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Oct
28
awarded  Nice Answer
Oct
24
comment Is there a standard mapping of symbols to terms for celestial and orbital mechanics
@Dieudonné Everyone used Roman-faced $\exp$, yes, but I don't see one prescribing $\mathrm{e}^\ldots$ rather than $e^\ldots$ when used Euler's number is referred to directly? Hmm..
Oct
24
comment Is there a standard mapping of symbols to terms for celestial and orbital mechanics
@Dieudonné That might be a good practice to adopt, but whose standard is it? I honestly can't recall even seeing even a single physics author uses a Roman-face $\mathrm{e}$ for Euler's constant. Out of sheer boredom, I've double-checked a few of the books in my immediate vicinity that had reasons to discuss electrons--ones by D.Griffiths (QM), J.J.Sakurai (QM), R.Shankar (QM), A.Zee (QFT), J.Polchinski (ST), J.D.Jackson (EM)--and every single one of them had an unremarkable $e$ for Euler's constant.
Oct
24
comment Mass of sun's core
@LCD3 pressure.
Oct
24
comment Is there a standard mapping of symbols to terms for celestial and orbital mechanics
@HDE226868 From any introductory quantum mechanics textbook, the radial part of the ground state is $2a_0^{-3/2}e^{-r/a_0}$, where $a_0 = 4\pi\epsilon_0\hbar^2/me^2$ is the Bohr radius; use of units of $4\pi\epsilon_0=1$ is a simplification. However, I confess that I've never seen it written out all at once with the Bohr radius substituted in and $e$ (as opposed to $\exp$) for the exponential, except as an illustration of just this point of overloading letters. (This particular use, IIRC, is from The Tau Manifesto.)
Oct
24
comment Is there a standard mapping of symbols to terms for celestial and orbital mechanics
I give you the radial component of the electron wavefunction for the ground state of hydrogen (in units of $4\pi\epsilon_0=1$): $$\psi(r) = \frac{m^{3/2} e^3}{\pi^{1/2} \hbar^3}\,e^{-m e^2 r/\hbar^2}\text{.}$$ Notably, $e$ plays a dual role even in the same equation (Euler's constant or fundamental charge). If I were evil, I'd also play with $\pi$ used for the transcendental number and conjugate momentum at once.
Oct
23
answered Mass of sun's core
Oct
23
comment How do we know that the speed of the influence of gravity is instant?
@KeithThompson yes, that's right, with minor caveats. We'd detect gravitational waves if the Sun's quadrupole moment changes violently in the collapse about 8 minutes afterward. (I phrase things this way because, e.g., a spherically symmetric core collapse wouldn't gravitationally radiate.)
Oct
16
comment How much would you weigh if Earth stopped orbiting the Sun?
@DavidHammen yes, I thought so to at first, that's why I answered both interpretations: freefall and held still, one after another. As to how it would be held still, that's not relevant; there are stranger unrealistic questions in introductory mechanics classes.
Oct
16
comment How much would you weigh if Earth stopped orbiting the Sun?
@DavidHammen no, what you're calculating are tidal forces. I interpreted the question as comparing the weight when the Earth is held still vs when it's orbiting, not at comparing different locations on the Earth. When it's held still, the Sun's $5.9\,\mathrm{mm}/\mathrm{s}^2$ is felt in addition to Earth's gravity (well, or subtractively, depending on location).
Oct
16
revised How much would you weigh if Earth stopped orbiting the Sun?
added 813 characters in body
Oct
16
answered How much would you weigh if Earth stopped orbiting the Sun?
Oct
16
comment What is the correct ratio of Newtonian to General Relativistic gravitational effects for Sun + single planet orbital system
David is of course correct in that this kind of comparison only makes sense for slow orbits in a weak-field approximation, though fortunately that's also the context of this question. It may be noted that for the specific case of Schwarzschild spacetime, orbits are exactly described by the effective potential; the approximation comes in when one treats the radial coordinate and proper time as if they were Newtonian, which is invalid in more general situations.
Oct
15
comment What is the correct ratio of Newtonian to General Relativistic gravitational effects for Sun + single planet orbital system
@steveOw yeah, I misread how the variables were defined too. Eh!
Oct
15
revised What is the correct ratio of Newtonian to General Relativistic gravitational effects for Sun + single planet orbital system
Rewrite; previous version based on silly misread of how variables were defined.
Oct
15
answered What is the correct ratio of Newtonian to General Relativistic gravitational effects for Sun + single planet orbital system
Oct
15
comment why do we look at dark energy as an energy?
You can apply the formula to find a mass density if you like, but the point was only that unlike the previous cases, you can't decompose dark energy into a collection of massive particles zipping about.
Oct
15
answered why do we look at dark energy as an energy?
Oct
14
comment Is it dark inside a black hole?
This is incorrect: "You wouldn't see the object in front of you since the light would not reach your eye." That would violate the equivalence principle; besides, a Penrose diagram of a black hole spacetime clearly implies that this is incorrect in without some substantial qualification.
Oct
14
answered Time period in which a planet rotates