# How did Kepler derive his laws WITHOUT law of gravitation?

• Hansa
In summary: It was not until Newton's time that a mathematical explanation for gravity was developed. Kepler, on the other hand, used Tycho Brahe's meticulous observations to determine that planets follow elliptical paths around the sun. He did not have a clear understanding of why this was the case, but he was able to accurately describe the motion through observations alone.
Hansa
How did Kepler derive his laws of Planetary Motion without knowing about Newton's law of gravitation? Specifically, the first law of planetary motion which says that planets follow elliptical paths - how did he figure that out without the knowledge of the gravitational pull of the sun? Was it purely based on observations?

Hansa said:
Was it purely based on observations?

I believe it was.

As far as I understand, Kepler gained access to all of Tycho Brahe's astronomical observational data when Tycho Brahe died. He used this data to model the solar system as heliocentric, with the planets orbiting the Sun in ellipses. He never developed an explanation for why they did this.

Thanks, that answers the question. :)

To use an movement low like ## x(t) = x_0 + v_0t + \frac{1}{2}at^2 ## I needn't any law of force or any other reason of motion. The motion is that I observe.

Hansa said:
Was it purely based on observations?

Is there another way?

andresB said:
Is there another way?
The alternative is to start with a force law and see what motion it predicts.

Kepler did not use a force law. He started with observations and determined a pattern of motion -- a traversal of an elliptical path at a rate determined by "equal areas in equal times". Newton was able to show after the fact that an inverse square central force law was consistent with this.

Hansa said:
How did Kepler derive his laws of Planetary Motion without knowing about Newton's law of gravitation? Specifically, the first law of planetary motion which says that planets follow elliptical paths - how did he figure that out without the knowledge of the gravitational pull of the sun? Was it purely based on observations?
According to a recent book, On the Shoulders of Giants, edited by Stephen Hawking, Kepler was hired by Tycho Brahe, who was an expert naked eye astronomer, to make sense of his observations of Mars. That was when Kepler found the planet was describing an ellipse.

I think Kepler not just get data from Thycho, but Kepler continue Thycho's work

Kepler continued to work in Tycho's observatory, but he had poor vision (relatively poor, near sighted, could read w/o difficulty) and could not really use any of the instruments. And Galileo's telescope was starting to be distributed so that Tycho's tools were obsolete within a few years of his death as well. Everyone WANTED to believe orbits were perfectly circular or were composed of epicircles (circles within circles). This idea could replicate the orbit of Mars to a very close approximation. Kepler also did NOT want to accept Tycho's observations, but knew Tycho was too good of an observer to not use his data.

Hansa said:
How did Kepler derive his laws of Planetary Motion without knowing about Newton's law of gravitation? Specifically, the first law of planetary motion which says that planets follow elliptical paths - how did he figure that out without the knowledge of the gravitational pull of the sun? Was it purely based on observations?
The funny thing is that Newton's law of gravitation is also based on observations.

## 1. How did Kepler discover his laws of planetary motion without knowledge of the law of gravitation?

Kepler used extensive observations of the planets' positions and movements to develop his three laws of planetary motion.

## 2. What evidence did Kepler use to support his laws without knowledge of gravity?

Kepler used precise measurements of the planets' orbits and observed that they followed certain patterns, such as the planets moving faster when closer to the sun and slower when farther away.

## 3. How did Kepler's laws differ from previous models of planetary motion?

Kepler's laws were based on empirical observations and mathematical calculations, while previous models relied on philosophical or religious beliefs.

## 4. Did Kepler's laws accurately predict the movements of the planets?

Yes, Kepler's laws accurately predicted the movements of the planets based on his observations and calculations. They also provided a more precise and accurate understanding of planetary motion than previous models.

## 5. How did Kepler's laws lay the foundation for Newton's theory of gravity?

Kepler's laws demonstrated that the planets' movements could be described by mathematical relationships, which inspired Newton to develop his theory of gravity to explain these patterns.

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