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The mass is already roughly there. One thing to bear in mind - if you replaced the Sun with a black hole of equal mass, planets wouldn't change orbits. It's the
by 46Bit 15y ago
The mass is already roughly there. One thing to bear in mind - if you replaced the Sun with a black hole of equal mass, planets wouldn't change orbits. It's the same gravity and centre of mass, just a different density/volume.
- TheEzEzz 15y agoThis is true for Newtonian gravity, but only approximately true for general relativity (or so I understand it).
- dakr 15y agoThis includes the effects of general relativity. As long as the mass is the same, the orbits of planets will remain the same.
- TheEzEzz 15y agoAccording to wikipedia[1] the converse of the Shell Theorem is (nearly) true: Suppose there is a force F between masses M and m, separated by a distance r of the form F = Mmf(r) such that any spherically symmetric body affects external bodies as if its mass were concentrated at its centre. Then what form can the function f take? The form of f allows Newtonian gravity but not Einsteinian. [1] http://en.wikipedia.org/wiki/Shell_theorem#Converses_and_generalisations http://en.wikipedia.org/wiki/Shell_theorem#Converses_and_gen...
- 46Bit 15y agoInteresting. However, I would have thought that planets are far out enough that classical is accurate enough. This sort of thing is why I specified planets as opposed to orbits in general.
- T-hawk 15y agoThe key point there is "spherically symmetric". The Sun isn't. It bulges around its equator thanks to rotation, as does everything. That does have effects on planetary motion; an object in an inclined orbit spends a bit more time a bit farther away from a bit of the Sun's mass. Replace the Sun with a black hole of equal mass and you don't have that oblateness. The effect on planetary orbits would be very small, so macroscopically the Solar System would still be the same, just with very slight differences in orbital speeds and periods.
- deleted 15y ago[deleted]