3 ms·
A rule of thumb in classical mechanics is that 0.1c is when you should start taking (special) relativity into account, I think it’s 0.5% contribution then. For
by quchen 4y ago
A rule of thumb in classical mechanics is that 0.1c is when you should start taking (special) relativity into account, I think it’s 0.5% contribution then.
For general relativity I don’t know such a cutoff rule of thumb. Astronomy-wise, Mercury is the only planet that is obviously general-relativistic (its orbit is not an ellipse because it’s so close to the sun). On Earth, we don’t have strong/inhomogeneous enough gravity, so unless you’re synchronizing satellites or atomic clocks, GR is not something to worry about.
- thfuran 4y agoSome of the most precise clocks can actually measure precisely enough that a few feet of elevation change makes a measurable difference, which I expect also means that what you've placed under the table it's on also could.
- deleted 4y ago[deleted]
- vkou 4y agoMercury's orbit is absolutely an ellipse. It is incredibly elliptical, with an apogee of 69.8 million km, and a perigee of 46 million km. The relativistic effects on Mercury concern its precession - the way that elliptical orbit rotates [1] around the sun. And it's not caused by Mercury's speed (Which is only ~59 km/s at its maximum, compared to the Earth's 30 km/s). It's caused by spacetime being curved by the immense gravitational field of the sun. If Mercury had a circular orbit, it would have no precession. [1] Precession is akin to spinning a hula hoop around your body - with the hula hoop representing an orbit. https://en.wikipedia.org/wiki/Apsidal_precession https://en.wikipedia.org/wiki/Apsidal_precession
- joe__f 4y agoI think a good rule of thumb is 'check what accuracy you need your answer to, and then include all effects relevant to that precision'. If you needed an answer accurate to four significant figures, then you'd include relativistic effects for v < 0.1 c