how is earth weighed?
It would be more proper to ask, "What is the mass of planet Earth?" 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:
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).
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.
Because we know the radius of the Earth, we can use the Law of Universal Gravitation to calculate the mass of the Earth in terms of the gravitational force on an object (its weight) at the Earth's surface, using the radius of the Earth as the distance. We also need the Constant of Proportionality in the Law of Universal Gravitation, G. This value was experimentally determined by Henry Cavendish in the 18th century to be the extremely small force of 6.67 x 10-11 Newtons between two objects weighing one kilogram each and separated by one meter. Cavendish determined this constant by accurately measuring the horizontal force between metal spheres in an experiment sometimes referred to as "weighing the earth."
Knowing the mass and radius of the Earth and the distance of the Earth from the sun, we can calculate the mass of the sun (right), again by using the law of universal gravitation. The gravitational attraction between the Earth and the sun is G times the sun's mass times the Earth's mass, divided by the distance between the Earth and the sun squared. This attraction must be equal to the centripetal force needed to keep the earth in its (almost circular) orbit around the sun.
The centripetal force is the Earth's mass times the square of its speed divided by its distance from the sun. By astronomically determining the distance to the sun, we can calculate the earth's speed around the sun and hence the sun's mass.
Once we have the sun's mass, we can similarly determine the mass of any planet by astronomically determining the planet's orbital radius and period, calculating the required centripetal force and equating this force to the force predicted by the law of universal gravitation using the sun's mass.
Remember that the strength of attraction between two small masses will be extremely small. Despite the weakness of the attraction, Henry Cavendish was able to perform an experiment to measure the force between two small objects which allowed him to measure the gravitational constant (G).
For his experiment in 1798, Cavendish hung a dumbbell from a fine string. He then placed two large lead weights below the dumbbell, and was able to see a small twisting in the string. From this small twist in the string he was able to measure the force between the objects. After measuring the force, masses, and distance, the gravitational constant could be calculated. Below is a modern version of the Cavendish experiment.
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:
- 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.
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).
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.
Because we know the radius of the Earth, we can use the Law of Universal Gravitation to calculate the mass of the Earth in terms of the gravitational force on an object (its weight) at the Earth's surface, using the radius of the Earth as the distance. We also need the Constant of Proportionality in the Law of Universal Gravitation, G. This value was experimentally determined by Henry Cavendish in the 18th century to be the extremely small force of 6.67 x 10-11 Newtons between two objects weighing one kilogram each and separated by one meter. Cavendish determined this constant by accurately measuring the horizontal force between metal spheres in an experiment sometimes referred to as "weighing the earth."
Knowing the mass and radius of the Earth and the distance of the Earth from the sun, we can calculate the mass of the sun (right), again by using the law of universal gravitation. The gravitational attraction between the Earth and the sun is G times the sun's mass times the Earth's mass, divided by the distance between the Earth and the sun squared. This attraction must be equal to the centripetal force needed to keep the earth in its (almost circular) orbit around the sun.
The centripetal force is the Earth's mass times the square of its speed divided by its distance from the sun. By astronomically determining the distance to the sun, we can calculate the earth's speed around the sun and hence the sun's mass.
Once we have the sun's mass, we can similarly determine the mass of any planet by astronomically determining the planet's orbital radius and period, calculating the required centripetal force and equating this force to the force predicted by the law of universal gravitation using the sun's mass.
Remember that the strength of attraction between two small masses will be extremely small. Despite the weakness of the attraction, Henry Cavendish was able to perform an experiment to measure the force between two small objects which allowed him to measure the gravitational constant (G).
For his experiment in 1798, Cavendish hung a dumbbell from a fine string. He then placed two large lead weights below the dumbbell, and was able to see a small twisting in the string. From this small twist in the string he was able to measure the force between the objects. After measuring the force, masses, and distance, the gravitational constant could be calculated. Below is a modern version of the Cavendish experiment.
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click here to go to article on discovery of Earth like planet which is orbiting a nearby Star
Click here for article about Voyager spacecraft that left our solar system and contains a golden record which is the first human message sent out into deep space
Click here for video explaining interstellar plan for drones to go to nearest star cluster outside our solar system and explore for habitable planet
click here for article about cycles in the Earth's orbital shape from circular to elliptical by the NYT
Click here for an article about the newly located planet "Goblin" that has an ecentric orbit
“Gravity is the force of attraction that makes things fall straight down.”
Well, yes — depending on what we mean by “force.” We can say gravitation is one of the four fundamental forces, but it’s such an outlier that the word “force” becomes nearly meaningless. The strong nuclear force (which keeps atomic nuclei intact) is about 100 times stronger than the electromagnetic force (which creates the light spectrum), which in turn is up to 10,000 times stronger than the weak nuclear force (which facilitates the subatomic interactions responsible for radioactive decay). Three forces, all within six orders of magnitude of one another. Then comes gravitation. It’s about a million billion billion billion times weaker then the weak nuclear.
To put that discrepancy into perspective, you can try this experiment at home. Place a paper clip on a tabletop. There it remains, unmoving, anchored to its spot by its gravitational interaction with the entire planet beneath it. The Earth’s mass is 6,583,003,100,000,000,000,000 tons. A paper clip’s mass is 4/100 of an ounce. Now take a refrigerator magnet and wand it over the paper clip. Presto! You have counteracted the gravitational “force” of the entire Earth with a wave of your hand.
Even more unnerving to physicists is that gravitation is the only force that doesn’t have a quantum solution — a theory that explains the force in terms of subatomic particles.
So let’s strike “force” from our answer. In that case: “Gravity is the attraction that makes things fall straight down.”
Well, yes — depending on what we mean by “attraction.” Two bodies of mass don’t actually exert some mysterious tugging on each other. Newton himself tried to avoid the word “attraction” for this very reason. All (!) he was trying to do was find the math to describe the motions both down here on Earth and up there among the planets (of which Earth, thanks to Copernicus and Kepler and Galileo, was one). Still, he was as powerless as a paper clip once the idea of attraction at a distance electrified the public.
So: “Gravity is what makes things fall straight down.”
Well, yes — depending on what we mean by “straight down.” The path seems straight only because you’re standing still relative to the Earth. As Galileo realized, if you drop a rock from the mast of a ship traveling on a river, its trajectory will appear to be an angle to an observer on the shore. Similarly, to someone outside the Earth who is observing a rock falling on our spinning planet, the path would appear to be on an angle. But the Earth is also orbiting the Sun, so that angle would actually be swooping, creating the appearance of a curve. And because the Sun is orbiting the center of the galaxy, that curve would be a very long curve. And the galaxy is moving toward other galaxies, and the universe is expanding, and the expansion is accelerating: How long and curlicued the rock’s trajectory appears depends wholly on where you are in relation to it.
So: “Gravity is what makes things fall.”
Well, yes — depending on what we mean by “fall.” We can just as easily argue — as Einstein did, expanding on Galileo’s ship/shore relativism — that the rock isn’t falling toward the Earth but that the Earth is rising toward the rock.
So: “Gravity is.”
Well, yes — depending on what we mean by “is.” We know what gravity does, in the sense that we can mathematically measure and predict its effects. We might anticipate what happens when two black holes collide or when we let go of a rock. But we don’t know how it does what it does. We know what its effects are, and we can give the name “gravity” to the cause of those effects, but we don’t know the cause of that cause.
Not that cosmologists particularly care. In science, knowing what you don’t know is a good start. In this case, it has led scientists to believe that finding a quantum solution to gravity is a key — perhaps the key — to understanding the universe on the most fundamental level. Until then, they will work with what they do know, no matter what every bone in their bodies tells them:
Gravity is not the force of attraction that makes things fall straight down.
Well, yes — depending on what we mean by “force.” We can say gravitation is one of the four fundamental forces, but it’s such an outlier that the word “force” becomes nearly meaningless. The strong nuclear force (which keeps atomic nuclei intact) is about 100 times stronger than the electromagnetic force (which creates the light spectrum), which in turn is up to 10,000 times stronger than the weak nuclear force (which facilitates the subatomic interactions responsible for radioactive decay). Three forces, all within six orders of magnitude of one another. Then comes gravitation. It’s about a million billion billion billion times weaker then the weak nuclear.
To put that discrepancy into perspective, you can try this experiment at home. Place a paper clip on a tabletop. There it remains, unmoving, anchored to its spot by its gravitational interaction with the entire planet beneath it. The Earth’s mass is 6,583,003,100,000,000,000,000 tons. A paper clip’s mass is 4/100 of an ounce. Now take a refrigerator magnet and wand it over the paper clip. Presto! You have counteracted the gravitational “force” of the entire Earth with a wave of your hand.
Even more unnerving to physicists is that gravitation is the only force that doesn’t have a quantum solution — a theory that explains the force in terms of subatomic particles.
So let’s strike “force” from our answer. In that case: “Gravity is the attraction that makes things fall straight down.”
Well, yes — depending on what we mean by “attraction.” Two bodies of mass don’t actually exert some mysterious tugging on each other. Newton himself tried to avoid the word “attraction” for this very reason. All (!) he was trying to do was find the math to describe the motions both down here on Earth and up there among the planets (of which Earth, thanks to Copernicus and Kepler and Galileo, was one). Still, he was as powerless as a paper clip once the idea of attraction at a distance electrified the public.
So: “Gravity is what makes things fall straight down.”
Well, yes — depending on what we mean by “straight down.” The path seems straight only because you’re standing still relative to the Earth. As Galileo realized, if you drop a rock from the mast of a ship traveling on a river, its trajectory will appear to be an angle to an observer on the shore. Similarly, to someone outside the Earth who is observing a rock falling on our spinning planet, the path would appear to be on an angle. But the Earth is also orbiting the Sun, so that angle would actually be swooping, creating the appearance of a curve. And because the Sun is orbiting the center of the galaxy, that curve would be a very long curve. And the galaxy is moving toward other galaxies, and the universe is expanding, and the expansion is accelerating: How long and curlicued the rock’s trajectory appears depends wholly on where you are in relation to it.
So: “Gravity is what makes things fall.”
Well, yes — depending on what we mean by “fall.” We can just as easily argue — as Einstein did, expanding on Galileo’s ship/shore relativism — that the rock isn’t falling toward the Earth but that the Earth is rising toward the rock.
So: “Gravity is.”
Well, yes — depending on what we mean by “is.” We know what gravity does, in the sense that we can mathematically measure and predict its effects. We might anticipate what happens when two black holes collide or when we let go of a rock. But we don’t know how it does what it does. We know what its effects are, and we can give the name “gravity” to the cause of those effects, but we don’t know the cause of that cause.
Not that cosmologists particularly care. In science, knowing what you don’t know is a good start. In this case, it has led scientists to believe that finding a quantum solution to gravity is a key — perhaps the key — to understanding the universe on the most fundamental level. Until then, they will work with what they do know, no matter what every bone in their bodies tells them:
Gravity is not the force of attraction that makes things fall straight down.