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The stellar age is the elapsed time since a star formed. A constant number formation rate on a finite interval gives a uniform distribution of present ages if every formed object remains counted, including stellar remnants. An age distribution inferred only from surviving main sequence stars generally differs because their lifetimes depend on mass.

A passing star perturbs a planetary or cometary system through its differential Newtonian gravitational field. A distant encounter is predominantly tidal; a sufficiently close one can substantially change specific orbital energy and angular momentum, eject a comet, or shift its periapsis into or out of the planetary region.

Outside a spherical star, its gravitational acceleration is $-G{M}_{\star }\mathbf{r}/r^3$. It provides the dominant central force for Kepler orbits in a star-dominated planetary system.

A stellar population is an ensemble of stars described by its formation times, initial masses, composition and present stellar evolution states. Number fractions must be distinguished from mass-weighted fractions. Shared formation times can correlate the states of components of a binary star even when their initial masses have independence.

The stellar relaxation time is the time on which random gravitational encounters change a star's velocity by an amount comparable to its characteristic random velocity. A weak straight-line encounter at relative speed $u$ and impact parameter $b$ gives a kick $2Gm/(bu)$. Three-dimensional encounter counting gives $d⟨|\Delta \mathbf{v}{|}^2⟩/dt=8\pi G^2{m}^{2}n\log (b_{\max }/b_{\min })/u$. Definitions of relaxation, velocity averaging and system structure alter order-one coefficients; the robust spherical scaling is $t_{\mathrm{rel}}\sim v^3/(G^2{m}^{2}n\log \Lambda )\sim (N/\log N)t_{\mathrm{dyn}}$. Collisionless simulation requirements depend on the duration and permitted fractional relaxation, not a universal minimum particle number.

For an edge-on orbit crossing the centre of a uniformly bright stellar disk at distance $r\gg R_{\star }$, projected speed is $h/r$ and chord time is $2R_{\star }r/h$. A steady cross-sectional-area current $J_{\sigma }=2fh$ therefore places area $4f{R}_{\star }r$ in front of the star, givingThis requires a geometrically narrow, optically thin wire with negligible overlap. A noncentral chord, limb darkening, finite angular extent and large optical depth change the estimate; it cannot predict dimming greater than one.