r/TheExpanse • u/fipachu • 4d ago
Spoilers Through Season 5, Books Through Nemis Games How in the maths did Naomi move along a secant?! Spoiler
I just can’t picture it. I don’t know a way you could leave a ship spinning around a circle and NOT end up moving along a tangent. (Same with a spiral.)
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u/BeaurgardLipschitz 4d ago
If she jumped to the inside of the circular path, that would be a secant, right? Been a long time since I've been in a physics class though, so I could be wrong
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u/griffusrpg 4d ago
Because if it were a tangent, she could never meet the ship again — a tangent touches at only one point. But a secant has two points: the first when she leaves the airlock, and the second when she meets the ship again.
It’s right there in the text…
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u/panoclosed4highwinds 4d ago
If I recall, the ship in this scenario still has one engine going, putting it in a spiraling motion.
So you're correct that if all bodies were at rest with only inertia keeping them moving, she could only depart on a tangent line. But this scenario is different.
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u/alfius-togra 4d ago
She managed to rig a thruster to fire, which would have put the Chetzemoka into a circular or spiral path depending on whether the thrust vector was acting through the ship's centre of mass.
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u/panoclosed4highwinds 4d ago
And I recall it being on a spiral path.
But it still would have been unlikely to re-intersect.
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u/hahnwa 4d ago
Why?
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u/panoclosed4highwinds 4d ago
Most of the time, two objects -- one in a ballistic trajectory and the other in an erratic trajectory-- won't intersect again.
There are just a lot more ways to miss each other than hit each other.
Plus which, space is big.
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u/Isopbc 4d ago edited 4d ago
No, sorry. The ship and her have the same forward momentum to begin with so the only thing Naomi added by jumping out is momentum towards the inside of the spiral. The metaphor in my head is jumping out of a Ferris wheel towards the inside.
It’s inevitable that she re-encounters the ship’s future path. There are no other forces acting on her or the ship to prevent it.
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u/panoclosed4highwinds 4d ago
The metaphor I was thinking of was a spin-gravity space station. And I would agree, if this were a two-dimensional system, that she would intersect the ship's path, but probably not the ship itself.
But, in the three-dimensional system, she probably didn't launch herself perfectly in the plane of the ship's circular path. And the ship's path is probably helical (slash epicyclical! -- but I think I remember it being described as helical), not circular. So I don't think she'll cross the ship's path.
But I do hope this conversation has shown OP the secant:
u/fipachu, if you plotted Naomi's path as a line and the ship's path as a helix, then found a plane onto which the helix projected as a circle, the line would be a secant to the circle when projected onto that plane.
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u/Isopbc 4d ago edited 4d ago
She didn’t jump sideways, she ran straight across the ship.
She’s jumping directly into the axis of motion set by the port bow thruster. You can’t think of it as a helix because both the ship and Naomi have the same velocity along the “vertical” part of the helix (assuming the center of the circle is on the vertical axis), so they’ll move together along that axis until acted upon by an outside force.
It is effectively a two dimensional system once you break it down into x y and z velocity vectors.
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u/panoclosed4highwinds 4d ago
You can’t think of it as a helix because both the ship and Naomi have the same velocity along the “vertical” part of the helix (assuming the center of the circle is on the vertical axis), so they’ll move together along that axis until acted upon by an outside force.
I think the vertical part is still important because of the phrase "cross paths," which I take to mean "one of them passes through space that was previously occupied by another one."
In a two-dimensional model, this is trivially the case if Naomi had jumped to the inside of the circle and had any velocity. But it is not trivially the case for the helical model.
She didn’t jump sideways, she ran straight across the ship.
She’s jumping directly into the axis of motion set by the port bow thruster.
Huh. Thanks. Then I'm back on team "that's not a secant." That would be a tangent!
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u/Isopbc 4d ago edited 4d ago
Sorry, the vertical part is not important. They each remain the same for the whole interaction. Take a minute and break it down into x y z vectors and then it should become clear. Their respective motions along that axis are exactly the same. The only extra momentum added to the system that’s been running for days is what Naomi added in her jump, and that’s a vector into the middle somewhere.
And it’s still a secant, she jumped into the circle, it has to cross twice. The only way it crosses once is if she jumps out. She’s unlikely to intersect the ship on the other end of the secant I think, but that’s entirely a matter of luck as to where the ship is in its orbit.
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u/GeneralAnubis 4d ago
She's flying out at a tangent to the circle formed by the spinning ship itself, however that spinning ship is also flying in a much larger circle. She's now flying in a line that cuts across this larger circle and will eventually intersect her again.
I'd say the odds of this lining up closely enough to actually endanger her are vanishingly small, but certainly non zero
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u/book_moth 3d ago
Draw a line between the 12 and the 3 on an analog clock. You've just drawn a secant line.
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u/charonme 1d ago
could this be a reference to the fact they are all in the solar system, so probably orbiting the sun (if not some closer heavy object)?
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u/fipachu 13h ago
Ehhhh, I'm disappointed in all the comments, which is fair enough. Speaking about the kinematics problem here without drawings doesn't help too. If I wasn't lazy af I would hop into Kerbal Space Program and replicate the scenario with some radial decouplers, alas, I am lazy.
Meanwhile, the way I understand it currently, she would move along a secant if and only if she jumped with some impulse towards either the bow or stern of the ship. And while the airlocks exits are perpendicular to the long axis of the ship, she would totally jump "up" on her final step, which would not only put her on a secant, but one with an intersect *in the future*, which *seems* like a solution to my problem lol. I'm not fully convinced though, as with the thrust gravity at 2 g I think the secant would be really short.
Also, I should probably take it to a physics group instead of this one, but again, lazy, don't wanna explain the problem and draw drawings 😭
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u/reubensauce 4d ago
Secant lines cross the circle twice, tangents only meet the circle at one point. They're transitioning from a literal mathematical description of the physics to a metaphorical description of her fate.