The original question, 'Can time on elliptical orbit be expressed analytically?' is a little vague. I think it means can the time into an orbit, i.e. the time since the planet was at the orbit pericenter (point of closest approach) be expressed as a function of the true anomaly (the angle of...
jebez: (irony, sarcasm) ...... I didn't notice the price! I bought the book several years ago and it wasn't expensive, I just checked and found 1 copy ! for #30.00 https://shopatsky.com/products/solving-keplers-equation
Inverting Kepler's equation (not Kepler's 1st law), i.e. calculating...
From the title, I think you want to be able to calculate orbit position as a function of time?
That's known as Kepler's Problem, which is to solve Kepler's Equation, which can be derived from Kepler's 3 laws.
Kepler's equation - https://en.wikipedia.org/wiki/Kepler's_equation
Kepler's problem...
There are 2 things to consider, are the Nature Physics quote and the APS/AAPT quote authoritative, i.e. correct, and, if they are correct, are they important?
To answer these questions it’s necessary to understand the context. There is the academic context – for 20-30 years there have been...
Dale: "Do they provide any evidence to support that claim? "
One of the authors, Caballero, is a one of the top honchos at PICUP, and he wrote a paper on the subject a few years ago ... "Prevalence and nature of computational instruction in undergraduate physics programs across the United...
<Mentor’s note: this thread is closed as a duplicate of https://www.physicsforums.com/threads/the-coming-revolution-in-physics-education.954664/ >
In the March 2024 issue of Nature Physics 'Computing in Physics Education' (https://www.nature.com/articles/s41567-023-02371-2) we read:
"In the...
Yes, my book .... Mathematical Modeling and Computational Calculus
See also ...
The Coming Revolution in Physics Education
A Revolution in Physics Education Was Forecast in 1989, Why Hasn't It Happened? What Will It Take?
A New Curriculum for Classical Physics
I'll give a controversial opinion .... assuming that the DE module is for a physics program. I'd begin by pointing out that classical physics is based on analyzing differential equation models of physical systems, but that, unfortunately, differential equation models of most physical systems...
I have a couple of playlists .. one for systems modeled by ODEs ...
and one for systems modeled by PDEs -
All the vids follow the same sequence - state the governing laws of physics for the system, model the system with DEs, translate the model to computational statements using Euler's...
"Not sure how universal it is, but my experience through half of my undergrad education gave me the impression that 90% physics was about exactly solvable problems."
Your impression was the result of an illusion. In reality very few problems in physics have exact solutions - even in...
? That doesn't make sense, I want it to be read... even debugged if necessary ...
Generally, things become much clearer when you actually have to program them and check if they work ... For example, it took me over an hour, and many corrections, to get that program to work.
That's not math, that's MATLAB.
In any case, now the question is, why does every book ignore the problem of an analytical solution for the 1-D gravity problem (as noted in the ref. in the wiki article, the guy looked at 100 physics books) and what is the solution?
From the reference in the...
By Jove ! ... and I've only been Matlabbing for 100 years !
G=6.7e-11; % gravitational constant m^3/(kg*s^2)
mEarth = 5.9742e24; % mass of Earth in kg
rEarth = 6.378e6; % radius of Earth in m
mu = G*(mEarth + 1);
y0 = rEarth;
t = 1;
x = (3/2*(pi/2-t*sqrt(2*mu/y0^3)))^(2/3);
y1...
Thanks, corrected ...
x = (3/2*(pi/2-t*sqrt(2*mu/y0^3)))^2/3;
However, now the apple is falling upwards ...
y0-y1 = ans =
-2.2703e+04
The last term in the series ... 2418092*x^7/62077640625
ans =
0.0028
but ... *y0 = 1.8177e+04
So, it's a long way from converging ... However, as t...
The freefall wiki entry wiki Freefall has an analytic solution for freefall distance in a gravitational field, but ... it doesn't seem to work ... at least i can't get it to work ... here is my MATLAB program to test it ...
clear
G=6.7e-11; % gravitational constant m^3/(kg*s^2)
mEarth =...