# If Earth started to lose mass, how would this affect its orbit around the sun?

Im building a world where the matter in the inner layers of the Earth starts to be replaced by a much lighter element causing earth to lose its mass. Would this eventually cause the Earth to leave the sun's orbit?

Edit: The matter is being replaced by a worm hole formed in the magma layer, of which leads to this lighter element (so its some sort of portal). I know it's not perfect science, but please assume the Earth loses its mass and heat and there are no other effects in play.

• If you are breaking physics, tell us all the ways that you are breaking physics. The question says that you are breaking the fundamental equivalence of mass and energy, because otherwise the immense gigantic humongous amount of energy liberated by the process would convert Earth into a dissipating cloud of plasma. It is essential to know whether you are also breaking conservation of momentum; that is, does the orbital speed of Earth increase so that the momentum is conserved, or does the orbital speed remain unaffected? Dec 26 '20 at 21:20
• If it happens on Earth, can such substitution happen on the Sun (and the Moon), too? Could such substitution have happened (repeatedly) in the past, changing both the Earth's orbit, the Moon's orbit, and the Sun's energy radiation greatly many times? (Which would, of course, preclude the development of complex life on Earth, so there won't be any observers to fret about the latest change) Dec 26 '20 at 21:24
• You need to explain specifically what this portal does. LIke, old molten rocks go away into the portal, fine. New lighter rocks come in, wait, with what velocity do they come in? In what direction are they going when they come in? You are speaking about a mind-blowing amount of reaction mass, basically a gigantic humongous reaction engine. You really need to specify which way this bigggg rocket engine is pointing. Feb 12 at 7:48
• (Simplest case: the old heavy rocks are replaced with new lighter rocks which have the exact same velocity with respect to the stars as the old rocks. In this case the orbit remains completely unchanged. The orbit of a body does not depend on the mass of the body, it only depends on the mass of the primary, the distance between the primary and the orbiting body, and the velocity of the orbiting body.) Feb 12 at 7:52

The orbit of a small object around a significantly more massive object is, for all intents and purposes, entirely unrelated to the mass of the small object. The sun is massive enough, and Earth is small enough by comparison, that the orbital equations can be simplified to a direct relationship between the orbital speed and orbital distance: $$v = \sqrt{\frac{GM}{r}}$$, where $$G$$ is the gravitational constant, $$M$$ is the mass of the larger body, and $$r$$ is the distance between the two centers of mass.

A 1.3 kilogram CubeSat, at the same orbital distance from the sun as Earth (1 AU), would have the same orbital period (1 year). The mass doesn't matter, even if the mass is changing.

What WOULD change is the orbit of the moon (and anything else orbiting Earth, natural or artificial). As Earth loses mass, its gravity will decrease, and Luna would begin to spiral outward into a higher orbit, farther away from the center of mass. Depending on how much mass is lost, Luna might escape Earth orbit completely.

Not at all. The gravitational pull the Earth gives the Sun is too slight for a planet that's slowly crumbling to have any big effect.

As the earth is light enough to not affect the sun earth barycenter a lot not much would happen to the orbit. The earth would retain its orbital velocity and continue in its track as normal. Now the surface is another matter. It might just melt due to the changes in preasure and density.

• "Earth would retain its orbital velocity": Only if the OP breaks conservation of momentum. Otherwise, the orbital speed will increase to compensate the diminution of mass. Since conservation of momentum is extremely fundamental in physics, I would think that the OP would have mentioned breaking it. (And if conservation of momentum is broken then all the physics is broken; nothing works the way it works in our world.) Dec 26 '20 at 23:31
• @AlexP The question assumes violation of conservation of mass. One may as well assume that momentum is lost in proportion. Dec 27 '20 at 2:18
• Conservation of momentum takes a FAR distant backseat to conservation of Mass, which the OP is not only violating, but making pay for the rohypnol used too. Feb 12 at 15:21