How do scientist measured the earth's mass?

Answer 1

Here's one way to do it:

-- Take a rock.

-- Fit it with a model-rocket engine of known force. Light the engine to propel the rock along an air-hockey
table or a smooth ice-skating rink, marked off in distance. Have several observers with stop-watches.

-- Get reliable measurements of exactly how long the model rocket engine burned, and exactly how far the rock
slid while the engine burned. Knowing the force of the model rocket engine, calculate the rock's mass.

-- Put the rock on a scale. Measure its weight. Another name for "weight" is "mutual gravitational force
between the earth and another object".

-- Knowing the mass of the rock, the distance between the center of the earth and the center of the rock
(the earth's radius), and the gravitational force between the earth and the rock (weight of the rock, use
Newton's law of universal gravitation to calculate the mass of the earth.

I tried this once many years ago, in a presentation to a church group of kids in Perry, Oklahoma.
It was called "Let's Weigh the Earth". Instead of a rock, we used a toy car with a model rocket engine
glued to it, running on a long table. We got as far as seeing the toy car go into orbit and take out the
light fixture on the ceiling, a split second after the model rocket engine burned a deep furrow into the
expensive table-top. The observers screamed and forgot to read their stop-watches, and we never did
weigh the earth. But I'm sure it hasn't changed much since then, and I wish you the best of luck in your
quest to succeed where I failed so dramatically, back when dinosaurs roamed Oklahoma.