{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture12 - Physics 344 Foundations of 21st Century Physics...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Fan Chen Office: PHYS 222 [email protected] Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! Help Session: Thursdays 2:00 – 4:00 in PHYS 154 Reading: Chapters 1 through 8 in Six Ideas that Shaped Physics, Unit R. Exam 1: Wednesday, October 5 at 8:00pm in WTHR 104
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The Aberration of Starlight As is often the case, care in choosing the coordinate system to represent a physical system can make it easier to predict and explain phenomena. In relativistic situations, one often has the added difficulty of dealing with two coordinate systems, S and S’ , at once. We require S’ to be in standard orientation relative to S so that we can use the standard form of the Lorentz transformation equations a to analyze situations Sun S : inertial frame in which the Sun is essentially at rest throughout the year. Earth location at t = 0 x y z Earth is moving in the x direction at speed V = 30 km/sec at t = 0. So, S’ in standard orientation and moving at speed V relative to S has the Earth momentarily at rest at the origin and is a good approximation to a coordinate system fixed in an observatory on Earth near t = t’ = 0. We are interested in observations of a star made near that time.
Image of page 2
Sun x y z The star in question is located on the positive y axis of S, so a photon that arrives at the Earth’s location at t = 0 has traveled straight down the y axis. The red dots are events on its worldline. The time and space separations measured between them in S are Δ t 21 , Δ x 21 = 0 and Δ y 21 = - c Δ t 21 . 1 2 We use the Lorentz transformation equations to determine the time and space separations between events 1 and 2 measured in S’ . 21 21 t t γ = ∆ 21 21 x V t γ = - 21 21 y c t = - ∆ y x 2 1 21 y 21 x We conclude that the star will be observed in the direction inclined at an angle θ toward the x’ axis and away from the y’ axis with 4 21 21 | | tan 10 radians | | x V y c γ θ θ - = = This is a bit more than 20 seconds of arc and easily measured by astronomers.
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Sun S : inertial frame in which the Sun is essentially at rest throughout the year. Earth location at t = 0 x y z Earth location at t = 6 months V arrowrightnosp Six months later, the position of this star measured in the Earth’s frame will be inclined at the same angle but in the opposite direction from the y’ axis. Q1. The direction of a star located on the x axis measured in the Earth observatory at these two times would be A) inclined 20 arcseconds away from the x’ direction, toward y’ direction at t = 0 and away at t = 6 months B) inclined 20 arcseconds away from the x’ direction, away from y’ direction at t = 0 and toward at t = 6 months C) along x’ axis at both times.
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern