# What does it mean to say that Kepler's Laws are 'empirical'?

'Empirical' means 'based in evidence and measurement'. Kepler's Laws describe the motion of planets in a solar system. By saying they are 'empirical', we are saying they are only descriptive, they do not have a theoretical explanation for the phenomena they describe.

Kepler's Laws were formulated before Newton's development of his theory of gravity. Kepler used mathematical rules to describe a large class of observations. He did not have a theoretical explanation for why the planets move as they do, but could describe their past motion and predict their future motion.

We sometimes say that theories in science must have descriptive, predictive and explanatory power. Empirical laws like Kepler's are descriptive and predictive, but don't explain the phenomena.

It was only when Newton developed an understanding of gravitation that it was possible to explain the reason why the planets move as they do.

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It means that Kepler's Laws were derived from observations and experimental data rather than from theoretical principles or mathematical derivations.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A model train, with a mass of #6 kg#, is moving on a circular track with a radius of #2 m#. If the train's rate of revolution changes from #4 Hz# to #6 Hz#, by how much will the centripetal force applied by the tracks change by?
- A model train, with a mass of #6 kg#, is moving on a circular track with a radius of #2 m#. If the train's kinetic energy changes from #27 j# to #36 j#, by how much will the centripetal force applied by the tracks change by?
- A model train with a mass of #3 kg# is moving along a track at #8 (cm)/s#. If the curvature of the track changes from a radius of #5 cm# to #24 cm#, by how much must the centripetal force applied by the tracks change?
- A model train, with a mass of #8 kg#, is moving on a circular track with a radius of #2 m#. If the train's kinetic energy changes from #36 j# to #48 j#, by how much will the centripetal force applied by the tracks change by?
- A model train, with a mass of #32 kg#, is moving on a circular track with a radius of #9 m#. If the train's kinetic energy changes from #18 j# to #21 j#, by how much will the centripetal force applied by the tracks change by?

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