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The depth of the ocean can be measured using principles such as sonar wherein a wave with a known speed is projected towards the bottom surface and the time lapsed until the wave returns is divided by two and them multiplied by the speed of the wave in order to calculate the distance traveled in one direction.

The diameter of the earth can be calculated numerous ways, one of which is to measure the change in angle of the earth between two points (e.g. the change in apparent height of a ship at sea level as the distance from the observer increases) and then extrapolate the total circumference of the earth, diameter can then be solved for by dividing the circumference by Pi.

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