3189: Conic Sections

Conic Sections

|< < Prev #3189 (January 2, 2026)

Title text: They're not generally used for crewed spacecraft because astronauts HATE going around the corners.

|< < Prev Random Explanation

Explanation

This is one of 63 incomplete explanations: This page was created recently. Don't remove this notice too soon. If you can fix this issue, edit the page!

A Kepler Orbit describes the simplified motion of two celestial objects around each other based only on their gravitational forces, ignoring any other factors such as gravity of other objects, atmospheric drag, and non-spherical bodies. Such an orbit will form a conic section. Conic sections are curves formed by the intersection of a plane and a cone. This results in four possible curves: a circle, ellipse, parabola, or hyperbola, depending on the angle of the plane relative to the cone's axis.

In real conic sections, the cone extends to infinity. In the comic, however, the "conic section" representing the satellite's orbit has a base, resulting in sharp corners where the base and the lateral surface meet. As alluded to in the title text, these corners would be extremely uncomfortable for an astronaut in a crewed spacecraft such an extreme and sudden change in direction would require a very large, potentially dangerous G-force.

Transcript

This is one of 34 incomplete transcripts: Don't remove this notice too soon. If you can fix this issue, edit the page!

[A view of the Earth, focused on Asia and the Indian Ocean with East Africa at left and the Western Pacific and Australia at right. A satellite is shown in an unusual orbit around the planet.]

[Caption below the panel:]

All Keplerian orbits are conic sections. For example, this one uses the base of the cone.

  Add comment        Create topic (use sparingly)       Refresh 

Discussion

Isn't the base of a cone, just a circle? How would this have "corners"? SDSpivey (talk) 01:41, 3 January 2026 (UTC)

The cone upon which a conic section exists doesn't actually have a base, it's just arbitrarily large (possibly infinitely so) in order for the section to only ever lay along the 'curve' of the cone part.

But, here, the base is wwhere you give up on plotting how far 'down the cone' you go, of the sufficiently large ellipse (or possibly parabolic/hyperbolic curve), which is indeed round but has an sharp (i.e. acute) angle between its flat (and incidentally circular) plane-section and the 'wrapped' pseudo-euclidean plane of the conic-section it intersects with. 92.23.2.208 01:50, 3 January 2026 (UTC)

Bring a jacket and spoon for orbits that go through the ice cream.Lord Pishky (talk) 01:43, 3 January 2026 (UTC)

I'm pretty sure this is the shape of the flat bottom of a cake cone. 71.212.56.254 03:02, 3 January 2026 (UTC)

They REALLY hate the flat-bottom cone orbits and the waffle cones make for a bumpy ride.Lord Pishky (talk) 18:57, 3 January 2026 (UTC)

It appears to be a cut-off section of an ellipse, so basically a regular orbit with a sharp line. (Desmos) Tanner07 (talk) 04:29, 3 January 2026 (UTC)

https://media.licdn.com/dms/image/v2/D5622AQH3CYoPXy1cqg/feedshare-shrink_2048_1536/feedshare-shrink_2048_1536/0/1727242249609?e=1769040000&v=beta&t=UdAX9TH3joo-vpvj4pRWXoCQyF6JVUPVmyONWghcj5E --PRR (talk) 05:06, 3 January 2026 (UTC)

I feel like there needs to some explicit acknowledgement that the cone in question is an ice cream cone.99.239.23.54 00:11, 4 January 2026 (UTC)

But ice-cream cones have the 'flat bit' (actually the opening; give or take the scoop of ice-cream, which is a ball, or else the soft-served 'twirly-dollop', which another more convoluted form of inverted cone) at the top. Which just really doesn't fit with anything the comic says about the conic. Unless you see some obscure connection that I'm just not getting out of it. (Beyond that both are considered 'cones', which is as tenuous as if I suggested traffic cones was the ultimate reference, for example.)

But if you can give any better referencing connection, you look like you should know how to edit things to enlighten those of us who are missing it. Explain away, as that's the point of this site... 82.132.236.68 01:39, 4 January 2026 (UTC)

Shouldn't the people from the title text also be following the same orbit? Cobl703 (talk) 18:35, 4 January 2026 (UTC)

Might depends on if they share the same precise centre of gravity (the Explanation goes into some detail about that sort of thing).

Or if the effective orbit obeys the idential 'cone-based' rules. At any given time (depending on where you last positioned yourself), you might effectively be floating in a very similar elliptical orbit (could be the same period, same semi-major, same semi-minor, same periapsis, same periapsis, inclination, etc, but in a very slightly rotated orientation), so hit the change to the 'conic-baseline' section at a different time.

That's if the orbit equation defines the location of the transition into the conic-base (e.g. effectively when hitting the "semi-parameter" 'width', but on the non-focuse side of the original ellipse), or there's always some particular definite absolute (or proportional?) distance between the hypothetical cone's tip and when the normal orbital effect 'runs out'.

Too many little questions need to be asked about what is forcing the orbit to be off-elliptical. And if it's not a mere function of reality, but a deliberate manoeuvre by the craft, then of course the occupants will feel the sudden change in motion that the accompanying thruster-kick invokes. 92.23.2.208 21:03, 4 January 2026 (UTC)

How far the cone extends and where these effect occur depends on the units of distance used and the number of digits & format used to represent the length of the cone on the computer. Larger units avoid cone-end effects but make for a bumpier ride, especially when the exponent changes.Lord Pishky (talk) 05:58, 5 January 2026 (UTC)
        Add comment