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Question
How much does planet Earth weigh
Answer
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.
The interesting sub-question is, "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:
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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.
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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.
أيضا هنا إيضاح آخر :http://www.grc.nasa.gov/WWW/K-12/airplane/wteq.html
Weight is the force generated by the gravitational attraction of the earth on any object. Weight is fundamentally different from the aerodynamic forces, lift and drag. Aerodynamic forces are mechanical forces and the object has to be in physical contact with the air which generates the force. The gravitational force is a field force; the source of the force does not have to be in physical contact with the object.
The nature of the gravitational force has been studied by scientists for many years and is still being investigated by theoretical physicists. For an object the size of an airplane flying near the earth, the descriptions given three hundred years ago by Sir Isaac Newton work quite well. Newton published his theory of gravitation with his laws of motion in 1686. The gravitational force, F, between two particles equals a universal constant, G, times the product of the mass of the particles, m1 and m2, divided by the square of the distance, d, between the particles.
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F = G * m1 * m2 / d^2
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If you have a lot of particles acting on a single particle, you have to add up the contribution of all the individual particles. For objects near the earth, the sum of the mass of all the particles is simply the mass of the earth and the distance is then measured from the center of the earth. On the surface of the earth the distance is about 4000 miles. Scientists have combined the universal gravitational constant, the mass of the earth, and the square of the radius of the earth to form the gravitational acceleration, g . On the surface of the earth, it's value is 9.8 meters per square second or 32.2 feet per square second.
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g = G * m earth / (d earth)^2
The weight W, or gravitational force, is then just the mass of an object times the gravitational acceleration.
W = m * g
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Since the gravitational constant (g) depends on the square of the distance from the center of the earth, we would expect that the weight of an object would decrease with altitude. Let's do a test problem to see how much the weight changes. If an airplane is flying at 35000 feet (about 7 miles) the distance to the center of the earth is about 4007 miles. We can calculate the change in the gravitational constant as the square of (4000/4007) which equals .9965. If the airplane weighs 10000 pounds on the surface of the earth, it weighs 9965 pounds at 35000 feet; it has lost 35 pounds, a very small amount compared to 10000 pounds.
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