The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: 9 out of 10 doctors agree on April 23, 2019, 08:53:43 PM

This is altogether a terrible article. Here's a breakdown of everything it gets wrong:
which has its roots in the unsuccessful attempts to simulate a heliocentric SunEarthMoon system.
The model isn't wrong—in fact, it actually simulates the Sun/Earth/Moon system quite well.
Due to the nature of Newtonian Gravity, a three body system inherently prefers to be a two body orbit and will attempt to kick out the smallest body from the system—often causing the system to be destroyed altogether.
The keyword there is attempt—it's not guaranteed to break the system. The Earth and Moon have far more binding energy than can be supplied by tidal forces from the Sun.
There are a limited range of scenarios in which three body orbits may exist. It is seen that those configurations require at least two of the three bodies to be of the same mass, can only exist with specific magnitudes in specific and sensitive configurations, … The slightest imperfection, such as with bodies of different masses, or the effect of a gravitational influence external to the system, causes a chain reaction of random chaos which compels the entire system to fall apart
The differential equation has unstable equilibria. Shocker.
"Describing the motion of any planetary system (including purely imaginary ones that exist only on paper) is the subject of a branch of mathematics called celestial mechanics. Its problems are extremely difficult and have eluded the greatest mathematicians in history." — Paul Trow, Chaos and the Solar System (Archive)
Eluded the mathematicians, but not the physicists.
Now add a third body, and everything falls apart. The problem goes from one that a smart undergraduate can tackle to one that has defied solution for 400 years.
An unsolvable differential equation can still describe reality. Is there a point to the quote?
Sections 23
The important thing to remember is that, for a long time—maybe a billion or two years—the solar system was unstable. If a body had a close encounter with a much larger mass, it had 3 possible outcomes: colliding with the larger mass, deflection into a more eccentric orbit, and acceleration into a larger orbit. Eventually most bodies either hit a planet, get too much eccentricity and falls into the Sun, or get ejected into the Kuiper Belt, resulting in the modern set of planets in orbits too far apart for any close encounters.
Also, minor gravitational interactions between planets are observed as slight orbital changes over decades or centuries. Even if a planet had enough energy to eject an adjacent planet (I haven't done the math yet but I doubt it), it would take hundreds of millions of years or more for perturbations to lead to encounters.
The problem with the 3body problem is that it can’t be done, except in a very small set of frankly goofy scenarios (like identical planets following identical orbits).
Again conflating unsolvable equations with bad models.
This is precisely the issue of modeling the Heliocentric System, and why its fundamental system cannot exist.
This issue relies on the assumption that there are no setups that can last long periods of time without being the equalmass solution that I've already dismissed as irrelevant.
Programming students participated in the New Mexico Supercomputing Challenge to simulate the solar system and found issues with creating basic orbits:
Simulation of Planetary Bodies in the Universe (NBody) (Archive) (Source Code)
I recognize that algorithm, having used it myself. One thing I can say is: this algorithm leaves out a key invariant, and that can cause instability in close encounters between objects, or even just over time.
It has often been claimed that this simulation provides evidence that the SunEarthMoon System and the Solar System are able to be simulated with Newtonian Gravity.
Universe Sandbox doesn't use Newtonian gravity. It uses general relativity.
Kidding. While it isn't technically using the Newtonian model, it's close enough at the scale of the solar system that it might as well be. Anyway, the quoted passage goes into how the simulation uses a set of 2body problems between bodies and their main attractors. The bolded phrases seem to be cherrypicked to indicate that the simulation uses this alternative model because using the normal model would reveal the inherent instability of an incorrect system. This is entirely wrong, it's a problem of time complexity.
In conclusion:
Every part of this article is either wrong or irrelevant, and it should be deleted.

No one has solved the three body problems of astronomy.
"It actually simulates the SunEarthMoon system quite well" is not evidence, or an argument. Your opinion is not an argument.
The Three Body Problem remains unsolved. See: https://wiki.tfes.org/Three_Body_Problem

No one has solved the three body problems of astronomy.
"It actually simulates the SunEarthMoon system quite well" is not evidence, or an argument. Your opinion is not an argument.
The Three Body Problem remains unsolved. See: https://wiki.tfes.org/Three_Body_Problem
Tell me, what do you think "solve" means in this context? Hint: it has nothing to do with testing the equations against reality.

Now add a third body, and everything falls apart. The problem goes from one that a smart undergraduate can tackle to one that has defied solution for 400 years.
An unsolvable differential equation can still describe reality. Is there a point to the quote?
"An unsolvable differential equation can still describe reality"
An interesting string of sentences, but I don't really see anything to discuss on the matter. Is there an argument somewhere? If you want to know what the three body problem is and its goals then I would suggest you do some research on the matter.

Now add a third body, and everything falls apart. The problem goes from one that a smart undergraduate can tackle to one that has defied solution for 400 years.
An unsolvable differential equation can still describe reality. Is there a point to the quote?
"An unsolvable differential equation can still describe reality"
An interesting string of sentences, but I don't really see anything to discuss on the matter. Is there an argument somewhere? If you want to know what the three body problem is and its goals then I would suggest you do some research on the matter.
Well, the argument seemed to be that since nobody has solved it, it can't be a working model. Which is wrong.

If no one has solved it, it means that they don't have a working model.

If no one has solved it, it means that they don't have a working model.
You're quite obviously conflating terms.
This is an example of a model (actually, most are second order, but this one is first order):
(http://mathurl.com/render.cgi?f%27%28x%29%3Df%28x%29%5C)
To solve this model means to find the set of functions that comprise solutions for any initial conditions, like so:
(http://mathurl.com/render.cgi?%5Cint%5Cfrac%7Bf%27%28x%29%7D%7Bf%28x%29%7Ddx%3D%5Cint%20dx%5C%5C%0A%5Cln%28f%28x%29%29%3Dx+C%5C%5C%0Af%28x%29%3Dke%5Ex%5C)
A working model means that the differential equation matches observations.

If the three body problem is unsolved then there is no working model. The idea that it "might" be solvable doesn't mean that there is a working model. There likely are no good solutions, since they have been searching for a way to simulate it for 400 years. The few available solutions and scenarios are extremely sensitive look nothing like heliocentric astronomy.

If the three body problem is unsolved then there is no working model. The idea that it "might" be solvable doesn't mean that there is a working model. There likely are no good solutions, since they have been searching for a way to simulate it for 400 years. The few available solutions and scenarios are extremely sensitive look nothing like heliocentric astronomy.
We haven't been searching for a simulation method for 4 centuries, we knew how to the whole time. (https://en.wikipedia.org/wiki/Euler_method)

The "Euler method" is shown in the article:
https://wiki.tfes.org/Three_Body_Problem#Poliastro
Poliastro, an astrodynamics software developer, shares several numerical methods for the restricted three body problem:
https://twitter.com/poliastro_py/status/993418078036873216?lang=en (Archive)
“ Look at this beautiful plot of several numerical methods for the restricted three body problem taken from Harier et al. "Solving Ordinary Differential Equations I". The use of high order RungeKutta methods is pervasive in Celestial Mechanics. Happy Monday! ”
(https://wiki.tfes.org/images/thumb/0/08/Three_Body_Problem.jpg/924pxThree_Body_Problem.jpg)

The "Euler method" is shown in the article:
Then why were you claiming that we didn't know how to simulate it?
Also, the simulation in the image doesn't use the orbit that the Moon has.

The "Euler method" is shown in the article:
Then why were you claiming that we didn't know how to simulate it?
I don't see a simulation of the heliocentric sunearthmoon system. Do you?
The restricted three body problem also assumes that one of the bodies, the moon in this case, is massless. That's the best they can do.
Also, the simulation in the image doesn't use the orbit that the Moon has.
Do you think that they were trying to simulate an incorrect model of the moon's orbit?

If the three body problem is unsolved then there is no working model. The idea that it "might" be solvable doesn't mean that there is a working model.
Tom, would you care to elaborate as to what you mean by "working model"?

The "Euler method" is shown in the article:
Then why were you claiming that we didn't know how to simulate it?
I don't see a simulation of the heliocentric sunearthmoon system. Do you?
Universe Sandbox is mentioned in the article.
The restricted three body problem also assumes that one of the bodies, the moon in this case, is massless. That's the best they can do.
Is that restriction necessary for an approximation though?
Also, the simulation in the image doesn't use the orbit that the Moon has.
Do you think that they were trying to simulate an incorrect model of the moon's orbit?
Funny thing, I looked up the orbit listed on the image, and it turns out it's not even an orbit for the Moon at all.

If the three body problem is unsolved then there is no working model. The idea that it "might" be solvable doesn't mean that there is a working model. There likely are no good solutions, since they have been searching for a way to simulate it for 400 years. The few available solutions and scenarios are extremely sensitive look nothing like heliocentric astronomy.
Hi Tom,
I’ve found for you some resources that detail central force problems and how we solve them to explain dynamics in the solar system.
https://courses.physics.ucsd.edu/2010/Fall/physics110a/LECTURES/CH09.pdf
I will track down a few more for your purview just to present a range of options for study.
Let me know if I might be of assistance in understanding them.

A few more resource for varied audiences:
1. Reduction of differential equations and modeling using simulations:
https://www.google.com/amp/s/www.wired.com/2016/06/waysolvethreebodyproblem/amp
2. A more detailed analysis:
https://arxiv.org/pdf/physics/0410149.pdf
3. Numerical estimates of 3 body problem before computers:
http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys7221/ThreeBodyProblem.pdf
4. A rigorous and lengthy analysis which details the solutions of 3 body problems without any constraints on the masses, thereby demonstrating that “it can only be done if two masses are equal” is a false statement. These general solutions are powerful, and using initial conditions, can describe the sunearthMoon system easily.
https://arxiv.org/pdf/1508.02312.pdf
5. A older numerical solution to the three body problem which does not constrain the masses or shapes of the orbits:
http://adsbit.harvard.edu//full/1967AJ.....72..876S/0000876.000.html
6. An example which demonstrates that we give our students this problem to solve as homework:
https://physics.stackexchange.com/questions/185555/solvingthethreebodyproblemnumerically
7. A science article which details the variety of solutions found for the threebody problem. Not only have they found the rather trivial case of the earthmoonsun system, but can also describe rather exotic and complicated orbits, demonstrating the sophistication of our knowledge in this area:
https://www.sciencemag.org/news/2013/03/physicistsdiscoverwhopping13newsolutionsthreebodyproblem
8. The earthmoonsun calculations in particular:
http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node100.html
9. Finally, a 300 page manuscript which covers in brutal detail the different solutions to the three body problem:
http://www.cds.caltech.edu/~marsden/volume/missiondesign/KoLoMaRo_DMissionBook_20110425.pdf
This all took me 15 minutes to find.

4. A rigorous and lengthy analysis which details the solutions of 3 body problems without any constraints on the masses, thereby demonstrating that “it can only be done if two masses are equal” is a false statement. These general solutions are powerful, and using initial conditions, can describe the sunearthMoon system easily.
https://arxiv.org/pdf/1508.02312.pdf
Stop lying QED. It says in the first sentence:
" Abstract. The threebody problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. "
This all took me 15 minutes to find.
If you have any input then we expect you to quote your sources directly rather than spamming articles that show you to be wrong. I would suggest reading the articles before posting them. 15 minutes to collect those links? That is just spam. We want quality posts.
The rest of those articles talk about two body approximations as a "solution" to the three body problem. No one found a "rather trivial" three body problem solution for the SunEarthMoon system. I would suggest you read your sources, since you admit that you do not. All sources will tell you that it is not really solvable or stable except with some very special and absurd scenarios.

The three body problem shouldn't even be on the FE wiki. Three body problem has absolutely nothing to do with proving flat earth or disproving a spheroid earth. Humans lack of ability to simulate the solar system with perfect accuracy doesn't mean the solar system doesn't exist, nor does it mean the earth is flat. The fact is there needs to be a better model, one that works better than what we understand now, to prove spheroid earth wrong.
Tom, you should be trying to work out a flat earth model that's better rather than silly attempts at poking holes in our understanding of the solar system. It's a childish endeavour. You're bringing strawman problems to another table rather than working solutions to your own and it's not a productive way to prove the earth is flat. If anything, by trying to find issues with current models and understandings it seems you're simply trying to buy time with strawmen to avoid coming to the inevitable truth that you could be wrong about the shape of the earth.
So by all means start working on a functional model before anything else. Separate yourself from trying to disprove spheroid earth and come up with actual, functional solutions to the flat earth. Currently you really have none. All I see is a bunch of 'what ifs' that don't work together to form a working model of the flat earth. Why is that? Maybe start with working out the three body problem for a flat earth? I look forward to your solution to the flat earth three body problem, Tom. Good luck!

4. A rigorous and lengthy analysis which details the solutions of 3 body problems without any constraints on the masses, thereby demonstrating that “it can only be done if two masses are equal” is a false statement. These general solutions are powerful, and using initial conditions, can describe the sunearthMoon system easily.
https://arxiv.org/pdf/1508.02312.pdf
Stop lying QED. It says in the first sentence:
" Abstract. The threebody problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. "
This all took me 15 minutes to find.
If you have any input then we expect you to quote your sources directly rather than spamming articles that show you to be wrong. I would suggest reading the articles before posting them. 15 minutes to collect those links? That is just spam. We want quality posts.
The rest of those articles talk about two body approximations as a "solution" to the three body problem. No one found a "rather trivial" three body problem solution for the SunEarthMoon system. I would suggest you read your sources, since you admit that you do not. All sources will tell you that it is not really solvable or stable except with some very special and absurd scenarios.
I encourage you to read the source. I know that it what it says in the abstract, but that is simply the stronger focus. If you follow the equations, it is shown blatantly that no conditions are imposed on the masses either. They do not specify this in the abstract because it is uninteresting  the problem is easy to solve without this constraint. This is precisely the information you were requesting.
My intent was not to spam, but to provide a sample of the wealth of sources which detail how we describe orbits.
I do not really feel inclined to complete your homework for you, and I suppose you are free to ignore all of this if you wish. But I hope that you do not. It may take some time, but here is a wealth of learning that will assist you in formulating better arguments against REers.
I know you probably don’t believe that is what I am trying to help you do, but it truly is!
The smoking gun evidence is right here, staring you right in the face. Let me know if I can be of any assistance understanding the mathematics. It can be daunting to the untrained, and it would be my pleasure to help.
All the best in your search for truth :)

I encourage you to read the source. I know that it what it says in the abstract, but that is simply the stronger focus.
If you follow the equations, it is shown blatantly that no conditions are imposed on the masses either. They do not specify this in the abstract because it is uninteresting
Very funny. First you admit to only a cursory glance at the articles, as it only took you '15 minutes' to find them, and now you claim to have read them and that it's abstractly 'in the equations' and never stated anywhere, and that the abstract makes a similar statement about the positions and velocities, but it was only a coincidence. You often rely on "it's too simple" and "everyone knows..."
Please quote your sources directly if you are going to make an argument. "My argument is buried in this paper somewhere and somehow" is an invalid debate tactic.

QED admits no where in any of the responses in this post that he took a cursory glance at the articles. That is an outright blatant lie, Tom. The only thing he states is that it took him 15 minutes to find the documents. He did not state that he took 15 minutes to read all of them. WOW.

Very funny. First you admit to only a cursory glance at the articles, as it only took you '15 minutes' to find them, and now you claim to have read them and that it's abstractly 'in the equations' and never stated anywhere,
Here's an equation from the paper showing that they have separate masses. This took me less than a minute of skimreading.

QED admits no where in any of the responses in this post that he took a cursory glance at the articles. That is an outright blatant lie, Tom. The only thing he states is that it took him 15 minutes to find the documents. He did not state that he took 15 minutes to read all of them. WOW.
Yes, sure. It took him 15 minutes to find them  and he took hours to head then all  but he didn't bother to tell us which part of the article supports his ideas since a follow up statement says that they are never stated anywhere.
Good one. How about you guys actually directly reference your sources rather than a convoluted argument based on abstract inference based on things that are never stated anywhere in your source?
Very funny. First you admit to only a cursory glance at the articles, as it only took you '15 minutes' to find them, and now you claim to have read them and that it's abstractly 'in the equations' and never stated anywhere,
Here's an equation from the paper showing that they have separate masses. This took me less than a minute of skimreading.
You think that an equation would only have one mass referenced to describe three bodies?
Separate masses != All masses are the different
I would recommend that you guys do more than a "skimreading".

"My argument is buried in this paper somewhere and somehow" is an invalid debate tactic.
Why do you think selective quoting is a valid debate tactic?
The paper makes it very clear that it is concerning the general 3 body problem where the masses of the bodies may be different.

"My argument is buried in this paper somewhere and somehow" is an invalid debate tactic.
Why do you think selective quoting is a valid debate tactic?
The paper makes it very clear that it is concerning the general 3 body problem where the masses of the bodies may be different.
More "skimreading," we can assume? Quote it for us.

You think that an equation would only have one mass referenced to describe three bodies?
Separate masses != All masses are the different
I would recommend that you guys do more than a "skimreading".
Tom, I would recommend that you read the article for yourself rather than rely on what other people tell you about it. After all, first had experience is the Zetetic way, isn't it?

You think that an equation would only have one mass referenced to describe three bodies?
Separate masses != All masses are the different
I would recommend that you guys do more than a "skimreading".
Tom, I would recommend that you read the article for yourself rather than rely on what other people tell you about it. After all, first had experience is the Zetetic way, isn't it?
I read the article and quoted from it. It t does not say what was alleged.

You think that an equation would only have one mass referenced to describe three bodies?
Separate masses != All masses are the different
I would recommend that you guys do more than a "skimreading".
If the masses were assumed to be the same, then the paper would use a single variable for mass instead of 3 variables.
And this is still besides my main point (in the OP) that a model doesn't need to be solvable to be accurate.

Quote it for us.
In the general threebody problem, three bodies of arbitrary masses move in a three
dimensional (3D) space under their mutual gravitational interactions

Quote it for us.
In the general threebody problem, three bodies of arbitrary masses move in a three
dimensional (3D) space under their mutual gravitational interactions
It's talking about the general three body problem... which is unsuccessful and has no solutions.
From the article on the general three body problem:
In the threebody problem, three bodies move in space under their mutual gravitational interactions as described by Newton’s theory of gravity. Solutions of this problem require that future and past motions of the bodies be uniquely determined based solely on their present positions and velocities. In general, the motions of the bodies take place in three dimensions (3D), and there are no restrictions on their masses nor on the initial conditions. Thus, we refer to this as the general threebody problem. At first glance, the difficulty of the problem is not obvious, especially when considering that the twobody problem has wellknown closed form solutions given in terms of elementary functions. Adding one extra body makes the problem too complicated to obtain similar types of solutions. In the past, many physicists, astronomers and mathematicians attempted unsuccessfully to find closed form solutions to the threebody problem. Such solutions do not exist because motions of the three bodies are in general unpredictable, which makes the threebody problem one of the most challenging problems in the history of science.
The position of the article is entirely contradictory to what you, the OP, and QED are "skimreading".

The position of the article is entirely contradictory to what you, the OP, and QED are "skimreading".
Huh? I was just opposing your point that the paper set all the masses to the same value.

If the three body problem is unsolved then there is no working model.
Why?
Surely not " ... because I (you) say so" ?

It's talking about the general three body problem... which is unsuccessful and has no solutions.
From the article on the general three body problem:
In the threebody problem, three bodies move in space under their mutual gravitational interactions as described by Newton’s theory of gravity. Solutions of this problem require that future and past motions of the bodies be uniquely determined based solely on their present positions and velocities. In general, the motions of the bodies take place in three dimensions (3D), and there are no restrictions on their masses nor on the initial conditions. Thus, we refer to this as the general threebody problem. At first glance, the difficulty of the problem is not obvious, especially when considering that the twobody problem has wellknown closed form solutions given in terms of elementary functions. Adding one extra body makes the problem too complicated to obtain similar types of solutions. In the past, many physicists, astronomers and mathematicians attempted unsuccessfully to find closed form solutions to the threebody problem. Such solutions do not exist because motions of the three bodies are in general unpredictable, which makes the threebody problem one of the most challenging problems in the history of science.
The position of the article is entirely contradictory to what you, the OP, and QED are "skimreading".
you absolutely have not read this article, and you don't understand the difference between a numerical solution vs an analytic solution. you just ctrlf and search for keywords that you think fit your narrative. i recommend not doing that and at least reading the section on numerical methods.
numerical methods are basically just doing a bunch of multiplication and addition. i don't get why you think computers can't do that.

There is no way to do it. The motions of the bodies are unpredictable.
From the above:
Such solutions do not exist because motions of the three bodies are in general unpredictable
Look up chaos theory, which directly spawned from attempts to solve the three body problem. Neither an analytical solution or a numerical solution can solve chaos theory.

There is no way to do it. The motions of the bodies are unpredictable.
From the above:
Such solutions do not exist because motions of the three bodies are in general unpredictable
Look up chaos theory, which directly spawned from attempts to solve the three body problem. Neither an analytical solution or a numerical solution can solve chaos theory.
It's not a numerical solution, it's an approximation. It has a known error bound. Nobody ever called it a "solution".

There is no way to do it. The motions of the bodies are unpredictable.
From the above:
Such solutions do not exist because motions of the three bodies are in general unpredictable
Look up chaos theory, which directly spawned from attempts to solve the three body problem. Neither an analytical solution or a numerical solution can solve chaos theory.
The fact that we claim the official orbiting model is defined by very specific laws and mathematical formulas.
The official round earth model is not even a 3 body problem. It's like a 90 body problem.
The fact that the three body problem has not been solved, and the official model is a 90+ body problem is something that definitely weakens some aspects of the official model and should be kept on the wiki.

There is no way to do it. The motions of the bodies are unpredictable.
From the above:
Such solutions do not exist because motions of the three bodies are in general unpredictable
Look up chaos theory, which directly spawned from attempts to solve the three body problem. Neither an analytical solution or a numerical solution can solve chaos theory.
The fact that we claim the official orbiting model is defined by very specific laws and mathematical formulas.
The official round earth model is not even a 3 body problem. It's like a 90 body problem.
The fact that the three body problem has not been solved, and the official model is a 90+ body problem is something that definitely weakens some aspects of the official model and should be kept on the wiki.
Once again, solvability has almost nothing to do with veracity. There are solvable models that are inaccurate, and there are unsolvable models that are accurate.

I encourage you to read the source. I know that it what it says in the abstract, but that is simply the stronger focus.
If you follow the equations, it is shown blatantly that no conditions are imposed on the masses either. They do not specify this in the abstract because it is uninteresting
Very funny. First you admit to only a cursory glance at the articles, as it only took you '15 minutes' to find them, and now you claim to have read them and that it's abstractly 'in the equations' and never stated anywhere, and that the abstract makes a similar statement about the positions and velocities, but it was only a coincidence. You often rely on "it's too simple" and "everyone knows..."
Please quote your sources directly if you are going to make an argument. "My argument is buried in this paper somewhere and somehow" is an invalid debate tactic.
Oh! You misunderstand. I’ve read all the technical sources before, I did not newly find them in 15 min. What I was able to do is build that collection using google in that time. The reason why I chose many of those sources in particular (instead of the dozens of others I had to choose from) was precisely because they are familiar to me.
I never stated that I took a cursory glance at them  this was an incorrect assumption.
Also, I am not trying to debate you. There is no debate here. I am simply trying to provide you with information to improve your understanding of these things so that YOU become a more effective debater with your adversaries in the future.
Believe you me, when you break through and publicly go up against physicists, you will appreciate having an arsenal of prior detailed knowledge of the arguments they will bring against you.
Do not let my lower fora posts muddle our efforts here: that is just careless childish venting (which is what those fora are meant for). I am on your side here.
I will pick out some relevant Trajectories for you from these sources and post them  so that future discussions can have a finer focus. But please do not let them take the place of your own study. Alone, they will be insufficient to prepare you for the future.
Best,
QED

Hi Tom,
I found a nice article that is very readable and rather short. It investigates the tidal perturbation effects of the Sun on the moon and Earth, and in these context provides the equations of motion for them. You will not be able to miss them: pp.1011.
I hope this assists in your pursuits. If I happen to come across others that I feel might be additional benefit, I will take the liberty of beginning a new thread, so as to avoid spamming this one, and allow conversation of other participants to continue.
https://www.ias.ac.in/article/fulltext/reso/010/08/00060024

If the three bodies concerned are the Sun, Earth and Moon, then wouldn't that make it exceedingly difficult to navigate a craft to and from the Earth, if the "equations" were wrong?
However, Israel managed it recently, China and Saudi Arabia not long before that, and in the past, USA, Russia, Japan and India have all managed it.

Hi Tumeni,
Great question. Computing space craft trajectories mainly requires the 2 body problem, as the sun is usually not relevant (of course, when we launch satellites to make measurements of the sun then it is).
What makes space travel so complicated (among many, many other reasons) is the level of precision we need to solve the equations. A rough estimate simply will not do! We need to have the craft flight plans computed very carefully, otherwise we will not achieve lunar orbit (for example), or we’ll skip that craft right off the atmosphere on its return trip (another example).
What is impressive to me is that NASA accomplished this before modern computers. The way this managed this was to have rooms full of “human computers” that calculated the pieces of it as a fulltime job!