Dark matter and dark energy (introductory)
Galaxies and cosmology · Physics
Solar system
Interactive 3DAll eight planets in orbit around the Sun, with Saturn's rings and Earth's Moon.
Controls
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Study notes
Worked example - weighing a galaxy with a rotation curve. Stars at radius r = 10 kpc orbit at v = 200 km/s. Step 1: for circular orbits, v^2 = G M / r, so M = v^2 r / G. Step 2: convert - v = 2 x 10^5 m/s, r = 10 kpc = 3.09 x 10^20 m, G = 6.67 x 10^-11. M = (4 x 10^10)(3.09 x 10^20) / 6.67 x 10^-11 = 1.85 x 10^41 kg. Step 3: divide by the Sun's mass (2 x 10^30 kg): ~9.3 x 10^10 solar masses inside 10 kpc. Visible stars and gas account for only ~4-5 x 10^10 - roughly half the gravity comes from unseen dark matter.