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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Hidden Symmetries Of The Kepler Problem, Julia Kathryn Sheffler
Hidden Symmetries Of The Kepler Problem, Julia Kathryn Sheffler
Senior Projects Spring 2022
The orbits of planets can be described by solving Kepler’s problem which considers the motion due to by gravity (or any inverse square force law). The solutions to Kepler’s problem, for energies less then 0, are ellipses, with a few conserved quantities: energy, angular momentum and the Laplace-Runge-Lenz (LRL) vector. Each conserved quantity corresponds to symmetries of the system via N ̈other’s theorem. Energy conservation relates to time translations and angular momentum to three dimensional rotations. The symmetry related to the LRL vector is more difficult to visualize since it lives in phase space rather than configuration space. To understand …
Brightening Of The Bridge: Reflections Of A Past Sgr A* Outburst In Galactic Center Molecular Clouds, Nathalie Kanoelani Takiko Jones
Brightening Of The Bridge: Reflections Of A Past Sgr A* Outburst In Galactic Center Molecular Clouds, Nathalie Kanoelani Takiko Jones
Senior Projects Spring 2021
The center of our Milky Way galaxy is located more than 200,000 trillion km from Earth in the constellation Sagittarius. At the very center of our galaxy is a super-massive black hole called Sagittarius A$^{*}$. The black hole is surrounded by many interesting objects, including molecular clouds. Molecular clouds are large, cold clouds of gas in which stars are formed. Telescopes like NuSTAR have observed X-rays (radiation 10,000 times higher in energy than visible light) coming from these molecular clouds. Since cold gas cannot create such high energy emission by itself, there must be some external source of radiation interacting …