Hello, need help with this lab. Very math orientated

Rowan Introduction to Astronomy Lab 4 I An Introduction to Kepler's 3 Laws Name: Score: AObjectives l> Reproducing ellipses via the \"string-and-pencil method,\" students will draw ellipses and determine their eccentricities. D By measuring the orbits of ve of Jupiter's moons, students will test Keple's third law. D By using characteristics of Pluto's orbit, students will conrm Kepler's second law. A Procedure Kepler's three laws are simply a mathematical way of describing motions of objects that orbit a large central rnass, such as the planets which orbit around the Sun or the moons which orbit around Jupiter. This lab explores each of Kepler's three laws. AKepler's First Law [45 pts; you must draw and submit two ellipses to receive credit for this part] Kepler's rst law states that orbiting objects travel in elliptical paths with the central mass at one focus. In this section, you will get acquainted with ellipses by sketching one yourself. Note that the string loops around the pins. Do NOT stick the pins into the string. Make sure there is enough slack in your loop of string. C perihelion Semi-major axis D K To draw an ellipse loop string around thumb tacks at C is the distance between the center of the each focus and stretch string tight with a pencil while ellipse {orbit} and one of the foci, F, which moving the pencil around the tacks. The Sun is at one typically is the Sun or a planet (like Earth) focus. that is being orbited. Steps to draw on elh'pse (a) Get two tacks or push pins and a piece of string. On your paper, place the two tacks or pins a small distance apart. Place your string loop around the pins. Be sure to leave some slack in the string. Use a piece of cardboard to help secure the pins or tacks. (b) Using the string as a guide (i.e., place the pencil inside the string loop and pull the loop taut), draw an ellipse. [ll] pts] Attach your sketch to this lab report. (c) Now measure and write down the distance between the foci ad the length of the major axis of the ellipse. [5 pts] distance between foci = mm length of major axis = m (d) Divide the distance between the foci by the length of the major axis. This quantity is known as the eccentricity, \"e.\" [5 pts] (distance between foci) e = + What is the eccentricity of the ellipse you drew? e = [round to 2 places] (length of major axrs) (e) What familiar shape (it is a conic section) is an ellipse with an eccentricity e = 0.0? [5 pts] Lab 4 1 An Introduction to Kepler's Three Laws 2 (f) Sketch Pluto's orbit, which has 3 = 0.245. (Note that eccentricity, e, is a quantity without units.) [10 pts for drawing] For a string loop that is 254 mm (10 in) long, the tacks or pins must be 99 mm (3.9 in) apart. (Note that the 10-inch length refers to the length of the 1009. The length of the string end to end will be double or 20 inches long.) Attach your sketch to this lab report. [m: This is a large ellipse. You will need to tape together 4 sheets of copy paper in order to t this ellipse.] From your ellipse of Pluto's orbit, determine the eccentricity: 9mm = [round to 2 places] [5 pts] (g) Eris, the largest Kuiper Belt Object found to date, has a perihelion distance (closest approach) of 38 AU and an aphelion distance (farthest approach) of 97 AU. Go to Eclipse Calculator at httg:waw.1728.comfellipse.htm; scroll down to \"Calculator Two.\" Click on the radio button for \"Perihelion Distance and Aphelion Distance.\" Input the perihelion and aphelion distances for Eris And press \"calculate.\" {5 pts] eccentricity = [round to 3 places] foci distance = AU [state to units only] AKepler's Third Law [15 pts] Kepler's third law states that the periods (P) and semi-major axes (a) of bodies orbiting a common object are related by 2 2 nch-1 _ 100ml;- 2 3 _ a Ham-1 am!) 2 In this section, you will verify this law for the ve largest moons of Jupiter: Almathea, Io, Europa, Callisto, and Ganymede. (a) Create a table to hold the values of orbital period (P), semimajor axis (a), and Flier} for all ve moons. [Table is worth 15 pts] J u piter's Moon Orbital Period (P) Semi-Major Axis [a] Pala3 Almathea 3 mm lo 3 mm Europa 3 mm Ganymede 3 mm Callisto 5 mm Express answers using decimalsj (b) Measure the semi-maj or axes of the moons on the screen with a ruler. (Use millimeters.) (Hint: Measure the entire width of each orbitthe major axisand divide by 2 to get the semi-major axis a.) (c) Measure the orbital periods either by noting the times in the movie or by timing with a watch (in seconds). (d) Look at your values or PZ/ag: Considering the limitations of the animation and your ability to measure accurately distance and time, does Kepler's third law hold? Your numbers are probably not exactly as you expected. Comment on sources of error. The instructor will supply the animated GIF of J upiter's moons. Save the .GIF file to a local drive and use QuickTime to view it so you can stop and start the movie at will. For Callisto and Ganymede, you will have to time half an orbital period and then multiply by two to get the complete period. Note that the one moon whose label is very hard to see is Io. AKepler's Second Law [40 pts] Kepler's second law states that objects in elliptical orbits sweep out equal areas in equal times. This implies that the orbital speed of a planet around the Sun is not uniform. The planet moves fastest at the point closest to the sun (known as the perihelion) and slowest at the point farthest away (known as aphelion). In this section, you will calculate the difference in this speed using Pluto as an example. Pluto's orbit has an eccentricity e = 0.25. Its semi-major axis, a. is 5.9 x 109 km. (E: Be sure to use scientic notation for a, b, c.)