Kepler's Laws and Universal Gravitation

Name: Kepler's Laws and Universal Gravitation
Author: StemPy Lab

The planets move on ellipses, and a planet moves faster when it is near the Sun. Kepler found these rules from many years of observations, and Newton explained them with one law. In this course we study the three laws of Kepler, we write Newton's law of gravitation and find the force between two bodies, and we find how the acceleration due to gravity changes with height, with depth and with the turning of the Earth.

3 lessons, about 1 h 15 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Kepler's laws of planetary motion
Kepler found three laws in Tycho Brahe's measurements. The planets move in ellipses, with the Sun at one focus. The line from the Sun to a planet sweeps out equal areas in equal times, so a planet is fastest when nearest. The square of a planet's year is proportional to the cube of its mean distance: $T^2 \propto a^3$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set
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Lesson 2about 25 min
Newton's law of gravitation
Every two bodies attract each other along the line joining them with $F = \dfrac{Gm_1m_2}{r^2}$ , where $G = 6.67 \times 10^{-11}\ \text{N m}^2/\text{kg}^2$ . The pulls on the two bodies are equal and opposite. A uniform sphere pulls as if all its mass were at its centre. The force is tiny between everyday objects and huge between planets.
1 simulation2 practice questions1 Python program4 problems
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Lesson 3about 25 min
Acceleration due to gravity and how it changes
At the Earth's surface, $g = \dfrac{GM}{R^2}$ , about $9.8\ \text{m/s}^2$ . Above the surface it falls as $\dfrac{1}{r^2}$ : $g' = g\left(\dfrac{R}{R + h}\right)^2 \approx g\left(1 - \dfrac{2h}{R}\right)$ for small $h$ . Below the surface of a uniform Earth it falls in a straight line, $g' = g\left(1 - \dfrac{d}{R}\right)$ , to zero at the centre. The Earth's spin and bulge make $g$ a little smaller at the equator.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 note
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Kepler's Laws and Gravitation: Practice Paper

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Kepler's Laws and Universal Gravitation

Course outline (3 lessons)

Kepler's laws of planetary motion

Newton's law of gravitation

Acceleration due to gravity and how it changes

Test Your Learning

Your teacher

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