Changelog

Reactions

An introduction to the classical three-body problem

5. Restricted three-body problem

The restricted three-body problem is a simplified version where one of the masses m₃ is assumed much smaller than the primaries m₁ and m₂. In the planar circular case, the primaries move in fixed circular orbits around their common CM with angular speed given by Kepler's third law. This system has 2 degrees of freedom associated to the planar motion of m₃, and therefore a 4-dimensional phase space just like the planar Kepler problem.

E = ½m₃ṙ² + ½m₃r²φ̇² − Gm₃(m₁/r₁ + m₂/r₂) ≡ T + Veff   (15)

Not a like button

Two intentions shape this, and neither is applause. The first is lightweight peer review: a fast, honest read on how others are taking a piece of public research, kept anonymous so no one’s name pulls your judgment along. The second is memory — a way to bookmark the passages you’ll want again, all of them waiting in your Reactions tab, next to the inbox. That’s the opposite of a Facebook or Slack reaction. It isn’t a signal to a crowd; it’s a tool for peer review, and for anyone whose library has outgrown what they can keep in their head.

One tap, three jobs

Every reaction does three things at once. It bookmarks the passage for your future self, teaches your agent what you care about, and adds to an anonymous, public quality layer on the text—so the crowd’s read on a paper builds up passage by passage, with no names attached.

Recall everything you reacted to

A library-wide Reactions tab gathers every snippet you ever reacted to, filterable by type. The sentence you flagged as a central claim last month is one click away, wherever it lives.

One place for all your research

Read, listen to, organize, and discuss your papers, with AI in the margin instead of another tab.

Try Curie