# First law of Kepler explained without mass ?

## Main Question or Discussion Point

Hello,

I have a question : is it possible to explain the first law of Kepler without any concept of mass ?

Kepler's first law states that satellites are moving on an ellipse and the object around which they are orbiting is localized at the focus of this ellipse. As far as I know Newton and Einstein explained this special natural behavior, in two different ways, and they needed to introduce the concept of mass to achieve this goal. However Galileo from the top of the Pisa tower, and the astronauts from the moon, experienced that bodies are falling at the same speed what ever their masses are. Therefore would it be possible to explain Kepler's first law without any use of the mass ?

Thanks for contributions.
Best regards
Herve

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If I recall my intro. to spacecraft performance//orbital mechanics, Kepler himself was essentially a strictly observational scientist, and derived his laws from hard astronomical observation (independent of the masses of the bodies in orbit).

cepheid
Staff Emeritus
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If I recall my intro. to spacecraft performance//orbital mechanics, Kepler himself was essentially a strictly observational scientist, and derived his laws from hard astronomical observation (independent of the masses of the bodies in orbit).
Ummm....you are correct that when Kepler originally arrived at his laws, they were empirical laws, meaning that the only justification for thinking that they should be so was because they were observed to be so.

However, the OP asked if it was possible to explain Kepler's laws (something which Kepler himself made no attempt to do because he did not have the tools and making mathematical models to explain nature was not really a discipline that was very well developed until Newton came along.) Furthermore, the OP asked whether this could be done without reference to the concept of mass. My answer would be that the theoretical foundation for Kepler's laws lies with Newtonian Mechanics and the equations of motion that follow from it. More specifically, all three of Kepler's laws can be explained if you know Newton's Law of Gravitation (whose formulation definitely includes a physical quantity known as "mass"). Therefore, I think the answer to the OP's question is, "no."

Even General Relativity, which abandons the notion of "gravitational force" and explains the curved paths of the planets as their most natural paths in a curved space-time, still talks about the quantity that causes that curvature, namely mass.

{~}
You mentioned that Galileo showed that the accelration of projectiles due to gravity is mass independent, but this is really only from an observational view and only when the masses involved negligibly attract the astronomical body in question (like the earth).

You mentioned that Galileo showed that the accelration of projectiles due to gravity is mass independent, but this is really only from an observational view and only when the masses involved negligibly attract the astronomical body in question (like the earth).
You're thinking in terms of relative acceleration. The universality of free fall is true even when the masses involved significantly attract the astronomical body. A golf ball in earth free fall will accelerate the same as the moon in earth free fall. If it were not true then the golf ball would require less velocity to maintain the same orbit as the moon.

Yes indeed Kepler produced the 3 laws as a result of observations but we had to wait for Newton, and then for Einstein, to give a theoretical interpretation of these observations. As I thought and as Cepheid explained Newton's gravitation and Einstein's general relativity need both to introduce the concept of mass to explain the laws.

Well, I think however that it is possible to give an explanation of Kepler's laws with the only help of kinematics and geometry but without the use of the mass. I wrote a short paper to explain it :http://www.oceanvirtuel.com/physics/geometrie_des_lois_de_kepler_en.pdf [Broken]. I would much appreciate if you could give me your opinion about it.

Best regards
Herve

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Ummm....you are correct that when Kepler originally arrived at his laws, they were empirical laws, meaning that the only justification for thinking that they should be so was because they were observed to be so.

However, the OP asked if it was possible to explain Kepler's laws (something which Kepler himself made no attempt to do because he did not have the tools and making mathematical models to explain nature was not really a discipline that was very well developed until Newton came along.) Furthermore, the OP asked whether this could be done without reference to the concept of mass. My answer would be that the theoretical foundation for Kepler's laws lies with Newtonian Mechanics and the equations of motion that follow from it. More specifically, all three of Kepler's laws can be explained if you know Newton's Law of Gravitation (whose formulation definitely includes a physical quantity known as "mass"). Therefore, I think the answer to the OP's question is, "no."

Even General Relativity, which abandons the notion of "gravitational force" and explains the curved paths of the planets as their most natural paths in a curved space-time, still talks about the quantity that causes that curvature, namely mass.
I think the crux of this matter lies within what is meant by 'explain.' Is there any kinematics that does not use the concept of mass? Kepler's Laws, if you look at the words at face value, are obviously kinematic(A planet moves...) but I do not know of a way one can understand kinematics without the use of mass.

I think the crux of this matter lies within what is meant by 'explain.' Is there any kinematics that does not use the concept of mass? Kepler's Laws, if you look at the words at face value, are obviously kinematic(A planet moves...) but I do not know of a way one can understand kinematics without the use of mass.
As I said the best would be to read this short paper : http://www.oceanvirtuel.com/physics/geometrie_des_lois_de_kepler_en.pdf [Broken]
It explains more clearly how to get Kepler's laws without using the mass. Any opinion about it would be appreciated.

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