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I have to write a research essay and have decided to write it on orbital mechanics where I would use data from the JPL to perform an experiment (simulation).

I was thinking of using the location data of Mercury to show the flaws in Newtonian mechanics. The thing is the essay has to be more original than simply demonstrating the flaws in Newtonian mechanics (which have many papers already written on the topic) so if anyone knows of an extension I could do or any other ideas of what I could do with this data? (I think it has pretty much all information needed to conduct any sort of simulation). I was also thinking of making a simulation of a gravity boost or to demonstrate Kepler's Laws but again my essay has to be more original (I have to analyze the data to demonstrate something useful with it, not just verify Kepler's Laws for example). So if anyone has any extensions to these ideas, such as not just simulating a gravity assist but showing how the effect of some variable could maximize the change in velocity (although this is quite a common topic and I think it would be quite hard to make such an accurate simulation) I would greatly appreciate it. I was also thinking about how orbital mechanics data could be used for the search of invisible objects (like how Neptune was predicted to exist before actually being discovered) so maybe that could be another idea.

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  • $\begingroup$ Welcome to the site @AlexanderIvanov. Unfortunately your question isn't focused enough to answer, and is therefore off topic and likely to be closed. If you have specific questions on how to achieve some of your ideas feel free to ask them, and good luck on your essay. $\endgroup$ – GdD Jun 16 '20 at 7:37
  • $\begingroup$ @GdD and yet there are two answers... $\endgroup$ – uhoh Jun 17 '20 at 3:54
  • $\begingroup$ @ukh - and that's potentially not a good thing... $\endgroup$ – Rory Alsop Jun 18 '20 at 19:46
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As for any research, the first question you need to answer for yourself is: "how much time do I realistically have and what happens if I don't finish this research in time?"

Organization

It seems like your scope is quite wide. From my experience, I would recommend organizing your research ideas into incremental steps. Each step feeds into the next step of your research. I'll emphasize that the first step of your research should be simple, e.g. "load the ephemeris in my Python script and query it."

A rule of thumb is the $\pi$-rule: take your first time estimate at completing some task, and multiply it by $\pi$. If it's your first time working on this problem, multiply by $\pi^2$. For example, if you think it's one day of work, and you've never done this before, expect more like 9.8 days.

Preemptively think about how you'll present the results of your research. Will these be plots? If so, plan the title of the plots even before you start any technical work. What kind of context will be needed for those plots?

Research ideas

The orbit of Mercury is an interesting topic!

Luckily for any mission designer and spacecraft navigator, NASA publishes the position of all the planets, and most moons and a number of asteroids. This data is available for free: https://ssd.jpl.nasa.gov/?ephemerides . You can either query the HORIZONS database with a specific time and "observer," or you can download one of the BSP ephemeris files (the latest version is de438.bsp I believe, but de405.bsp is still very commonly used despite being a few years old).

Here are some miscellaneous ideas:

  • Compare the true position of Mercury as computed by NASA and a celestial dynamics simulation where you ignore relativistic effects and the mass of any other object in the solar system.
  • Then, use a pre-existing software for N-body dynamics and compute the orbit of Mercury assuming two or three of the most influential masses (I would guess Sun, Venus and Jupiter, but check the maximum gravitational pull each planet could produce on Mercury if it was as close as it could be to it).
  • Finally, extend this other planets.

Gravity assists

Two variables determine the usefulness of gravity assists. First, the mass of the object which you'll use, and second the radius of periapse passage around that planet. This is further explained on this NASA page, but I would also recommend searching for Dr. Kate Davis who teaches interplanetary mission design at the University of Colorado at Boulder. I think there's a PDF handout online which explains the calculations.

The point of a gravity assist maneuver is the transfer some of the energy of the planet to your spacecraft. Hence, the more mass a planet has, the more energy it has, and therefore the more you can "harvest." (In theory, you also slightly slow down the planet, but in practice of course the numbers of negligible). Therefore, a gravity assist around Mercury would not be all that interesting, but one around the Sun would be! And has been used.

Best of luck!

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You can look into these right here in Stack Exchange!

Departure from Newtonian gravity and other relativistic effects:

The Pioneer anomaly

The Flyby anomaly:

Conjunctions, eclipses, occultations, parallax (non-Earth based):

Minimoons:

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