Angular diameter distances (flat $\Lambda$CDM, $H_0=70$, $\Omega_m=0.3$): $D_l \approx 900$ Mpc, $D_s \approx 1700$ Mpc, $D_ls \approx 1000$ Mpc (roughly).
Thus $M \approx 10^11 M_\odot \times (2/1)^2 \times 0.5^-1 \times (0.9)^-1$? Let’s approximate: physics galaxy discussion questions solutions
: As (d \to R^+), (F \to -\infty) (image charge (q') increases and distance to image decreases). The force becomes very strong — but before touching, the point charge induces large surface charge density, leading to possible discharge or breakdown. If the sphere is grounded, then image charge (q' = -\fracRd q) still holds but total charge on sphere is not zero. The force becomes very strong — but before
Two meetings after (t=0) ⇒ two positive roots of ( \frac12 a t^2 - v_0 t + n L = 0 ) for (n=1) and maybe (n=2) depending on parameters. After arriving at a solution, ask if it makes physical sense
After arriving at a solution, ask if it makes physical sense. For instance, a calculated velocity should not exceed the speed of light, and pressure should not be negative in standard conditions. Where to Find Solutions
| Concept | Key Physics | Typical Observation | |---------|-------------|----------------------| | Rotation curve | Newtonian gravity + DM halo | HI 21 cm line | | Tully-Fisher | L ~ v⁴ | Optical + Hα rotation | | Oort limit | Poisson eqn + vertical motions | Stellar number counts + proper motions | | M/L variation | IMF + star formation history | Colors + spectral indices | | AGN feedback | Jet heating vs. cooling | X-ray cavities + radio lobes | | Lensing | GR deflection | Multiple images, Einstein rings |