity of spacetime curvature there, only gentle smooth changes throughout.

15. ### JELRegistered Member

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The way I read your post there seems to be no contradiction with what I said (Regarding what effectively happens), or maybe I'm missing something?

To try to reiterate:

The boat-in-the-water analogy was just to visualize the ripples moving outward from the center-of-gravity (The ripples symbolizing the gravitational effect moving at the speed-of-light from the center and outwards)

It looks circular (Observed from 'above') as long as the boat is not accelerating, but becomes shifted (The CoG is no longer at the exact center of the circle) if the boat is accelerating.

The sun and its gravitational well are both moving at the same relative velocity, giving you an apparent circle extending from the center (Just as a snow-ball laying still on the ground has the same ball-shape as one flying fast through the air)

It's not until the head-on collision (Here I'm assuming a very large relative speed-change of course, not a small bump between 2 systems that are already moving at almost the same relative velocity) that this 'perfect' circle is disrupted (With the disruptive effect extending at the speed-of-light from the CoG and outward)

Say the solar-system, as a whole, is moving at half the speed-of-light, and then the sun has a frontal collision with an equivalent sun also moving at half the speed-of-light (Except in the opposite direction)

Assuming they cancel each other's velocity out, meaning they stop each other's movement, then Saturn should keep orbiting normally for 80 minutes before its orbit would be disrupted (Meaning that Saturn would actually orbit a non-existent CoG for 80 minutes, because Saturn itself would not observe the disruption of this CoG until after 80 minutes of its true disruption. To Saturn, the CoG continues to exist for 80 minutes, because that's how long it takes for the 'gravity-information' to go from the CoG to Saturn's position)

If we shine a laser out the side-window of a moving car, the laser will draw a straight line extending from the side of the car (It will remain at 90 degrees angle, and thus appear to be 'static'), but the individual information-packets (Or waves) will move both forward and sideways (Forward at the same speed as the car, and sideways at the speed-of-light), meaning that the individual info-packet's trajectory is less than 90 degrees (Since it already has some forward momentum, given to it by the car's forward-moving momentum, at the time of its transmission from the moving car)

Instead of the car and laser you could also think of a flying aircraft dropping a bomb. The bomb doesn't fall straight down at 90 degrees angle, but has forward velocity (Relative to the ground, but near-zero relative to the aircraft)

I read your post as basically agreeing with this, but I'm not a native English-speaker so we may of course use/interpret words differently (Or I may have an incorrect understanding of this 'system' and its behavior of course)

16. ### exchemistValued Senior Member

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Ah so you want to explore what would happen if the sun's gravitational field were suddenly to change? Is that it?

17. ### James RJust this guy, you know?Staff Member

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Approximately, I guess. 99% of the mass of our solar system is in the Sun. The vast majority of the total "spin" (technically, the total angular momentum) of the solar system is also in the Sun. The orbital motions of all the non-solar bodies in the solar system, around the Sun, are all quite "slow", relative to the Sun (and relative to various typical extra-solar astronomical velocities).

That's actually a very good analogy. In this example, the effects of the Earth's gravity are effectively irrelevant while the snowball is in the air, if you happen to be riding on one piece of snow looking at other pieces of snow in the ball, because the force of Earth's gravity on a piece of the snow, although orders of magnitude larger than the gravitational forces between two pieces of snow, acts on all of the separate pieces of snow in the same way.
That's also approximately true, but not because of the speed of light. It is because the gravitational force decreases rapidly with distance.
Not necessarily. If two solar systems were to collide, the specific effects would depend on the precise locations of the various planets in relation to one another at any given time, for example.

We can observe entire galaxies colliding due to a mutual gravitational attraction. It can be shown that in such a collision, involving possibly billions of individual solar systems, it is possible that no two stars will actually collide physically (i.e. actually touch one another). But it is still the case that the two colliding galaxies are profoundly changed by the collision.
Not really. See exchemist's explanation, above. The Sun's gravitational field is essentially static (i.e. unchanging), from the point of view of the Sun. There is no need for a message of any kind to propagate from the Sun to Saturn, say, to keep Saturn in its orbit.
Glad I could help.

18. ### JELRegistered Member

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I am performing a 'mid-journey course-correction', in a manner of speaking

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I find that it's sometimes a good exercise to pause for a moment and re-visit topics one thinks one has under full control (Similar to how you need to work-out to remain fit)

Along the lines of how you can forget things you learned in school, or how such teachings can get skewed/blurry/faded, if you don't think about them for a long time.

Basically I'm just trying to make sure I haven't accidentally fallen into some blinding mis-leading 'rabbit-hole of misconceptions' over time without noticing

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I find, like fashion-changes, such 'deviations-of-understanding' can creep up on you over time with little notice (Since new science-discoveries keep pushing how we perceive things to work in reality, and how it can warp how we think we understand things)

And clearly I had become a bit rusty and had lulled myself into partly forgetting how a solar-system can be a circular disc when information-propagation is limited to the speed-of-light.

And I think this thread has removed some blur that had built up in my mind over time (So thanks to all who replied)

I thought I had it, but then your reply here makes me wonder again.

Are you sure about your own views on this?

In this post it is claimed that gravity (The effects of gravity, so it doesn't have to be thought of as a force) propagates at the speed-of-light:
https://www.physicsforums.com/insights/how-fast-do-changes-in-the-gravitational-field-propagate/

From that, is my understanding at least, should follow that the gravitational effect caused by the sun, whether a radiated force or a bending of 'space-time', should not be observed by Saturn before 80 minutes after it was caused by the sun.

And that, as long as the sun is not accelerating, this gravity-field will appear to (Effectively at least) be a static uniform circle around the sun (As if the sun was stationary)

But you seem to say that is not the case?

I read you as saying the effect of gravity is instantly happening between the sun and Saturn, despite the 2 being separated by 80 light-minutes.

To go back to the music-record analogy; if we place a record, that we assume has a diameter of 1 light-year, flat on a big table, and then drag that record along the table with a pencil stuck into its center-hole, which we assume is the gravitational-center (So the pencil is the sun (The hole in the middle of the record) and the record's outer circular edge is Saturn's orbit (This is where we usually thread the pickup when beginning to play a record), would the outer edges of the record not lay still for ½ a year before moving? (Since the distance between center and outer-ring is ½ a light-year)

If you say the outer-ring (The edge of the record) can begin its movement at the same time (Basically keeping the circular shape of the record completely intact without warping it) as the sun in the center begins movement (Movement here being the acceleration that might happen from a frontal collision with an object equivalent to the sun in mass, if we perhaps picture the 2 suns like in-destructible billiard-balls that would transfer kinetic energy cleanly), then it must follow that the outer-ring 'knows' that the center (Which is ½ a light-year away) is moving before ½ a year has passed?

A human observer on Saturn would not see the lights from the collision before 80 minutes after it took place, so are you saying they would feel the change in gravity 80 minutes before seeing the collision?

Would that not imply some 'information' in the universe can be faster than the speed-of-light? (The curvature of space also being a type of 'information')

Last edited: Feb 9, 2023
19. ### DaveC426913Valued Senior Member

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What does this analogy have to do with gravity of the solar system? The SS was not "stopped" at some point and did not have a delay before starting moving. It's a terrible analogy.

The Sun's gravity is a funnel in curved spacetime. It has been that way since the SS was just a cloud of dust and gas (which, itself, had a funnel-shaped curvature in space time, albeit diffuse).

A rogue dwarf star - with its own small funnel - falls into the system. As it approaches the sun, the orbits of the planets (and the sun itself) are perturbed. The star's funnel moves slowly because the star is moving slowly, and eventually it merges with the Sun.

It's not really about how fast any changes in the star's funnel propagate; its really about how fast the movement of the mas and its funnel is.

20. ### JELRegistered Member

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I am picturing the 'gravity-funnel' in 2 dimensions = a flat disc.

So you say a mass-created funnel (The sun) has instant effect on a neighboring mass (Saturn) faster than light can travel between these 2 masses?

21. ### exchemistValued Senior Member

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It is really important that you keep crystal clear whether you are talking about changes in gravity or just a gravitational field. Both James and I are saying that changes would propagate at c, but the field itself from the sun is static. If you had another massive body moving in towards the sun then yes the resulting change in gravitational field would in principle propagate outwards at c.

22. ### DaveC426913Valued Senior Member

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Nothing is travelling.
The sun's spacetime curvature is already there.
You are only talking about changes in the curvature.
And yes, those changes propagate at the speed of light.

23. ### JELRegistered Member

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+

I can't say I understand what it would mean to say the field is static, if changes through-out it are not (That seems a contradiction to me)

I also can't say I understand how anything created by mass could be static (Understanding 'static' as something that is acting infinitely fast on whatever it acts upon)

But I can of course accept that that may simply be because I fail to understand these concepts properly (And if it's a problem with my understanding I obviously wouldn't know how to correct that)

I can understand the concept of a system being perceived as static (Say, 2 cars moving at the same speed side-by-side on the freeway, or a tractor-truck hauling a trailer, which would make them appear to stand still relative to each other), but only as a concept, not as something physically real that is truly static.

Maybe it's just a matter of semantics (As mentioned; I'm not a native English-speaker, so maybe something gets lost in translation)

At any rate, if we agree that Saturn will not be affected instantly by acceleration-changes performed by the sun (If the sun could somehow do a U-turn in a few minutes and reverse its direction around the galaxy, for example), but that it will take 80 minutes for such a change in acceleration by the sun to manifest as a change in the gravity Saturn observes, then that's close enough I think.

Thank you (If physics were easy for humans to grasp, it probably wouldn't have taken all the generations before Einstein, Bohr, Newton, and many others, to reach the current level of understanding)