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Kepler’s Laws of planetary motion Newton’s law of universal gravitation Free fall acceleration on surface of a planet Satellite motion Lecture 13: Universal.

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Presentation on theme: "Kepler’s Laws of planetary motion Newton’s law of universal gravitation Free fall acceleration on surface of a planet Satellite motion Lecture 13: Universal."— Presentation transcript:

1 Kepler’s Laws of planetary motion Newton’s law of universal gravitation Free fall acceleration on surface of a planet Satellite motion Lecture 13: Universal gravitation

2 Brief history of cosmology Ptolemy (85 - 165) geocentric theory Nicolaus Copernikus (1473-1543) heliocentric theory

3 Tycho Brahe (1546-1601) Johannes Kepler (1571-1630) Laws of planetary motion

4 Galileo Galilei (1564 - 1642) telescope discovered moons orbiting Jupiter observed phases of Venus

5 Kepler’s Laws: 1 st Law The planets move in elliptical orbits with the sun at one focus of the ellipse. http://www.walter-fendt.de/ph6en/keplerlaw1_en.htm

6 Kepler’s 2 nd Law A line drawn between the sun and a planet sweeps out equal areas in equal intervals of time http://www.walter-fendt.de/ph6en/keplerlaw2_en.htm

7 Kepler’s 3 rd law The square of a planet’s orbital period is proportional to the cube of the semi-major axis length.

8 Newton’s Law of Universal Gravitation Sir Isaac Newton (1643 - 1727)

9 Gravitation near Earth’s surface ⟶ Find free-fall acceleration on any planet of mass M and radius R

10 Find mass of Earth

11 Satellite Motion Kepler’s 3 rd Law

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