Is momentum conserved as a body falls through a gravitational field?

In summary, momentum is not conserved for a single body falling through a gravitational field when considering the system in isolation, as the gravitational force acts on the body, causing a change in momentum. However, if the system includes both the falling body and the Earth, momentum is conserved overall, as the increase in the body's momentum is balanced by an equal and opposite change in the Earth's momentum.
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cianfa72 said:
Why not ? Could you be more specific ?
Because the energy and momentum "stored in a gravitational field" cannot be localized the way energy and momentum stored in an EM field can be. In more technical language, there is no stress-energy tensor for the "gravitational field" in GR, the way there is for the EM field.
 
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