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 transcript:

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

Brief history of cosmology Ptolemy ( ) geocentric theory Nicolaus Copernikus ( ) heliocentric theory

Tycho Brahe ( ) Johannes Kepler ( ) Laws of planetary motion

Galileo Galilei ( ) telescope discovered moons orbiting Jupiter observed phases of Venus

Kepler’s Laws: 1 st Law The planets move in elliptical orbits with the sun at one focus of the ellipse.

Kepler’s 2 nd Law A line drawn between the sun and a planet sweeps out equal areas in equal intervals of time

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

Newton’s Law of Universal Gravitation Sir Isaac Newton ( )

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

Find mass of Earth

Satellite Motion Kepler’s 3 rd Law

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