# What did Newton add to our understanding of Kepler's laws?

Newton's work on gravity introduced the mechanic for the motion of the planets.

Kepler believed that some force from the sun pushed the planets around in their orbits, but he was unable to identify the force. Kepler derived his laws of planetary motion from the massive amounts of data collected by Tycho Brahe. Brahe's observations were accurate enough that he was able to derive not only the shape of the planets' orbits, but their speeds as well.

Newton's law of universal gravitation, when applied to the planets and the Sun, accurately predicts the motion of the planets. Almost a century later, Newton's work on gravity explained why the planets orbit the way they do.

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Newton added the concept of universal gravitation, which explained why Kepler's laws worked the way they did.

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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.

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- A farmer is purchasing irrigation equipment for a circular field and needs to know the circumference of the field. The radius of the field is 525 yards. What is the circumference of the field?
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- A model train with a mass of #5 kg# is moving along a track at #4 (cm)/s#. If the curvature of the track changes from a radius of #16 cm# to #12 cm#, by how much must the centripetal force applied by the tracks change?
- A model train with a mass of #5 kg# is moving along a track at #14 (cm)/s#. If the curvature of the track changes from a radius of #84 cm# to #28 cm#, by how much must the centripetal force applied by the tracks change?

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