Planetary motion: Let’ s try this animation again! Venus, Mars

1. Planetary motion: Let’s try this animation again! Venus, Mars http://astro.unl.edu/naap/ssm/animations/configurationsSimulator.html • Copernicus’ heliocentric theory of planets provided simple explanation of the complicated motion of the planets that we observe: • Inner planets, Mercury and Venus, never seen at large angles from sun • Outer planets, Mars, Jupiter, Saturn move slowly eastward (over weeks and months) but about once a year, reverse their motion, go west for a distance, then reverse again to move eastward

2. So, what is a theory? A law? The word "theory" means something very different in everyday language than it does in science: to the average person, a theory is just an idea… A scientific theory is an explanation of something that has been demonstrated through repeated experiments or testing. A scientific law is often part of the theory, expressing a mathematical relationship A scientific theory also makes predictions that can be tested. What can we predict about the appearance of Venus when seen through a telescope?

3. Galileo, in 1609, was the first to look at the planets through a telescope. What he saw when he looked at Venus strongly supported the heliocentric theory Suppose early in the morning you look at Venus, through a telescope, and it appears like this: In the following weeks, its angular distance from the sun gets smaller, and finally it disappears in the sun’s glow.

4. But Venus reappears, this time in the western evening sky. You watch it for several more months as its angular distance from the sun increases to about 45 degrees, then Venus starts to move closer to the sun again Again, you look at it in a telescope. What to you think it will look like compared to the first time? (hint: remember how the moon changes depending on how we view it!)

5. Here is what you see:

6. Kepler: planets move in almost circular orbits Kepler lived at the same time as Galileo, both born shortly after Copernicus published his book. He used the careful observations made by Tycho Brahe to modify Copernicus’ idea of circular motion. He realized, from the orbit of Mars, that the planets move not on circular, but in elliptical orbits. You will hopefully have a chance to explore these in a computer lab. The web page looks like this:

7. On-line Simulator, Worksheet for Kepler’s Laws http://astro.unl.edu/naap/pos/animations/kepler.swf Plan B, should computer lab not be available: Lect-tutorial, p 21

9. Kepler’s Three laws, summarized: Newton used these relations to formulate the law of gravity… • Planets orbit the sun in an ellipse • Line connecting sun and planet sweeps out equal areas in equal time: the result is that the planets moves fastest when closest to the sun. • The Period (“Year”) squared = separation cubed • Period X period = separation x separation x separation

10. Sir Isaac Newton, 1642-1727: He was responsible for breakthroughs in mechanics, optics, gravity, mathematics. (He invented calculus to solve the problem of the moon’s orbit) • Newton’s Law of Gravity: Force at a distance, or why does an apple fall? What keeps the moon in orbit around the earth? And what holds you to the surface of the earth? • The force of attraction between two bodies is directed along a line joining them: • The force increases with the mass of either body • It decreases with the square of the distance between the two bodies

11. Let’s express as an equation

12. Examples: 1. Suppose mass Mb doubles. What happens to the force? (What’s an example of M doubling?) 2. Suppose distance, r, doubles. What happens to the force?

14. Do the astronauts in space station feel gravity? Let’s explore this. What is the diameter of the Earth? How far above the Earth does the space shuttle orbit? How much farther from the center of the earth are the astronauts? (Suppose the distance r increases by 5% (0.05)Does the force change very much?) The space shuttle, and the astronauts inside, are falling around the earth!

15. And the moon is falling around the earth And the earth-moon system is… How far from a body (earth, sun, etc) does gravity exist? (does this force ever reach zero?)

16. Suppose an astronaut lands on the moon, which has a mass 0.012 that of the earth, and a radius 0.27 of the earth. What happens to the force between the astronaut and the moon- what we call his weight? A quick calculation (!) shows that the astronaut’s weight (the force pulling him down) is only 0.17 what it was on earth.

17. The law of gravity in astronomy:(Period (“Year”) 2)(Ma + Mb) = semi-major axis cubedP2 (Ma + Mb) = R3 Combination of the law of gravity and Kepler’s third law allows us to calculate: Masses of stars: binary star systems Mass of our galaxy: how many stars in it Mass of other galaxies