2006-09-08 05:42:17 · 12 answers · asked by F S 1 in Science & Mathematics ➔ Earth Sciences & Geology
Using Newtons Law of Universal Gravitation, F=GMm/r^2. The gravitational constant G can be measured in the lab by measuring the attractive force between two objects. Then, knowing the radius of the Earth, you can calculate the mass of the Earth from the acceleration of gravity at the surface. First done by Cavendish in 1798.
2006-09-08 05:54:15 · answer #1 · answered by injanier 7 · 1⤊ 1⤋
It would be more proper to ask, "What is the mass of planet Earth?" (1) The quick answer to that is: approximately 6,000,000,000,000,000,000,000,000 (6E+24) kilograms.
Now, How did anyone figure that out? It's not like the planet steps onto the scale each morning before it takes a shower. The measurement of the planet's weight is derived from the gravitational attraction that the Earth has for objects near it.
It turns out that any two masses have a gravitational attraction for one another. If you put two bowling balls near each other, they will attract one another gravitationally. The attraction is extremely slight, but if your instruments are sensitive enough you can measure the gravitational attraction that two bowling balls have on one another. From that measurement, you could determine the mass of the two objects. The same is true for two golf balls, but the attraction is even slighter because the amount of gravitational force depends on mass of the objects.
Newton showed that, for spherical objects, you can make the simplifying assumption that all of the object's mass is concentrated at the center of the sphere. The following equation expresses the gravitational attraction that two spherical objects have on one another:
F = G * M1 * M2 / R2
R is the distance separating the two objects.
G is a constant that is 6.67259x10-11m3/s2 kg.
M1 and M2 are the two masses that are attracting each other.
F is the force of attraction between them.
Assume that Earth is one of the masses (M1) and a 1-kg sphere is the other (M2). The force between them is 9.8 kg*m/s2 -- we can calculate this force by dropping the 1-kg sphere and measuring the acceleration that the Earth's gravitational field applies to it (9.8 m/s2).
The radius of the Earth is 6,400,000 meters (6,999,125 yards). If you plug all of these values in and solve for M1, you find that the mass of the Earth is 6,000,000,000,000,000,000,000,000 kilograms (6E+24 kilograms / 1.3E+25 pounds).
(1) It is "more proper" to ask about mass rather than weight because weight is a force that requires a gravitational field to determine. You can take a bowling ball and weigh it on the Earth and on the moon. The weight on the moon will be one-sixth that on the Earth, but the amount of mass is the same in both places.
To weigh the Earth, we would need to know in which object's gravitational field we want to calculate the weight. The mass of the Earth, on the other hand, is a constant
2006-09-08 05:52:51 · answer #2 · answered by roshpi 3 · 3⤊ 1⤋
In addition to calculating the mass of the Earth based on the gravitational attraction it has on other objects, it is also possible to approximate that mass based on the size and density of the planet.
We know that the Earth is about 8000 miles in diameter, and we know that the average density of the Earth is about 5.5 g/cc. Computing these together, we can figure out how much the planet weighs, and what gravitational attraction it possesses.
We can do this for other planets as well. If you know the diameter of the planet, and how much gravitational attraction it possesses, you can figure out how dense the planet is (so we know that Saturn has an average density below that of water). You can also use it to figure out how much stronger a planet's gravitational pull would be if it were made of denser material (such as planet made of lead, or neutronium)
2006-09-08 06:04:21 · answer #3 · answered by Anonymous · 0⤊ 1⤋
hmm you can't really weigh the earth becuase there is no giant scale, and weight is only the measurement of gravity between two objects so... tech earth has no weight. but you could measure the mass of the earth, probably using radar waves to get the density.
2006-09-08 05:45:08 · answer #4 · answered by michaeln_2006 2 · 1⤊ 2⤋
With a very large scale...the kind used to weigh Roseanne Barr.
2006-09-08 05:56:56 · answer #5 · answered by Hugh Jafro 2 · 0⤊ 1⤋
Just the earth? Or buildings, cars, human beings, animals, etc.
2006-09-08 05:44:20 · answer #6 · answered by horrorfan 3 · 0⤊ 1⤋
Well you can't you can only aproximate.
unless someone has an idea on how much it weighs then find out how he did it.
2006-09-08 05:44:12 · answer #7 · answered by Anonymous · 0⤊ 2⤋
Use a very, very large scale scale.
2006-09-08 05:56:34 · answer #8 · answered by beast 6 · 1⤊ 0⤋
huh??? weigh the earth/?? im confused!!!!!!!
2006-09-12 03:48:21 · answer #9 · answered by krista 2 · 0⤊ 0⤋
the gravitational force law allows the mass of the earth to be measuresd based on how it gravitationally attracts the moon
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2006-09-08 05:43:29 · answer #10 · answered by absoluteao 3 · 2⤊ 3⤋