3189: Conic Sections

2026-01-04T03:34:54Z

2601:647:667F:1740:798A:7054:CBC6:65E9: /* Transcript */

{{comic
| number = 3189
| date = January 2, 2026
| title = Conic Sections
| image = conic_sections_2x.png
| imagesize = 288x322px
| noexpand = true
| titletext = They're not generally used for crewed spacecraft because astronauts HATE going around the corners.
}}

==Explanation==
{{incomplete|This page was created by a section through a scone. Don't remove this notice too soon.}}
A {{w|Kepler orbit}} describes the simplified motion of one celestial object relative to another. Such an orbit will form a {{w|conic section}}. A conic section is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes considered a fourth type, while intersections of the plane with the point of the cone (just that point, a straight line through that point or else four converging lines that all meet at the point) are possible constructions that are usually excluded.

In reality, this model is based only on the most simple modeling of two point masses, and ignores any other factors such as the gravity of other objects, atmospheric drag, each object being a non-spherical(/non-point) body of non-uniform density and any {{w|Relativistic angular momentum#Orbital 3d angular momentum|relativistic effects}}, but it serves as a good basis for most orbital calculations before needing further refinements to cover the most relevant additional perturbations for a given scenario.

[[File:TypesOfConicSections.jpg|thumb|alt=Example conic sections|How conic sections emerge from various planar intersections with bidirectional cones, which technically continue beyond the 'top' and 'bottom' of each diagram.<br/>In this comic, the shape is similar to the one in figure 3 (a {{w|parabolic trajectory}} that does not technically 'orbit' the focal mass), or (given the implication of this being based upon a mostly standard non-circular orbit) may be more that of figure 2 except for the correctly-angled plane for the ellipsoidal intersection being sent through the respective cone too close to the nominal 'end' of it.]]

In real conic sections, the cone extends to infinity. In the comic, however, the "conic section" representing the satellite's orbit (with its unseen point pointing generally to the left of the image) has been assumed to have its circular base (somewhere close to vertical, towards the right of the image) set at a distance that inconveniently crosses the indicated orbital path (that might be assumed to be fully elliptical, otherwise), resulting in sharp corners where the angled planar intersection through the cone meets that base. 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.

Being in a free orbit necessarily means following an ellipse (or very similar, outside of the mathematically strict {{w|two-body problem}}) in which there is net zero acceleration, combining the pull of gravity and the forces that would be felt due to the continually changing direction alone. Being forced off this ellipse to move across the totally imaginary and arbitrary conic-base would force an instantaneous acute change of direction for no other reason than to follow the imperfectly understood mathematical 'model' at two arbitrary inflection points (reaching the baseline and rejoining the true curve again), which would technically require infinite acceleration each time.

Even if the weird nature of space-time in the locality means that point-masses are seemlessly redirected via the off-elliptic part of the route, spacecraft are not dimensionless points. Even if only briefly, different parts of the spacecraft are likely to encounter the inexorable redirection of motion at different times (and maybe in subtly different manners). Even if that is somehow not a problem, anything (or anyone) sufficiently loose within the spacecraft hull may be considered to be charting their own more subtly individual 'conic-based' version of the orbit, the freefalling drift either suddenly sending them off into the side of the vessel and/or tending to continue onwards as the vessel effortlessly navigates its own {{w|Automan#Features|sudden change of direction}}.

Alternately, deliberately 'cutting the corner' of an orbit (without the fabric of reality conspiring to enforce this) would require the best effort of the spacecraft to stick to the truncated-orbital path, requiring as much {{w|Delta-v|thrust}} by the craft as it can muster (which any occupants would have to endure), including along the less uncomfortable but still forceful passage along the 'straight' bit of the orbit through the curved space-time of the {{w|gravitational field}} of the parent body. We also aren't given any indication of how the 'radial' velocity might be intended to change during the 'flat' phase, such as if it obeys the same {{w|Kepler's laws of planetary motion#Second law|constant 'area sweeping' rule}} as for the elliptic part of the path.

{{clear}}

==Transcript==
{{incomplete transcript|Don't remove this notice too soon.}}
:[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. This orbit is similar in shape to an ellipse, except it has two corners and a straight edge on one side, giving it a hill-like appearance.]
:[Caption below the panel:]
:All Keplerian orbits are conic sections. For example, this one uses the base of the cone.
{{comic discussion}}<noinclude>

[[Category:Space]]
[[Category:Geometry]]

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3189: Conic Sections