No, Earth’s mass changes constantly because *it is not a closed system*. Material is constantly being added to Earth from space, and other material is constantly being lost from Earth into space as well. Compared to the mass of Earth, this mass gaining and losing is very small, but in absolute terms it’s quite a bit of stuff:
* **Earth is gaining 45,000 tons per year**, mostly from picking up space dust and pulling in small meteorites. But
* **Earth is losing about 100,000 tons per year** from the loss of the atmosphere’s lightest gases drifting off into space.
That comes out to a **net loss of about 55,000,000 kg per year**! Multiply that by 1000x to get the change in grams like you were asking about.
However, even that large-seeming mass is actually smaller than the +/- range on our current best estimate of Earth’s mass, so this mass loss is too small to affect the estimate right now.
[https://en.wikipedia.org/wiki/Earth_mass#Variation](https://en.wikipedia.org/wiki/Earth_mass#Variation)
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