What would happen if one planet was just deleted?

All bodies have a gravitational impact on all other bodies, but that impact is usually small enough to ignore.

For example, take Jupiter.  It is 1/1000th the mass of the Sun and 5 times farther away.  So Newton's F=GMm/(R^2) indicates the effect of Jupiter on the Earth is 1/25000 that of the effect of the Sun on Earth.  That is pretty negligible.  It's possible Jupiter's contribution has resulted in a slight increase in the Earth's orbital eccentricity - but not enough that our lives would be different if Jupiter had never existed.

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Robert Frost on Quora:

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