Timeline for Units for orbital period and gravitational constant
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 24 at 14:54 | comment | added | David Hammen | @uhoh That's how the au is defined since 2012. The astronomic unit formerly was defined as the distance from the Sun at which a particle of negligible mass would have an unperturbed circular orbit about the Sun with a mean motion of 0.0172020989500 radians per day, or $2\pi$ radians per 365.256898326 days, the value that astronomers at the start of the 19th century thought to be the length of a sidereal year. (The currently accepted value is 365.256363004 days.) Note that 0.0172020989500 is the numerical value of the Gaussian gravitational constant. | |
| Feb 24, 2022 at 23:40 | comment | added | uhoh | @Walter potentially, but an AU is defined by the speed of light and the second and not Earth's semi-major axis, and year is based on a second which is based on "transition between the hyperfine levels of the unperturbed ground state of the 133Cs atom" and not Earth's period, so I'm not sure in the end which one is is going to turn out to be closer. Because of all the perturbations from Venus and Jupiter et al. I'm not sure how periodic Earth's orbit even is. | |
| Feb 24, 2022 at 18:50 | comment | added | Walter | This is more exact than using SI units, since $GM_{Sun}$ is much more precisely known than either $G$ or $M_{Sun}$. | |
| Feb 23, 2022 at 20:18 | comment | added | Norman Gray | ...and, put another way, we can see this explicitly by simply converting units (ie, there's nothing exotic going on). $G=6.67x10^{-11} N.m^2.kg^{-2} = 6.67x10^{-11} m^3.s^{-2}.kg^{-1}$. With the unit conversions above, that turns directly into $39.47 AU^3.yr^{-2}.Msun^{-1}$. Lovely: I'd never thought of $G=(2\pi)^2$ in the right units (of course, it's also G=1 in the other right units...) | |
| Feb 23, 2022 at 1:21 | comment | added | TLW | If anyone is wondering how on Earth this works out - remember that ~1 AU is the distance at which a body in orbit around a ~1 solar-mass body has an orbital period of ~1 year. | |
| Feb 22, 2022 at 22:07 | history | edited | uhoh | CC BY-SA 4.0 |
Thanks to PM2Ring
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| Feb 22, 2022 at 13:17 | history | edited | uhoh | CC BY-SA 4.0 |
added 11 characters in body
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| Feb 22, 2022 at 13:12 | history | answered | uhoh | CC BY-SA 4.0 |