Timeline for Kepler's second law in General Relativity
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 31, 2020 at 6:47 | history | bounty ended | Faber Bosch | ||
| Dec 31, 2020 at 6:45 | vote | accept | Faber Bosch | ||
| Dec 30, 2020 at 4:08 | history | edited | user142288 | CC BY-SA 4.0 |
add discussion on correction
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| Dec 28, 2020 at 8:45 | vote | accept | Faber Bosch | ||
| Dec 28, 2020 at 15:44 | |||||
| Dec 28, 2020 at 8:02 | vote | accept | Faber Bosch | ||
| Dec 28, 2020 at 8:02 | |||||
| Dec 28, 2020 at 7:14 | comment | added | user142288 | 1, $dA=\sqrt{\gamma} dr d\phi$; 2, taking the limit, such that the sun can be regarded as point, 3, the $1/2$ comes from the integrating out the $dr$ | |
| Dec 28, 2020 at 7:11 | comment | added | Faber Bosch | I don't see where the factor of half comes from. Can you please elaborate? $dA=\sqrt{\gamma}rd\phi=r^2/\sqrt{1-r_s/r}d\phi$ ?. We are not allowed to use the formula $\frac{1}{2}(\text{base})(\text{height})$ in curved spaces, right? | |
| Dec 28, 2020 at 7:04 | comment | added | user142288 | The mesure is $\sqrt{\gamma}=r/\sqrt{1-1/r}$, then take the limit, where the sun can be regarded as point. | |
| Dec 28, 2020 at 7:01 | comment | added | Faber Bosch | Okay, I see. I didn't refresh the page earlier. Please write down the precise formula for $dA$ before taking the limit. Because I want to know the order of the error. | |
| Dec 28, 2020 at 6:56 | comment | added | user142288 | @Faber Bosch see the renewed answer. | |
| Dec 28, 2020 at 6:55 | comment | added | Faber Bosch | State the reason why you think @JerrySchirmer 's comment is irrelevant? How do you calculate infinitesimal area on the $r$-$\phi$ plane? and how do you adjust for the $\sqrt{-g_{00}}$ factor for considering coordinate time instead of proper time? | |
| Dec 28, 2020 at 6:49 | comment | added | user142288 | @Faber Bosch, I think that is sufficient. | |
| Dec 28, 2020 at 6:48 | history | edited | user142288 | CC BY-SA 4.0 |
improve
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| Dec 28, 2020 at 6:21 | comment | added | Faber Bosch | Showing $r^2\frac{d\phi}{d\tau}$ is not sufficient. See @JerrySchirmer 's comment. | |
| Dec 28, 2020 at 5:43 | history | answered | user142288 | CC BY-SA 4.0 |