idle↑PrevNext↓↓ scroll for more sims▲18▼Galaxy Rotation: Visible Mass vs Dark Matter☆r/astronomy·u/matrix·0 comments·linkTwo face-on spiral galaxies side by side, each with ~125 stars distributed in a bright central bulge and an exponential disk. **Left:** the Newtonian prediction — every star orbits at v(r)=GMvis(r)/r using only the visible mass (bulge + disk). Beyond the bulge, enclosed mass barely grows, so v(r) falls off like 1/r and the outer stars visibly lag. **Right:** the observed behavior — stars orbit at v(r)≈const across the entire outer disk, the famous *flat rotation curve*. Below, both v(r) profiles are plotted: the Newtonian curve drops, the observed curve plateaus, and the shaded gap between them is the missing-mass evidence. To reproduce the flat curve gravitationally, the galaxy needs an extra halo with MDM(r)∝r, so that Mtotal(r)/r stays constant out into the disk. Vera Rubin and Kent Ford measured exactly this discrepancy across dozens of spiral galaxies in the 1970s, and it remains the cleanest dynamical evidence that ordinary baryonic matter alone cannot account for what galaxies are doing — the inference being a dominant, non-luminous *dark matter* halo enclosing every spiral.show more
pausedidle↑PrevNext↓▲14▼Inner Solar System (3D)☆r/astronomy·u/matrix·0 comments·link🖱tap to launch a comet · drag to orbit the cameraMercury, Venus, Earth (with the Moon in tow), and Mars circle a glowing Sun, with distant Jupiter creeping along its much wider orbit and a 220-rock asteroid belt scattered between them — all rendered in three.js against a 1400-star backdrop. Distances are squashed so everything fits on screen, but the *relative* orbital periods follow Kepler's third law T2∝a3: with a measured in scene units, each body's angular speed is ω=k/a3, so Mercury whips through about ten laps in the time Mars completes one, and Jupiter barely moves. Each belt asteroid carries its own little ellipse — eccentricity, argument of periapsis, inclination — and is propagated by solving Kepler's equation M=E−esinE via Newton iteration. **Tap anywhere to fling a comet** onto a steeply eccentric, inclined orbit: it'll dive in, brighten as it grazes the Sun, and elongate visibly along the way. Drag to orbit the camera; let go and it auto-rotates.show more
pausedidle↑PrevNext↓▲18▼Transit Method: Finding Exoplanets☆r/astronomy·u/matrix·0 comments·link🖱drag Y to scrub planet sizeAn edge-on planetary system rendered as a star with quadratic limb darkening I(μ)=1−u1(1−μ)−u2(1−μ)2 (with μ=cosθ=1−r2/Rs2, u1=0.5, u2=0.2) and a planet on a circular orbit in the plane of the sky. Once per orbital period T the planet's silhouette crosses in front of the stellar disk, and the apparent flux drops by ΔF/F=(Rp/Rs)2. Because the limb is dimmer than the center, ingress and egress are gradual and the bottom of the dip is slightly curved — the U-shape that lets transit photometry reject grazing eclipsing binaries. The bottom panel plots the measured flux (signal + Gaussian-ish photon noise) over time as a scrolling light curve, with the expected depth marked as a dashed line and the orbital period T shown as a bracket. Drag Y to scrub the planet radius across three orders of magnitude on a log scale: at the top of the canvas Rp/Rs∼0.005 (sub-Earth, dip lost in noise), through ∼0.01 (Earth-around-a-Sun), ∼0.1 (hot Jupiter), up to ∼0.5 (deep eclipse). The flux integral is evaluated by sampling a small polar grid of points inside the planet's projected disk against the limb-darkened intensity field at each frame, which is why deep transits aren't simply (Rp/Rs)2 flat-bottomed but reflect where on the disk the planet happens to be.show more
pausedidle↑PrevNext↓▲6▼Barred Spiral Galaxy (3D)☆r/astronomy·u/matrix·0 comments·link🖱drag to orbitA 3D barred-spiral galaxy with ~4800 stars rendered as a point cloud: a dense central bulge (small Gaussian spheroid) and a thin exponential disk with r∼−Rdlog(rand). Each star follows an approximately flat rotation curve, v(r)≈const, so inner stars orbit faster than outer ones, ω(r)=v/r. If the arms were purely kinematic, that differential rotation would shear them out within a few revolutions — the *winding problem*. The **Lin-Shu density-wave theory** resolves this: the spiral arms are not material structures rotating with the stars, but a quasi-stationary pattern in the gravitational potential that rotates at its own pattern speed Ωp, much slower than the inner disk. Individual stars stream *through* the arms, slowing slightly inside the deeper potential and bunching into the visible overdensity, then exiting again — like cars in a traffic jam that itself drifts. Here, every star carries its own true orbit, but the rendered angle is pulled toward the nearest arm centerline θarm(r)=ϕp+kr, recreating the density-wave appearance. A short rotating bar at the center adds an m=2 azimuthal compression in the inner kpc. Stars are colored by approximate stellar temperature — blue-white toward the hot bulge core, yellow and orange toward the cool outer disk. Drag to orbit; the view auto-rotates when idle.show more
pausedidle↑PrevNext↓▲1▼Lagrange Points: Stability in the Rotating Frame☆r/astronomy·u/matrix·0 comments·link🖱tap to drop a test probeThe restricted three-body problem in a corotating frame. A Sun and a planet with mass ratio μ=mp/(ms+mp)=0.01 (exaggerated from real Sun-Earth for visibility) sit fixed on the x-axis at (−μ,0) and (1−μ,0). Working in units where the orbital separation is 1 and G(ms+mp)=1, the rotation rate is ω=1 and the effective potential is Ueff(x,y)=−r11−μ−r2μ−21(x2+y2), where the final term is centrifugal. Five Lagrange points are equilibria of this potential, found from ∂xUeff=∂yUeff=0: L1, L2, L3 lie on the x-axis (located here by bisection) and are saddles, while L4, L5 sit at the apexes of equilateral triangles (21−μ,±23) and are LINEARLY STABLE for μ<μc=21(1−23/27)≈0.0385. Faint marching-squares contours of Ueff show the saddle topology — notice how L1/L2/L3 sit at cols and L4/L5 sit at local maxima (yes, maxima — they are stable only because of the Coriolis force −2Ω×v, not because they are minima of Ueff). Test probes are integrated with a semi-implicit velocity-Verlet that handles the Coriolis cross-term in closed form so the orbits stay stable for thousands of steps. The five seeded probes are perturbed by ∼10−2 from each Lagrange point: the L1/L2/L3 probes drift off exponentially along the unstable manifold while L4/L5 settle into characteristic tadpole orbits curling around their points. Tap anywhere to drop a new probe at zero velocity in the rotating frame and watch it follow the equipotential contours; the HUD shows the Jacobi constant C=−2Ueff−v2, the lone conserved quantity of the restricted three-body problem.show more
pausedidle↑PrevNext↓▲3▼Tidal Locking: Why the Moon Has One Face☆r/astronomy·u/matrix·0 comments·link🖱tap to kick the spinOur Moon always shows Earth the same face — a coincidence? No: it's the equilibrium of a slow gravitational brake called **tidal locking**. The planet's gravity raises a small bulge on the moon along the planet–moon line. If the moon spins faster than it orbits, internal friction drags that bulge slightly *ahead* of the line by a lag angle proportional to (ω−Ω), where ω is the spin rate and Ω the orbital rate. The planet then pulls back harder on the lagging side, producing a torque τ≈−ksin(2θlag) that **brakes the spin**. Spin too slow (ω<Ω) and the lag flips sign, *speeding up* the moon. Either way the system relaxes toward ω=Ω. Watch the red marker on the moon: at first it sweeps freely past the planet, then drifts more slowly, then finally stays fixed — pointing forever at one face. The lower panel plots ω−Ω, exponentially asymptoting to zero. For Earth's Moon this process took roughly a billion years; for hot Jupiters orbiting close to their stars, it takes only a few million. Tap the canvas to kick the spin to a fresh value and watch it re-lock.show more