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May
3
comment On a log-log plot of surface gravity to planet mass, what is the meaning of the y-intercept?
That $4k_2$ should be $2k_2$ in my comment (typo).
May
3
comment On a log-log plot of surface gravity to planet mass, what is the meaning of the y-intercept?
@RobJeffries The OP is far-extrapolating gas giants, so there $\rho$ is also strongly dependent on $M$--but that shouldn't change the correspondence to mean density for any particular fixed $M$, which was actually OP's question as stated. Really, though, the OP's extrapolation is physically inappropriate, and for light exoplanets ($M\lesssim 4$ in units of $R_\oplus = M_\oplus = 1$), Seager et al. (2007) $$\renewcommand{\lg}{\log_{10}} \lg R = k_1 + \frac{1}{3}\lg{M}-k_2M^{k_3}\text{,}$$ and so $\lg g = \frac{1}{3}\lg M - 2k_1 + 4k_2M^{k_3}$.
May
3
comment On a log-log plot of surface gravity to planet mass, what is the meaning of the y-intercept?
Shouldn't that be $g = (\tfrac{2}{3}\sqrt[3]{6\pi^2})(G\sqrt[3]{\rho^2M})$? Note that the OP's question is actually mostly about $\log M\to 0$, but otherwise, I agree, the most straightforward physical thing it corresponds to is mean density, fit to the data.
Apr
29
comment Could someone see anything while being inside black hole?
crap, you're right. Just considering this problem in reverse from the origin and at escape velocity makes it trivial. My thinking was in a rut formed by cycloidal relations for the finite-apsis case.
Apr
29
comment Could someone see anything while being inside black hole?
ah, thanks for the info. That would be a cute homework exercise for me to do. ;)
Apr
28
comment Could someone see anything while being inside black hole?
+1, but as a side note, I get about $67\,\mathrm{s}$ as an upper bound for the horizon-to-singularity time for Sgr A*-massed Schwarzschild black hole (freefall from rest near the horizon; all other times will be shorter because of higher inward velocity at the horizon, but it's unclear what initial condition would give $26\,\mathrm{s}$).
Apr
20
awarded  Enlightened
Apr
20
awarded  Nice Answer
Apr
19
comment Why are there no green stars?
@HyperLuminal It means that a green blackbody is literally impossible, and since the spectra of stars is that of a blackbody plus some relatively spectral line corrections, green stars should be impossible too. I'm not entirely sure how to quantify a deviation from greenness, though. In any case, you can see from the color space that there's nothing special about green in this way, as you stars actually miss almost all the colors.
Apr
19
answered Why are there no green stars?
Apr
17
answered Years, Months, Day, and Weeks?
Apr
16
answered Does the Sun's light travel fast enough to have a straight path to Earth?
Apr
15
comment Time according to the gravity of Sagittarius A?
For a hypothetical Sgr A*-massed Schwarzschild black hole, the tidal forces across $1.8\,\mathrm{m}$-tall human near the horizon should be on the scale of $10^{-4}\, \mathrm{gee}$ or so. Supermassive black holes don't spaghettify until well past the horizon. The time dilation calculations are misleading because the Schwarzschild radial coordinate does not straightforwardly correspond to a radial distance. For example, if $r_\text{ft} = r_\text{S}+1\,\mathrm{m}$, then $r_\text{hd} = r_\text{ft} + 16\,\mathrm{\mu m}$ for the human. That's one way to think about why the tidal forces are small.
Apr
12
comment Is the sun too small to self-ignite?
Sounds like a somewhat garbled explanation of quantum tunneling through the Coulomb barrier, which is a probabilistic effect that, in this case, allows fusion at lower energies than would be required without tunneling. Regardless, it's plainly not true that the Sun is too small to self-ignite, and it does actually have sufficient gravity.
Apr
7
comment Is it certain that dark matter consists of particles? (And not just curved space)
I don't think that's adequate. You can have nonvanishing Weyl curvature without matter/energy density anywhere in spacetime. The reasoning in this answer therefore must be supplemented with something else, e.g., an appeal to the Friedmann equations for the large-scale or perhaps Raychaudhuri equation for gravitational lensing.
Mar
24
awarded  Fanatic
Mar
16
comment In theory, is there anywhere in the universe where velocity=0?
To be fair to the pre-Einstein folk, the principle of relativity goes back to Galileo, and plenty of people didn't agree with Newton that space was absolute. (And for Newton himself, Galilean invariance of physics is actually a theorem in Principia, but he thought that space must be absolutely anyway for conceptual reasons.) Note that having space relative is enough for the answer to this question to be morally the same, even if time was thought to be absolute.
Mar
15
comment Is there a connection between black holes and dark matter/energy?
I suppose technically some MACHOs could be black holes, but certainly not supermassive ones, and MACHOs need to be lighter than astrophysically reasonable black holes in order to explain an appreciable fraction of dark matter anyway.
Mar
13
comment visualisation of the universe's expansion
+1, but the loaf analogy is no less accurate in general; it's just different. For the case of an infinite flat FRW universe, an infinite loaf is better than the balloon. However, the balloon analogy is more accurate finite positive-curvature FRW universe. ... So it depends on what cosmological model you're trying to describe.
Mar
11
revised Looking for help in understanding how black holes can move
clarification and response to comment