Editing 3189: Conic Sections

{{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 two celestial objects around each other. 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. In reality, this model is based only on their basic gravitational forces and ignores any other factors such as the gravity of other objects, atmospheric drag, each object being a non-spherical(/non-point body) and any {{w|Relativistic angular momentum#Orbital 3d angular_momentum|relativistic effects}}, but it serves as the basis for most orbital calculations before further refining with the most relevent additional perturbations.

In real conic sections, the cone extends to infinity. In the comic, however, the "conic section" representing the satellite's orbit has been assumed to have a base, resulting in sharp corners where the angled planar section 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}}) without ''any'' experienced net acceleration, as adding up the forces due to external gravity and your path's continually changing direction will zero out. 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 points (reaching the baseline and rejoining the true curve again), which would technically require infinite acceleration each time. Alternately, deliberately 'cutting the corner' would require the best effort of the spacecraft to stick to the truncated-orbital path, requiring as much complex and wasteful thrusting as the craft could provide (which any occupants must endure), including the less uncomfotable but still forceful passage along the 'straight' bit of the orbit through the curved gravitational field of the parent body.

[[File:TypesOfConicSections.jpg|thumb|alt=Example conic sections|How conic sections emerge from the planar intersection with a bidirectional cone, which technically continues beyond the 'top' and 'bottom' of this diagram.]]The conic section as depicted in the comic will be familiar to many readers, since models illustrating these curves using a cone with a base are commonplace and anyone who has learned about these curves in a mathematics class is likely to have seen one.

==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.]
:[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]]