Newton measures the speed of gravity

In summary, The conversation is about trying to figure out what equation Newton used for gravity before the force of gravity and the mass of the Earth were known. The equation (Gm1m2)/r^2 = (m2v2)/r is mentioned, but it is determined that Newton could not have used it because he did not know the values of G or the mass of the Earth. Another equation (a = v^2/r) is also considered, but it is noted that Newton did not know the acceleration. The conversation ends with the suggestion that the acceleration of the moon and an object on the surface of the Earth can be used to determine the 1/r^2 relationship.
  • #1
bobsmith76
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Homework Statement



This doesn't come from a textbook but it's like a homework question so I thought it would be more appropriate here.

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Screenshot2012-02-26at72340PM.png

I'm trying to figure out what equation Newton used since the force of gravity or the mass of the Earth was not known until Cavendish. I'm looking for an equation that has the square of the distance or the radius, but all I can find is

(Gm1m2)/r^2 = (m2v2)/r

But Newton couldn't have used that one because he didn't know G or the mass of the Earth. I also thought about a = (v^2)/r but Newton didn't know the acceleration.
 
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  • #2
In this case, you can calculate the acceleration of the moon from its angular speed and radius:

a = v^2/r = 4∏^2r/T^2

By measuring the acceleration of the moon and of an object on the surface of the earth, you get the 1/r^2 relationship.

AM
 
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FAQ: Newton measures the speed of gravity

What is Newton's method for measuring the speed of gravity?

Newton's method for measuring the speed of gravity involves using his law of universal gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. By measuring the force of gravity between two objects and knowing their masses and distance, Newton was able to calculate the speed of gravity.

How did Newton determine the speed of gravity?

Newton determined the speed of gravity by conducting experiments with falling objects. He measured the distance that an object fell under the influence of gravity and calculated the time it took to fall. By using his law of universal gravitation and his second law of motion, he was able to calculate the speed of gravity.

What is the value of Newton's measurement for the speed of gravity?

The value of Newton's measurement for the speed of gravity is approximately 9.8 meters per second squared. This is the acceleration due to gravity on Earth, which is commonly denoted as "g". However, it is important to note that Newton's measurement was an estimate and the actual speed of gravity may vary in different conditions.

How accurate is Newton's measurement for the speed of gravity?

Newton's measurement for the speed of gravity is considered to be relatively accurate for his time. However, with advancements in technology and scientific understanding, more precise measurements have been made. For example, the current accepted value for the acceleration due to gravity on Earth is 9.80665 meters per second squared, which is slightly different from Newton's measurement.

Why is Newton's measurement for the speed of gravity important?

Newton's measurement for the speed of gravity is important because it provided a foundational understanding of gravity and its effects on objects. It also helped to support his theory of universal gravitation, which revolutionized the field of physics and greatly influenced scientific thinking. Additionally, Newton's measurement is still used as a basis for understanding the acceleration due to gravity on Earth and is an important concept in many fields of science and engineering.

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