Kepler's second law says that planets sweep equal areas in equal times in their orbits; the closer a planet is to its parent body, the faster it moves; the farther it is, the slower it moves. This is explained by the conservation of angular momentum, which is $m * v * r$.

$m$ is the planet's mass

$v$ is the planet's orbital velocity

$r$ is its distance from the parent body

As $r$ decreases, $v$ must increase to maintain the momentum.


Why is $v$ "chosen by the Universe" to be the value that changes in this phenomena and never $m$? I've only heard of mass being modified theoretically, when something is attempting to increase $v$ beyond the speed of light. If that's true, why does mass remain immutable until that point?

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    $\begingroup$ People, don't flag this question for deletion: it doesn't show lack of effort. It shows a confusion about basic concepts that would be pretty hard do solve your own. $\endgroup$
    – stafusa
    Aug 31, 2017 at 20:19

1 Answer 1


The universe doesn't make such assumptions. We do. In the majority of the problems you will use conservation of angular momentum for, the nature of the problem dictates that the mass will remain the same. Mass doesn't appear out of nowhere! Mass is conserved. Velocity is not.

There are plenty of physics problems which involve the sudden addition of mass (such as if someone throws an object at you and you catch it). In these cases, mass can change rather than velocity. Or both can change!

As for why mass is conserved, that's a philosophical question which stems beyond science. That's where we have to start admitting that things like "conservation of mass" is a model of how reality works, not the definition of how reality works. However, if we are willing to handwave that aside and say that "conservation of mass" is such a good model that we can treat it as though it is reality, then we're back to my first paragraph -- we assumed the mass didn't change, because the model says it wont.

  • $\begingroup$ In other words, mass, like angular momentum, is protected as a conserved property (antimatter annihilation stuff aside) while velocity isn't, so velocity is what changes to conserve momentum while also conserving mass, and why some properties are conserved while others aren't (which I guess is what my question migrates to) is fundamentally unknowable? $\endgroup$ Aug 31, 2017 at 23:00
  • $\begingroup$ @Kat Correct. Or, to be a bit more precise, the question of "why" the universe does what it does, at the most fundamental level, is fundamentally unknowable using the empirical approaches of science. If you are interested in the topic, two key words you can look at are ontology and epistemology. Science, in its truest form, is an epistemological way of thinking. In particular, it is empirical, which is a subset of epistemology. $\endgroup$
    – Cort Ammon
    Aug 31, 2017 at 23:03
  • $\begingroup$ Sometimes science can explain one phenomena using a lower level phenomena, such as explaining magnetism via relativistic effects on electric fields, but if you follow those rabbit holes all the way down, asking "why" at each layer, you eventually will reach topics where we have no ontological answer, and all we can say is "all empirical evidence suggests that it works this way." $\endgroup$
    – Cort Ammon
    Aug 31, 2017 at 23:05

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