Unit 7 Lab

* Title of the Laboratory: Modeling the orbits of planets and satellites * Objective: Formulate models to inter the shape of orbits of planets and satellites.
Collect and organize data for aphelion distances and perihelion distances of objects as they orbit the sun
Draw conclusions about Kepler’s first and second laws of motion. * Materials: Piece of cardboard, metric ruler, sheet of blank, sharp pencil or pen, white paper, four small pieces or tape string (25cm), two push pins * Procedure: In the book says the procedure * Data Table Data Table | Object | Eccentricity (e) | d(cm) | MeasuredA | MeasuredP | Experimentale | %Error | Circle | 0 | 0 | 10 | 10 | 0 | 0 | Earth | 0.017 | .28 | 9.8 | 7.6 | .009 | -9.1 |
Measure the aphelion distance, A, by measuring the distance between one focus and the farthest point in the orbit along the major axis. Record your data in the data table. 2. Measure the perihelion distance, P, by measuring the closest distance between one focus and the closest point in the orbit along the major axis. Record the data in the data table. 3. Calculate the experimental eccentricity for each of the objects and record your data in the data table. Use the following equation: 4. Error analysis calculates the percent error for each object using the experimental eccentricities compared to the known eccentricities. Record your values in the data table 5. Analyze why is the shape of the orbit with e = 0 a circle? * An object orbits in an ellipse and a circle is a ellipse where the eccentricity is zero. 6. Compare how does earth’s orbit compare to a circle? * the earth's orbit is in the shape of an ellipse, which is pretty much like an oval, however its really close to a circle, in the earth's case, just a little bit squished 7. Observe which of the orbits truly looks
Does the orbit model you constructed obey Kepler’s first law? Explain. * Yeap! The orbits of planets are ellipses. 9. Kepler studied the orbit data of Mars (e=0.093) and concluded that planets move about the sun in elliptical orbits. What would Kepler have concluded if he had been on Mars and studied Earth’s orbit? * Earth's orbit is very close to circular. Mars has an orbit that is about 8 times more eccentric than Earth's, which is why Tyco’s very accurate tables of Mars gave Kepler the data necessary to break away from the circular orbit claims and go to the ellipse, which solved the problem. It was very demanding work so much so that Tyco needed Kepler's math skills to do it. 10. Where does a planet travel fastest: at aphelion or perihelion? Why? * Perihelion, Due to angular momentum, a comet will travel fastest at perihelion and will slow down as it approaches aphelion. 11. Kepler’s second law helps to determine the ratio between Pluto’s velocity at aphelion and perihelion (va/vp). To determine this ratio, first calculate the area swept out by Pluto’s orbit. This area is approximately equal to the area of a triangle: area = 1/2 (distance to the sun) current velocity X time. If the area that the orvit weeps out in a fixed amount of time, such as 30 days, is the same at aphelion and perihelion, this relationship can be written. What is the ratio vp/va for