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3h
reviewed No Action Needed How does this strategy for chasing the sunset work?
13h
comment What is a low mass Black Hole?
I would dispute it; in my experience, people who say that tend to confuse the singularity of a black hole with the black hole itself. The volume isn't tending to zero except perhaps in a frame of passing by it at ultrarelativistic velocities, etc., and those limits aren't relevant here. Your link correctly says that the volume of a Schwarzschild black hole is nigh-infinite in the Schwarzschild frame, but it incorrectly implies that $\frac{4}{3}\pi r^3$ doesn't describe the volume (it does, but in a different frame). See also here.
14h
comment What is a low mass Black Hole?
Black hole volumes are frame-dependent, but they do have them. (Their surface areas are frame-independent.)
16h
comment Hulse Taylor Binary Pulsar - How is “Cumulative Periastron Time shift” calculated?
@steveOw No, it is based entirely on whether $M(t)$ is well-approximated, and by Taylor's theorem the error has about the magnitude of the the third-order term, which I've explicitly examined to be negligible. (To be fully rigorous, the remainder term needs to be examined explicitly, but it not essentially different.) Since cumulative periastron shift is $t - NP_0$ exactly and $N = M(t)/2\pi$ exactly, all I'm doing is plugging in the approximation for $M(t)$ to substitute for $N$. No other approximations are used, not even implicitly.
2d
reviewed Leave Open How can there be anything “beyond” the CMB?
2d
answered How can there be anything “beyond” the CMB?
Nov
23
comment Why does a particle feel no force at radii greater than itself?
+1 Huh. Honestly, even with the title of the question, this interpretation didn't even occur to me. But you are very likely correct that this is where the source of OP's confusion.
Nov
23
reviewed No Action Needed Astronomy Olympiad Books
Nov
23
awarded  Custodian
Nov
23
reviewed Close Humans surviving in space
Nov
23
answered Why does a particle feel no force at radii greater than itself?
Nov
23
reviewed No Action Needed Yellow object between δ Ori and η Ori
Nov
22
comment Hulse Taylor Binary Pulsar - How is “Cumulative Periastron Time shift” calculated?
@steveOw It's not assumption; it's just vocabulary. If $P$ were constant, then $1/P$ is orbital frequency; in time interval $\Delta t$, the number of (or fraction of) orbits completed is $\Delta t/P$. $P$ actually varies continuously, but that's what calculus is for: over infinitesimal $\mathrm{d}t$, the fraction of orbit traversed is $\mathrm{d}t/P$, and integration is adding them. Thus, $\int\mathrm{d}t/P$ is the exactly correct orbital count, regardless of whether one wishes to call its $2\pi$ scaling 'mean anomaly' or not. If prefer not, just replace 'mean anomaly' with 'orbital phase'.
Nov
16
comment Hulse Taylor Binary Pulsar - How is “Cumulative Periastron Time shift” calculated?
I've followed up on the PPN calculations for the $\dot{P} = KP^{-5/3}$ formula, and while your $K$ is a function of $e$, $e$ is itself not constant (should have checked sooner). But this makes very little difference because the rate of change of $e$ turns out to be quite negligible.
Nov
16
revised Hulse Taylor Binary Pulsar - How is “Cumulative Periastron Time shift” calculated?
failed to realize K is not actually a constant; corrected
Nov
16
revised Hulse Taylor Binary Pulsar - How is “Cumulative Periastron Time shift” calculated?
Cleaned up a bit and explained small time shift
Nov
16
revised Hulse Taylor Binary Pulsar - How is “Cumulative Periastron Time shift” calculated?
Added exact constant-K periastron shift formula
Nov
16
revised Hulse Taylor Binary Pulsar - How is “Cumulative Periastron Time shift” calculated?
added 1 character in body
Nov
16
comment Hulse Taylor Binary Pulsar - How is “Cumulative Periastron Time shift” calculated?
@steveOw $\dot{M} = 2\pi/P\,\implies\,\ddot{M} = -2\pi\dot{P}/P^2$. You have an extra factor of $2$.
Nov
16
revised Hulse Taylor Binary Pulsar - How is “Cumulative Periastron Time shift” calculated?
added 1528 characters in body