Bibliographic Details
| Title: |
Legendre Functions, Feynman's Disk Paradox, Electromagnetic angular momentum. |
| Authors: |
Khosravi, Sepand1 sepandkhosravi1@gmail.com |
| Source: |
Latin-American Journal of Physics Education. Dec2025, Vol. 19 Issue 4, p1-4. 4p. |
| Subject Terms: |
Lane-Emden equation, Stellar structure, Numerical solutions to equations, Equations of state, Astrophysics |
| Abstract (English): |
We present numerical solutions of the Lane-Emden equation for selected polytropic indices using a fourth order Rnnge-Kutta integrator with series expansion initial conditions. The method is validated against the analytical cases n = 0 and n = 1, then applied to the astrophysically relevant indices n = 1.5 and n = 3. The computed first zeros are 𝜉1 ≈3.654 (n = 1.5) and 𝜉1 ≈6.897 (n = 3), and the resulting density profiles show that increasing n produces more extended, less centrally concentrated models. The n = 3 polytropic model yields a solar radius of the correct order of magnitude, showing that even a simplified pressure-density relation can capture the essential structural scaling of real stars like the Sun. [ABSTRACT FROM AUTHOR] |
| Abstract (Polish): |
Presentamos soluciones numéricas de la ecuación de Lane-Emden para índices politrópicos seleccionados utilizando un integrador Rnnge-Kutta de cuarto orden con condiciones iniciales de expansión en serie. El método se valida frente a los casos analíticos n = 0 y n = 1, y posteriormente se aplica a los índices astrofísicamente relevantes n = 1,5 y n = 3. Los primeros ceros calculados son 𝜉1 ≈3,654 (n = 1,5) y 𝜉1 ≈6,897 (n = 3), y los perfiles de densidad resultantes muestran que al aumentar n se obtienen modelos más extendidos y con menor concentración central. El modelo politrópico n = 3 proporciona un radio solar del orden de magnitud correcto, lo que demuestra que incluso una relación presión-densidad simplificada puede capturar la escala estructural esencial de estrellas reales como el Sol. [ABSTRACT FROM AUTHOR] |
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| Database: |
Education Research Complete |
