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Subject If I travelled towards the centre of the earth would my mass increase or decrease?

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Original Message If gravity theory is correct then I should increase in mass due to the closer distance to the core?
But at the core the mass must be 0!?
As in if we drilled a hole all the way through the earth and jumped in then we would accelerate and exceed the center then reverse in slowly reducing cycles until we end up stationary in the center...

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