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you can calculate the mass with gravitational attraction between 2 objects from the equations:
F = (G) x (M1 x M2) / R2
G is a constant value
R2 is the radius between the 2 objects squared
M1 and M2 are the masses of the two objects.
using this formula, you can calculate the mass of the earth ecause we know what the value of F on earth: the gravitational constant 10 m/s2. G is a constant calculated by physics to be 6.7 x 10(-11). We know the radius of the earth to be 6400 kilometers.
after all that, it comes out to 6 x 10(24) kilograms in mass.
also you can never get the weight of earth calculated or estimated cause weight has to do with gravitational pull on an object. like you on earth have a weight cause earth pulls you down to it. the force you put out due to your mass is your weight. your weight will be different on other planets cause of mass and gravitational pull of planet, asteroid, star, or satelite(moon). since earth is not bound to anything then there is no weight for it. like magnus said the mass is calculated.
Answer this Question: "Earth"
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Earth
How do scientists know the weight of the earth do they have big scales.