Oumuamua - mathematical question

[DeckerdSmeckerd]

I am thinking most people here are familiar with this event. I think about it sometimes and I have wondered about alternate theories. Is it possible that Oumuamua was not necessarily accelerating away from us under it's own power but the Solar System is accelerating along its flight path due to some other force or early event?

I don't offer any explanation as to why the solar system is accelerating in this scenario. I just wonder if it is mathematically possible. 

If the solar is system were accelerating at some rate, could the behavior of Oumuamua be explained?

[swansont]

While velocity is relative, acceleration is not. You can tell if you are accelerating.

[DeckerdSmeckerd]

13 minutes ago, swansont said:

While velocity is relative, acceleration is not. You can tell if you are accelerating.

Thanks Swansont. Suppose I take two objects, the Sun and Oumuamua. If I stand on the Sun, it appears Oumuamua accelerates as it departs. If I stand on Oumuamua, it appears the Sun accelerates as it departs. 

[swansont]

11 minutes ago, DeckerdSmeckerd said:

Thanks Swansont. Suppose I take two objects, the Sun and Oumuamua. If I stand on the Sun, it appears Oumuamua accelerates as it departs. If I stand on Oumuamua, it appears the Sun accelerates as it departs. 

But you can do a measurement to see if you’re the one accelerating.

If I toss a ball to you and we’re on a platform with perpendicular acceleration, the ball will deflect in the opposite direction. (This principle is used in some inertial sensor designs.)

[DeckerdSmeckerd]

9 minutes ago, swansont said:

But you can do a measurement to see if you’re the one accelerating.

If I toss a ball to you and we’re on a platform with perpendicular acceleration, the ball will deflect in the opposite direction. (This principle is used in some inertial sensor designs.)

Can you recall what that measurement is called? I have only an ordinary grasp of physics but I would like to read about it. If not, I can try google.

[swansont]

17 minutes ago, DeckerdSmeckerd said:

Can you recall what that measurement is called? I have only an ordinary grasp of physics but I would like to read about it. If not, I can try google.

This is an accelerometer using a proof mass. I’m familiar more with attempts using atoms as a proof mass,  

http://ridl.cfd.rit.edu/products/pfq2 speaker videos/slides/PfQ2 July 2020 Choy.pdf

Start with slide 6

 

[DeckerdSmeckerd]

46 minutes ago, swansont said:

This is an accelerometer using a proof mass. I’m familiar more with attempts using atoms as a proof mass,  

http://ridl.cfd.rit.edu/products/pfq2 speaker videos/slides/PfQ2 July 2020 Choy.pdf

Start with slide 6

 

Thank you for that. I looked at it and I get the main idea. Mostly over my head. As a side thought, if I generate an electro-magnetic wave that travels at a certain speed and I put some antennas far enough, but at an equal distance away, to the east, west, south, north, etc. When I generate a single pulse, a single wave, they should all arrive at the antennas at the same time, if the generating device and antennas are all traveling on the same vehicle (planet, spaceship, etc). However, doing this on a vehicle that is accelerating, would that cause a discrepancy in the arrival time of the wave at some antennas? (assuming no other factors can affect the speed of the wave). 

 

edit: You don't really have to answer that.

Edited November 14, 2021 by DeckerdSmeckerd

[DeckerdSmeckerd]

I guess what I am getting at in this post is this. How can you have an expected flight path of an interstellar object? Unless you assume our solar system is stationary. If you assume our solar system is not stationary, then you wouldn't be able to predict the path of an interstellar object.

Is this logic not sound?

For example: I am not implying that this is what is actually happening, but if the solar system were swinging back and forth as if it were on a pendulum, and it was traveling the length of the arc each year, so that every 2 years the solar system would be back in the same location, if 2 objects were on the exact same flight path through the galaxy, except that they were a year apart, and they passed through the solar system when the solar system was at the midpoint of its flight path, then wouldn't the objects appear to pass through the solar system differently, with difference being more or less pronounced depending on the speed of the solar system's flight? (For the sake of argument, pretend the solar system is in an identical state and behaving identically when the objects pass through).

Edited November 15, 2021 by DeckerdSmeckerd
Added a question and example

[swansont]

You can get a pretty good solution with just Newton's laws of motion and Newtonian gravity, as long as there were just the two bodies. Which is a reasonable approximation absent any close fly-by of a substantial body. The sun can be treated as if it were at rest; any deviation from an inertial frame can be ignored.

 

People can predict comets pretty well

 

[DeckerdSmeckerd]

29 minutes ago, swansont said:

You can get a pretty good solution with just Newton's laws of motion and Newtonian gravity, as long as there were just the two bodies. Which is a reasonable approximation absent any close fly-by of a substantial body. The sun can be treated as if it were at rest; any deviation from an inertial frame can be ignored.

 

People can predict comets pretty well

 

I don't personally have the math skills at hand, but if the flight path of Oumuamua can be projected around the Sun using Newton's laws of motion and Newtonian gravity, and what I want to do is calculate what changes are needed in the location of the Sun, to produce the flight path of Oumuamua, then I need a formula that has the location of both Sun and Oumuamua as variables.

[beecee]

https://phys.org/news/2021-11-aliens-oumuamua-wasnt-nitrogen-iceberg.html

Not saying it was aliens, but 'Oumuamua probably wasn't a nitrogen iceberg:

On October 19, 2017, astronomers made the first-ever detection of an interstellar object (ISO) passing through our solar system. Designated 1I/2017 U1 ′Oumuamua, this object confounded astronomers who could not determine if it was an interstellar comet or an asteroid. After four years and many theories (including the controversial "ET solar sail" hypothesis), the astronomical community appeared to land on an explanation that satisfied all the observations.

The "nitrogen iceberg" theory stated that "Oumuamua was likely debris from a Pluto-like planet in another stellar system. In their latest study, titled "The Mass Budget Necessary to Explain "Oumuamua as a Nitrogen Iceberg," Amir Siraj and Prof. Avi Loeb (who proposed the ET solar sail hypothesis) offered an official counter-argument to this theory. According to their new paper, there is an extreme shortage of exo-Plutos in the galaxy to explain the detection of a nitrogen iceberg.

In the paper where he broached the possibility, Loeb indicated that "Oumuamua's unusual character and behavior were consistent with a solar sail. This included the highly-reflective nature of the object and its profile, which appeared to be either cigar-shaped or pancake-like. More importantly, its sudden acceleration and deviation from its expected orbit appeared to be the result of radiation pressure, which is precisely how solar sails achieve propulsion.

There was also the way it entered our solar system, which allowed it to make a flyby of Earth after passing closest to our sun (perihelion). In other words, its orbital dynamics allowed it to get a close look at the only habitable planet in our solar system, which is precisely what one might expect of an interstellar probe. These arguments were detailed further in Loeb's book, "Extraterrestrial: The First Sign of Intelligent Life Beyond Earth."

At the time of the book's writing, all attempts to explain "Oumuamua in terms of natural phenomena fell short. Basically, there was no single explanation that could account for its brightness, profile and acceleration while acknowledging that there was no evidence of outgassing. In addition, the sudden acceleration could not be attributed to gravitational forces since these should have been slowing "Oumuamua down at the time.

 

more at link.......................

 

the paper:

https://arxiv.org/pdf/2103.14032.pdf

The Mass Budget Necessary to Explain ‘Oumuamua as a Nitrogen Iceberg:

ABSTRACT:

Recently, a nitrogen iceberg was proposed as a possible origin for the first interstellar object, 1I/2017 U1, also known as ‘Oumuamua. Here, we show that the mass budget in exo-Pluto planets necessary to explain the detection of ‘Oumuamua as a nitrogen iceberg chipped off from a planetary surface requires a mass of heavy elements exceeding the total quantity locked in stars with 95% confidence, making the scenario untenable because only a small fraction of the mass in stars ends in exo-Plutos

[DeckerdSmeckerd]

6 hours ago, swansont said:

The sun can be treated as if it were at rest; any deviation from an inertial frame can be ignored.

This is true for any object that has the same inertial frame as the sun. If Oumuamua has a different inertial frame then the difference between them has to be a part of the mathematics to determine its route through the solar system, or for a object that will be captured by the solar system, it is a factor until the inertial frames are equalized. Do you agree?

 

edit: They must have thought about all of this already since this stuff seems like common knowledge in the field of physics. Of course they would have thought about whether the sun was accelerating! Inertial frames are on the Wikipedia and are well understood! 

Edited November 16, 2021 by DeckerdSmeckerd

[DeckerdSmeckerd]

10 hours ago, beecee said:

https://phys.org/news/2021-11-aliens-oumuamua-wasnt-nitrogen-iceberg.html

Not saying it was aliens, but 'Oumuamua probably wasn't a nitrogen iceberg:

On October 19, 2017, astronomers made the first-ever detection of an interstellar object (ISO) passing through our solar system. Designated 1I/2017 U1 ′Oumuamua, this object confounded astronomers who could not determine if it was an interstellar comet or an asteroid. After four years and many theories (including the controversial "ET solar sail" hypothesis), the astronomical community appeared to land on an explanation that satisfied all the observations.

The "nitrogen iceberg" theory stated that "Oumuamua was likely debris from a Pluto-like planet in another stellar system. In their latest study, titled "The Mass Budget Necessary to Explain "Oumuamua as a Nitrogen Iceberg," Amir Siraj and Prof. Avi Loeb (who proposed the ET solar sail hypothesis) offered an official counter-argument to this theory. According to their new paper, there is an extreme shortage of exo-Plutos in the galaxy to explain the detection of a nitrogen iceberg.

In the paper where he broached the possibility, Loeb indicated that "Oumuamua's unusual character and behavior were consistent with a solar sail. This included the highly-reflective nature of the object and its profile, which appeared to be either cigar-shaped or pancake-like. More importantly, its sudden acceleration and deviation from its expected orbit appeared to be the result of radiation pressure, which is precisely how solar sails achieve propulsion.

There was also the way it entered our solar system, which allowed it to make a flyby of Earth after passing closest to our sun (perihelion). In other words, its orbital dynamics allowed it to get a close look at the only habitable planet in our solar system, which is precisely what one might expect of an interstellar probe. These arguments were detailed further in Loeb's book, "Extraterrestrial: The First Sign of Intelligent Life Beyond Earth."

At the time of the book's writing, all attempts to explain "Oumuamua in terms of natural phenomena fell short. Basically, there was no single explanation that could account for its brightness, profile and acceleration while acknowledging that there was no evidence of outgassing. In addition, the sudden acceleration could not be attributed to gravitational forces since these should have been slowing "Oumuamua down at the time.

 

more at link.......................

 

the paper:

https://arxiv.org/pdf/2103.14032.pdf

The Mass Budget Necessary to Explain ‘Oumuamua as a Nitrogen Iceberg:

ABSTRACT:

Recently, a nitrogen iceberg was proposed as a possible origin for the first interstellar object, 1I/2017 U1, also known as ‘Oumuamua. Here, we show that the mass budget in exo-Pluto planets necessary to explain the detection of ‘Oumuamua as a nitrogen iceberg chipped off from a planetary surface requires a mass of heavy elements exceeding the total quantity locked in stars with 95% confidence, making the scenario untenable because only a small fraction of the mass in stars ends in exo-Plutos

Thanks for the information Beecee.

Well, if there was/is a difference in the inertia frames between Oumuamua and our Sun, perhaps it will inexplicably do one or more of the following, slow down, turn, and then come back. If it does all of those, well, everyone will think it's aliens. If there was/is a difference in inertia frames then it wasn't traveling that fast, relative to the Sun's rate of travel because of its mass alone. Then perhaps it is lighter than expected which means,maybe, it still won't travel as predicted.

 

[swansont]

15 hours ago, DeckerdSmeckerd said:

I don't personally have the math skills at hand, but if the flight path of Oumuamua can be projected around the Sun using Newton's laws of motion and Newtonian gravity, and what I want to do is calculate what changes are needed in the location of the Sun, to produce the flight path of Oumuamua, then I need a formula that has the location of both Sun and Oumuamua as variables.

You assume the sun it at rest and find the motion relative to the sun. 

5 hours ago, DeckerdSmeckerd said:

Well, if there was/is a difference in the inertia frames between Oumuamua and our Sun

They are in different frames, because there is relative motion. But if the motion is inertial, you can treat either as if it were at rest, and all of the physics will be the same. If one is accelerating, you'll see evidence of non-inertial motion (which we already have; Oumuamua felt an acceleration from the sun, regardless of any self-propulsion) The sun, being much more massive, would only have a tiny acceleration, which can safely be ignored, since we won't have the precision in the data to discern it.

If you do the analysis in the sun's frame of reference, it simplifies everything.

[DeckerdSmeckerd]

10 hours ago, DeckerdSmeckerd said:

This is true for any object that has the same inertial frame as the sun. If Oumuamua has a different inertial frame then the difference between them has to be a part of the mathematics to determine its route through the solar system, or for a object that will be captured by the solar system, it is a factor until the inertial frames are equalized. Do you agree?

Scratch that. I used the wrong term to describe my thought. Instead:

This is true for any object that has the same non-inertial frame as the sun. If Oumuamua has a different non-inertial frame then the difference between them (their acceleration) has to be a part of the mathematics to determine its route through the solar system, or for a object that will be captured by the solar system, it is a factor until the non-inertial frames are equalized.

 

I look at this event with Oumuamua with an ordinary eye, untrained in physics or mathematics. That doesn't mean I don't have a sense of physics that is based on what I have learned. I think the corrected paragraph describes what my sense tells me. 

5 hours ago, DeckerdSmeckerd said:

Thanks for the information Beecee.

Well, if there was/is a difference in the inertia frames between Oumuamua and our Sun, perhaps it will inexplicably do one or more of the following, slow down, turn, and then come back. If it does all of those, well, everyone will think it's aliens. If there was/is a difference in inertia frames then it wasn't traveling that fast, relative to the Sun's rate of travel because of its mass alone. Then perhaps it is lighter than expected which means,maybe, it still won't travel as predicted.

 

Likewise, I must correct this too.

Well, if there was/is a difference in the non-inertia frames between Oumuamua and our Sun, perhaps it will inexplicably do one or more of the following, slow down, turn, and then come back. If it does all of those, well, everyone will think it's aliens. If there was/is a difference in non-inertia frames then it wasn't traveling that fast, relative to the Sun's rate of travel because of its mass alone. Then perhaps it is lighter than expected which means, maybe, it still won't travel as predicted.

The dangers of trying to talk with people that are knowledgeable about physics with only the Wikipedia. I think the correction describes my thought better.

Thank you both for helping give some shape to my impression about Oumuamua. Maybe, for reasons I don't understand, it doesn't make any sense to a trained physicist that the Sun would be a accelerating, or maybe this idea has been eliminated for other reasons, or perhaps they just have tunnel vision and as an ordinary person, maybe I can't see that tunnel. I really don't know. Talking about this kind of thing, with such incomplete knowledge, it isn't apparent to me if I make any provable sense at all or that I am actually stating gibberish while using physics terms.

Edited November 16, 2021 by DeckerdSmeckerd

[swansont]

1 hour ago, DeckerdSmeckerd said:

Well, if there was/is a difference in the non-inertia frames between Oumuamua and our Sun, perhaps it will inexplicably do one or more of the following, slow down, turn, and then come back. If it does all of those, well, everyone will think it's aliens. If there was/is a difference in non-inertia frames then it wasn't traveling that fast, relative to the Sun's rate of travel because of its mass alone. Then perhaps it is lighter than expected which means, maybe, it still won't travel as predicted.

Mass typically drops out of these calculations, at least when you analyze the simplest systems. It will come into play because you can't treat it as a point object, but that might or might not be a large factor. As I recall, the object had rotational motion, and if that changed, you'd need to account for the energy and momentum. But as far these factors can be ignored, the mass won't matter. A baseball or an asteroid would have the same motion.

 

1 hour ago, DeckerdSmeckerd said:

The dangers of trying to talk with people that are knowledgeable about physics with only the Wikipedia. I think the correction describes my thought better.

Thank you both for helping give some shape to my impression about Oumuamua. Maybe, for reasons I don't understand, it doesn't make any sense to a trained physicist that the Sun would be a accelerating, or maybe this idea has been eliminated for other reasons, or perhaps they just have tunnel vision and as an ordinary person, maybe I can't see that tunnel. I really don't know. Talking about this kind of thing, with such incomplete knowledge, it isn't apparent to me if I make any provable sense at all or that I am actually stating gibberish while using physics terms.

If the sun were accelerating in some strange way we'd be accelerating along with it. Our motion about the sun and around our axis is analyzed with significant scrutiny. Such an acceleration would be noticed if it were large enough to matter.

[DeckerdSmeckerd]

36 minutes ago, swansont said:

Mass typically drops out of these calculations, at least when you analyze the simplest systems. It will come into play because you can't treat it as a point object, but that might or might not be a large factor. As I recall, the object had rotational motion, and if that changed, you'd need to account for the energy and momentum. But as far these factors can be ignored, the mass won't matter. A baseball or an asteroid would have the same motion.

Is the reason two objects of different mass fall at the same rate because they have no momentum?

 

However, doesn't a more massive object conserve its momentum longer when moving away from a gravity well?

[swansont]

19 minutes ago, DeckerdSmeckerd said:

Is the reason two objects of different mass fall at the same rate because they have no momentum?

They have momentum, individually. The system does not, because the earth moves imperceptibly toward the dropped mass, with the imparted velocity being inversely proportional to the mass. 

IOW, the dropped object of mass m acquires a speed v, so it has a momentum mv (downward). The earth has this same momentum upward, which is also MV (M being the mass of the earth and V being its velocity) 

mv = MV so the earth would have a velocity of V = mv/M in the upward direction

But the object's mass, be it 1 kg or 100 kg or 1000 kg, is so small compared to the earths mass of about 6 x 10^24 kg that there is no way to measure V. For all practical considerations, the earth remains at rest. 

(a similar argument applies to the sun, whose mass is about 2 x 10^30 kg, and any small object interacting with it)

 

19 minutes ago, DeckerdSmeckerd said:

However, doesn't a more massive object conserve its momentum longer when moving away from a gravity well?

When you move out of a gravity well you would slow down, because of gravity, absent any independent propulsion. 

For an individual object, momentum is conserved when there is no net force acting on it, so it would not apply to such an object subject to gravity.

[DeckerdSmeckerd]

37 minutes ago, swansont said:

For an individual object, momentum is conserved when there is no net force acting on it, so it would not apply to such an object subject to gravity.

I see. Then it might make more sense to say:

Two objects gain momentum from a gravity well at the same rate. Mass doesn't make a difference. 

When two objects leave a gravity well, they lose momentum at the same rate but an object with greater mass has greater momentum. 

Are either of these statements factual? 

Edit: assuming they leave at the same speed on the same flight path.

Edited November 16, 2021 by DeckerdSmeckerd
Phrasing and added condition

[swansont]

46 minutes ago, DeckerdSmeckerd said:

I see. Then it might make more sense to say:

Two objects gain momentum from a gravity well at the same rate. Mass doesn't make a difference. 

No. Momentum is mass*velocity

They accelerate at the same rate, so they gain velocity at the same rate. The one with more mass will have more momentum

 

46 minutes ago, DeckerdSmeckerd said:

When two objects leave a gravity well, they lose momentum at the same rate but an object with greater mass has greater momentum. 

Are either of these statements factual? 

Edit: assuming they leave at the same speed on the same flight path.

The one with greater mass has more momentum, yes, but it loses more momentum 

[DeckerdSmeckerd]

2 hours ago, swansont said:

No. Momentum is mass*velocity

They accelerate at the same rate, so they gain velocity at the same rate. The one with more mass will have more momentum

 

The one with greater mass has more momentum, yes, but it loses more momentum 

Would you say that a spaceship flying toward a planet doesn't need to know it's mass to achieve orbit?

 

Would say a spaceship that wants to slingshot around a planet doesn't need to know it's mass to slingshot into a particular direction?

 

I appreciate your attention to my thread. You are helping me a lot. 

Edited November 16, 2021 by DeckerdSmeckerd

[swansont]

3 minutes ago, DeckerdSmeckerd said:

Would you say that a spaceship flying toward a planet doesn't need to know it's mass to achieve orbit?

 

Would say a spaceship that wants to slingshot around a planet doesn't need to know it's mass to slingshot into a particular direction?

 

I appreciate your attention to my thread. You are helping me a lot. 

You can look at the Hohmann transfer equations

https://en.wikipedia.org/wiki/Hohmann_transfer_orbit

and see that they only depend on the mass of the planetary body, as long as the mass of the craft is small in comparison.

 

One reason you might need to know the mass of a craft is if it is going to be providing thrust, but as long as the motion is passive, the mass drops out of the equations.

 

[DeckerdSmeckerd]

Also, if a spaceship was in orbit around a planet, let's say Saturn, would the spaceship have to make corrections after orbit was achieved if the planet was falling toward the the sun along it's orbit and picking up speed?

3 minutes ago, swansont said:

You can look at the Hohmann transfer equations

https://en.wikipedia.org/wiki/Hohmann_transfer_orbit

and see that they only depend on the mass of the planetary body, as long as the mass of the craft is small in comparison.

 

One reason you might need to know the mass of a craft is if it is going to be providing thrust, but as long as the motion is passive, the mass drops out of the equations.

 

Thanks. I will look. I don't want to turn this thread into a full time job for you. 😄