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Mar 1, 2021 at 8:35 comment added timm I agree with your answer with this exception: "We constructed this system to be static, and static it is. The distance between the objects will not change over time". The proper distance will change over time because $\ddot{a}$ changes over time due to decreasing matter density (we talk about the $\Lambda$ dominated FRW-universe).
Feb 28, 2021 at 5:16 history answered benrg CC BY-SA 4.0