1 / 6

Newton: Understanding Kepler’s Laws & Orbits

Newton: Understanding Kepler’s Laws & Orbits. Review: orbits as revealed by Kepler’s Laws for motion of the planets – a simulation (click on link below when in slide show): http://astro.unl.edu/naap/pos/animations/kepler.html

boris
Download Presentation

Newton: Understanding Kepler’s Laws & Orbits

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Newton: Understanding Kepler’s Laws & Orbits • Review: orbits as revealed by Kepler’s Laws for motion of the planets – a simulation (click on link below when in slide show): http://astro.unl.edu/naap/pos/animations/kepler.html • Experiments: how does period P depend on semi-major axis a? on e? • This explains (and was motivated by) retrograde motion: http://mars.jpl.nasa.gov/allabout/nightsky/nightsky04-2003animation.html • Experiments: how is synodic period, S, of conjunction related to sidereal period, P? If Mars were closer to Earth, would synodic period be longer or shorter? • But how to understand why and how orbits work? Need to introduce concepts of force, mass (and inertia) and acceleration… Oct. 2, 2007

  2. Deconstructing force, mass&acceleration • Start with mass: the quantity of matter (which is proportional to its weight, but not equal – your mass does not change when you are weightless in Shuttle!) • Mass is what “causes” inertia. Push on a car vs. a bike, and your ability to move it with fixed strength (force…) is a measure of its inertialmass • Inertial mass is same in space shuttle on orbit as on ground. Mass is a direct measure of number of atoms (or molecules, or ions, etc.) in a given object; not dependent on location • Mass is what will govern the fate of the stars Oct. 2, 2007

  3. And now for Force and Acceleration • Force was just defined: it’s what must be applied to overcome inertia and move a mass • To “move a mass” by “applying a force”, we must accelerate the mass: change its velocity, from 0 (rest) • The force needed to achieve a given acceleration, a, is directly proportional to the mass, M: F = M a Oct. 2, 2007

  4. Connection to Orbits? • The force needed to continuously change the direction of an orbiting object with mass m is due to Gravity between it and mass M, F = GMm/R2 = m a where G is Newton’s constant and R is the distance between M and m (and is the semi-major axis, a, of an orbit) • The acceleration of mass m moving about M at velocity V can be shown to be a = V2/R so GMm/R2 = m V2/R and thus V2 = GM/R Oct. 2, 2007

  5. Newton’s form of Kepler’s 3rd Law • But orbital velocity V around an orbit with “radius” or semi-major axis R is just V = 2π R/P = circumference/period So substituting this for V we have P2 = (4π2/GM) R3 Or, P2 = R3/M Oct. 2, 2007

  6. Discussion of Errors…. • Concept of uncertainties in our labs • Examples (on blackboard) of measurements and their “scatter” about a mean • Conversion of this scatter into estimate of overall uncertainty: • Mean error • “Root Mean Square” (rms) error Oct. 2, 2007

More Related