LAB 2

.pdf

School

Pace University *

*We aren’t endorsed by this school

Course

150

Subject

Physics

Date

Apr 3, 2024

Type

pdf

Pages

7

Uploaded by BaronWillpowerBarracuda36

Report
1 EXPERIMENT# 2 KEPLER’s LAWS By reproducing ellipse via the “string -and- pencil method,” the students will draw ellipses and determine the eccentricities; by measuring the orbits of five of Jupiter’s moons, and the students will test Kepler’s third law; and by using characteristics of Mercury’s orbit, the students will confirm Kepler’s second law. APPARATUS String, pin, paper, ruler, and a computer THEORY: 1. Kepler’s First Law: Orbiting objects travel in elliptical paths with the central mass at one focus. 2. Kepler’s Second Law: Objects in elliptical orbits sweep out equal areas in equal times. This implies that orbital speed of the a planet around the sun is uniform it moves fastest at the point closest to the Sun (known as the PERIHELION) and slowest at the point farthest away (known as APHELION) a. To do this, we need to find the area swept out by planet’s orbit. This can be approximately described as a triangle with: i. Area = ½ x (Distance to the Sun) x (Current Velocity) x (Time) b. The law states that planets sweep out equal areas in equal times: this means that the area swept out in a fixed time interval (say a week) is the same at the perihelion as it at the aphelion. Therefore we can say: i. ½ x (D perihelion ) x (V perihelion ) x (time) = ½ x (D aphelion ) x (V aphelion ) x (time) c. And finally the ratio between distances and orbital speed can be found as: i. (D perihelion ) x (V perihelion ) = (D aphelion ) x (V aphelion ) 3. Kepler’s Third Law : The periods and semi-major axes of bodies orbiting a common object are related by a. 𝑃 𝑏𝑜𝑑𝑦1 2 ? 𝑏𝑜𝑑𝑦 1 3 = 𝑃 𝑏𝑜𝑑𝑦2 2 ? 𝑏𝑜𝑑𝑦 3
2 PROCEDURE 1. Kepler’s First Law: In this section you will get acquainted with ellipses by sketching one yourself a. Get two thumb tacks and a piece of string. On your paper, place the two tacks a small distance apart, pinning down the ends of the string. Be sure to leave some slack in the string b. Using the string as a guide (i.e., place the pencil inside the string loop and pull the loop taut), draw an ellipse. As shown in image 1. Image 1: Image of drawing the ellipse. Source: https://www.grasshopper3d.com/forum/topics/gardener-ellipse-with-grasshopper-and-galapagos c. Now measure with a ruler and write down the distance between the foci AND the length of the major axis of the ellipse. i. Distance between foci = ____10.6_______ cm ii. Major axis = ___17.1______ cm
3 d. Divide the distance between the foci by the length of the major axis. This quantity is known as the eccentricity, “e”. i. e = (???????? ??????? ????) (𝑀???? ????) e. What familiar shape is an ellipse with an eccentricity e=0.0? e = 10.6 / 17.1 = 0.62 f. Sketch Mercury’s orbit, e = 0.206. For the semi-major axis (a), (c) is the distance between the foci and (b) is the semi-minor axis. c = e x 2a c = 0.206 x 20 c = 4.12 b = √ (2a^2 – c^2) b = √ (20^2 – 4.12^2) b = 19.71 a = 10 Hint: draw a rough sketch but you need to choose the major axis and the distance between foci to give you the required eccentricity. I didn’t have pins and rope to do it.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help