Kepler’s Laws of Orbital Motion

Planets orbit the Sun in ellipses with the Sun at one focus Kepler’s 1st Law Planets orbit the Sun in ellipses with the Sun at one focus perihelion aphelion

Planets orbit the Sun in ellipses with the Sun at one focus Kepler’s 1st Law Planets orbit the Sun in ellipses with the Sun at one focus The eccentricity of the ellipse is a measure of how “squished” the circle is: 0 ≤ e ≤ 1 e = 0  circle e = 0.02  slightly ovalized e = 0.967  Comet Halley e = 1.00  parabolic orbit perihelion aphelion

Kepler’s 2nd Law A line from the Sun to the planet will sweep out equal areas in equal times

Kepler’s 2nd Law A line from the Sun to the planet will sweep out equal areas in equal times

(Average distance)3 = (Period)2 Kepler’s 3rd Law (Average distance)3 = (Period)2 When expressed in “Earth terms” (AU and years) 1 AU = average distance from Sun to Earth

If there were a planet twice as far from the Sun as the Earth is, what would its orbital period be in Earth years? A. B. C. D. E.

The book puts it like this: Kepler’s 3rd Law The book puts it like this: T = (constant) r3/2

The book puts it like this: T = (constant) r3/2 Kepler’s 3rd Law The book puts it like this: T = (constant) r3/2 How do we come up with the constant?

Newton’s Law of Gravity and Uniform Circular Motion

Newton’s Law of Gravity and Uniform Circular Motion “Newton’s Version of Kepler’s 3rd Law”

Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth’s center is twice that of satellite A. What is the ratio of the centripetal force acting on B compared to that acting on A? 1 8 1 4 1 2 It’s the same. 2 Answer: B

The international space station orbits approximately 250 miles (402 km) above the Earth’s surface. What is its orbital period?

A geosynchronous satellite is one that has an orbital period equal to the Earth’s rotation period: one sidereal day = 23 hours, 56 min, 4 sec. A geostationary satellite has that period and also a circular orbit along the equator (and thus appears stationary in the sky). At what altitude above the Earth’s surface must a geostationary satellite orbit?

“Newton’s Version of Kepler’s 3rd Law” is also how we can determine the mass of a planet with moons, or a star with planets. Use the period and distance of Jupiter’s moon Callisto to determine the mass of Jupiter.