Measuring the Mass of the Earth Measuring the acceleration of an object dropped to the ground enables you to find the mass of the Earth. You can rearrange the gravity acceleration relation to solve for the mass M to find M = g d 2 /G . Close to the Earth's surface at a distance of 6.4 × 10 6 meters from the center, g = 9.8 meters/second 2 . The distance is given in meters to match the units of the gravity acceleration---when you do a calculation, you must be sure you check that your units match up or you will get nonsense answers. The big G is the universal gravitational constant, approximately 6.7×10-11 m 3 / (kg sec 2 ). Plugging in the values, you will find the Earth's mass = 9.8 × (6.4×10 6 ) 2 / (6.7 × 10-11 ) kilograms = 6.0 × 10 24 kilograms. If you are unsure of how to work with scientific notation, read the scientific notation section in the mathematics review appendix (pay close attention to the part describing how to enter scientific notation on your calculator!). You can determine masses of stars and planets in a similar way: by measuring the acceleration of
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