Default steps 2D plots are too visible

[astrojuanlu]

🐞 Problem

With the default number of points, the steps in the pericenter are too visible:

Before	After

This came after the propagation changes in plotting and the different way to compute the data points.

🎯 Goal

Make the plots smooth again.

💡 Possible solutions

• Increase the default num_points
• Other?

📋 Steps to solve the problem

• Comment below about what you've started working on.
• Add, commit, push your changes
• Submit a pull request and add this in comments - Addresses #<put issue number here>
• Ask for a review in comments section of pull request
• Celebrate your contribution to this project 🎉

[astrojuanlu]

Another side effect:

This is a slightly different issue, namely that the pericenter is not always included in the propagation.

[astrojuanlu]

Notice that, while fixing the previous one, one might step into #265.

[nikita-astronaut]

Started working on this issue

[astrojuanlu]

Thanks @nikita-astronaut, keep us posted! Notice that the propagation might fail and distract you, see the last comment in this issue.

[astrojuanlu]

This is a good moment to say that just increasing the number of points is not going to be the preferred solution. In the report "The generalized Sundman transformation for propagation of high-eccentricity elliptical orbits" we can read:

Because of the large number of satellites, attention must be paid to the total time of computation.
For very eccentric orbits, satisfactory accuracy can be maintained with a larger step size near apogee
than is used at perigee

Take a look at this plot:

We are now in the situation of Figure 2.d), since we're uniformly sampling the true anomaly:

https://github.com/poliastro/poliastro/blob/24a9299f/src/poliastro/twobody/orbit.py#L295-L302

And before we introduced the sample method, we were doing almost the same thing:

https://github.com/anhiga/poliastro/blob/cd0a31ca3e7ffc99a3/src/poliastro/plotting.py#L169-L182

The most immediate fix for this issue, in my view, would be to use a uniform sample of the eccentric anomaly instead of the true anomaly. However, from the same report:

Merson (Ref. 13) introduced the idea of using the value n = 3 / 2 in the generalized Sundman transformation, with an intent not of regularization per se, but of maximizing computational efficiency; see also Ref. 14. He gave an analysis showing that this value of n equally distributes the integration error around a full orbit, even if the eccentricity is high.

I will therefore accept a pull request (with plots of the before/after situation) that use the eccentric anomaly as a first step, but implementing an s-integrator as described in the report would be a great next step (see #253).

[astrojuanlu]

I found another book that might be useful: "Regularization in Orbital Mechanics: Theory and Practice" (https://doi.org/10.1515/9783110559125)

[nikita-astronaut]

I will now read the report and try to implement the s-integration.

[astrojuanlu]

Great! Nevertheless this issue has been fixed in #320, so I'm closing. Let's continue the discussion in #253, or in the upcoming pull requests.

[astrojuanlu]

Or in #265, for that matter. Notice that, when we have a working propagator, we can include the pericenter in all the samplings if we consider it appropriate, see #294 (comment).

[astrojuanlu]

Another nice before/after table:

Before	After

This is with the same number of points. Veeeeeeeeery nice :)