How did Newton and others do it?

[Cosmo_Ken]

Exactly how did astronomers before Newton come up with all of the values for the various characteristics of the solar system bodies, i.e. orbital parameters, mass of the bodies, etc, so that they could predict the motions of the planets and their moons back then? There wasn't much that they could directly measure!

 

Exactly how did Newton come up with his Laws of Motion and his Law of Universal Gravitation? How did he come up with a value for the gravitational constant "G" in F=GMm/r2, r2 is actually r squared? For the surface of the Earth, GMm/r2 = mg, where "g" is the acceleration due to gravity on the surface of the Earth, M as the mass of the Earth and r is the radius of the Earth. The small m's cancel out so you get GM/r2=g or G=gr2/M, but you need to know M, r and g to calculate G. How did they come up with values for all of the variables?

 

I have ordered a book that will hopefully shed some light on my questions, but it would be against the rules to link to the Amazon page selling it.

Edited January 23, 2017 by Phi for All
No advertising, please.

[Janus]

Exactly how did astronomers before Newton come up with all of the values for the various characteristics of the solar system bodies, i.e. orbital parameters, mass of the bodies, etc, so that they could predict the motions of the planets and their moons back then? There wasn't much that they could directly measure!

 

Exactly how did Newton come up with his Laws of Motion and his Law of Universal Gravitation? How did he come up with a value for the gravitational constant "G" in F=GMm/r2, r2 is actually r squared? For the surface of the Earth, GMm/r2 = mg, where "g" is the acceleration due to gravity on the surface of the Earth, M as the mass of the Earth and r is the radius of the Earth. The small m's cancel out so you get GM/r2=g or G=gr2/M, but you need to know M, r and g to calculate G. How did they come up with values for all of the variables?

 

I have ordered a book that will hopefully shed some light on my questions, but it would be against the rules to link to the Amazon page selling it.

For r^2, he used Kepler's laws which were based on observations of how the planet's moved.

 

Newton did not know what G was. The value if G was first determined by Henry Cavendish in 1797. He did this by placing large brass spheres of known mass at the end of a rod that was suspended on a piano wire. similar spheres were placed near these spheres so that the gravitational attraction be between them would twist the piano wire. By measuring the amount the wire twisted, he knew how much force was acting between the spheres. Since he also knew the mass of the spheres and the distance between them, he could calculate G

[Cosmo_Ken]

For r^2, he used Kepler's laws which were based on observations of how the planet's moved.

 

Newton did not know what G was. The value if G was first determined by Henry Cavendish in 1797. He did this by placing large brass spheres of known mass at the end of a rod that was suspended on a piano wire. similar spheres were placed near these spheres so that the gravitational attraction be between them would twist the piano wire. By measuring the amount the wire twisted, he knew how much force was acting between the spheres. Since he also knew the mass of the spheres and the distance between them, he could calculate G

 

Thanks, that helps a bit, but how did Kepler figure out the orbits? I am sure that the book I ordered will have a bunch of stuff on Kepler, etc. It is called "The History of Planetary Astronomy, Part B: From the Renaissance to Astrophysics".

[Danijel Gorupec]

I cannot recall where I read this and I cannot tell if the source was reliable... but I once read that most precise measurements of that time came from work of Tycho Brahe and Kepler was his assistant (according to Wikipedia).

 

Edit: If you ask why those measurements were made, the same source gives following answer - to make horoscopes. Apparently horoscopes were very popular at that time and noblemen did invest into it. Brahe was given lot of money to build very powerful observation facility. Brahe, the same source says, apparently published 'corrected' results (to make it inline with theory of that time), but Kepler possibly had access to raw measurement data.

Edited January 24, 2017 by Danijel Gorupec

[Bender]

The orbits where known long before Kepler, by measuring the position of the planets in the sky with ever increasing accuracy and fitting them to a model (either geocentric or heliocentric models were used). I think Kepler was the first to speak about elliptical orbits, as his first law describes (at least, he was the one to become known for this, as happened often throughout history of science, he may not actually have been the first).

 

Newton did not know what G was. The value if G was first determined by Henry Cavendish in 1797. He did this by placing large brass spheres of known mass at the end of a rod that was suspended on a piano wire. similar spheres were placed near these spheres so that the gravitational attraction be between them would twist the piano wire. By measuring the amount the wire twisted, he knew how much force was acting between the spheres. Since he also knew the mass of the spheres and the distance between them, he could calculate G

 

In fact, it was John Michell who built the setup, but he died when he was finished and Cavendish executed the experiments. Those were very impressive measurements and it took a long time to improve them; probably the most impressive experiment predating the digital age. Even now our best estimate of G is barely more accurate.

[DrP]

Wasn't it Newton that was famous far stating that if he had pushed the boundaries of science further anyone else it was because "he was standing on the shoulders of giants"?

[Bender]

Yes, but I thought Michell deserved mentioning because of how sad his story is.

[Sensei]

Exactly how did astronomers before Newton come up with all of the values for the various characteristics of the solar system bodies, (...)

 

Imagine how would you do it with the Sun:

place stick with known length f.e. 1 meter in the flat ground. It'll be casting shadow on the ground.

Then every hour, every day of year, record position of tip of shadow on the ground.

 

Do you remember Pythagorean theorem.. ?

 

Length of shadow is line AB,

length of stick is line BC,

and distance between AC = sqrt(AB^2+BC^2)

sin(angle)=BC/AC

 

A is shadow tip point. It's changing position minute by minute, hour by hour, day by day.

B is point where stick is put in the ground. Center of the whole "device". Constant.

C is top of stick (it's casting shadow). Also constant.

 

Additionally you have yet another angle between B, and A, on the ground.

Used by ancients as Sun clock.

 

Stick's method would also work with Moon.

 

For other planets more advanced variation of this method is needed, as they don't emit/reflect a lot of light.