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  1. M

    I Orbit simulations, tidal forces and planetary oblateness

    I've managed to find a way to correct for the obleateness, and the results are pretty remarkable with regards to to Gallian moons, The absolute error on Europa's position has been reduced to about 32000 km, a vast improvement. However I am at a loss what is causing the huge errors on Saturn...
  2. M

    I Orbit simulations, tidal forces and planetary oblateness

    Please do :) Do you have any idea on how to compensate the oblateness of the bodies?
  3. M

    I Orbit simulations, tidal forces and planetary oblateness

    Yes I've noticed Saturns error is very high which I can't explain. The numbers I posted are the largest deviations that occur in a 3 year period. Europa deviates by about 100 degrees while with Io, it's deviation is >180 degrees, it it remains it the same orbit as the reference. I get your...
  4. M

    I Orbit simulations, tidal forces and planetary oblateness

    I don't experience any significant changes in accuracy when changing using 15 steps/hour compared to 10 steps/hour. And as most bodies are simulated quite accurately, I don't expect it to be a issue with the integrator. I am using Velocity Verlet, Below is a exhaustive list of the bodies that...
  5. M

    I Orbit simulations, tidal forces and planetary oblateness

    Thanks, can you point me to some resources on how to do that? I am making a solar system simulator, and the errors I get when simulating the larger moons of jupiter are about the diameter of their orbits when simulating three years. I have made some animations and can see that they fall behind...
  6. M

    I Orbit simulations, tidal forces and planetary oblateness

    How does one correct for tidal forces when (classically) simulating the orbits of solar system bodies?
  7. M

    C/++/# Velocity Verlet C++ implementation

    Thank you, Mark44, for your reply. It was helpful in finding the bug. .. Mads
  8. M

    C/++/# Velocity Verlet C++ implementation

    I have been working on implementing a solar system system simulator in C++ - but am getting incorrect results on the order of 10^10 km, and it seems that the planets are moving directly away from the sun. I suspect that there is a mistake in the integrator (Velocity Verlet) that I have posted...
  9. M

    I Solar system simulation -- Significant deviation of some Jovian moons

    A smaller timestep fixed it, sorry for not looking before posting.
  10. M

    I Solar system simulation -- Significant deviation of some Jovian moons

    I am working on a simulation of the solar system, but I am having problems with the orbits with Europa and Io shown in the image below, the orbits of Jupiter, Ganymede and Callisto are consistent with NASA's simulations. For all bodies I have used identical parameters in generating the initial...
  11. M

    C/++/# Library that supports multidimensional Arrays

    Thank you all for your suggestions. @Mark44 Is correct that I am used to Python with only a passing familiarity with C++. The project I am working on is N-Body simulator for predicting Solar System orbits in Python, and I would like to speed up the computations without loosing the graphical...
  12. M

    C/++/# Library that supports multidimensional Arrays

    And that, like Mark44's post, does not answer my question.
  13. M

    C/++/# Library that supports multidimensional Arrays

    Perhaps I wasn't clear. What I'm looking for is a numpy-like library for C++.
  14. M

    C/++/# Library that supports multidimensional Arrays

    I have N x N 1x3 vectors that I need to be able to sum element-wise row-wise. I also need to do element-wise calculations on N x 3 arrays.
  15. M

    C/++/# Library that supports multidimensional Arrays

    I'm am looking for a C++ library that supports high-dimensional arrays ( 3=< ) and element-wise calculations. Is there such a thing?
  16. M

    I Computer friendly list of bodies in the asteroid belt?

    Is there a computer friendly list with the known bodies in the Solar System astroid belt, that contains their physical properties, position and velocities?
  17. M

    I Solar system simulation errors

    Errh.. I had accidentally chosen a another coordinate center than the one I intended. It simulates beautifully now! So thank you very much, all of you, for your help.
  18. M

    I Solar system simulation errors

    Hi, Below are the starting values, each line is one body and the order is Sun Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto The format is x, y, z, vx, vy, vz and the units are meters and meters/second. X, Y, Z...
  19. M

    I Solar system simulation errors

    Hi all. Before I tried Verlet, I had written a RK4 integrator where I got the same results. I have rewritten the program and (still) get the same results. Would it be helpful for me to post the code for the new integrator (still Verlet) here, or should I post it on the programming forum?
  20. M

    I Solar system simulation errors

    I am using GM, I rechecked the values and they seem correct. Thanks for the suggestion :)
  21. M

    I Solar system simulation errors

    The initial values for the simulations, x, y, z position and velocities in all three dimensions, are the first entries in the two diagnostic data sets. The simulator does not estimate the velocities, even though the diagnostic data set does include velocities. The two diagnostic data sets where...
  22. M

    I Solar system simulation errors

    The initial values are from the same dataset as the diagnostics. The main loop is given below: def gen_coords(): if not os.path.exists('trajectories/'): os.makedirs('trajectories/') # Generate coordinates and save to file # NumPy arrays for coordinates trajectory_earth =...
  23. M

    I Solar system simulation errors

    Hi, as a side project I am making a solar system simulator in Python, but I am getting extreme inaccuracies. As the image shows - I am comparing the simulation to data obtained from NASA's Horizon. I have written a a basic Verlet integrator in the Python class posten below: import numpy as...
  24. M

    Is there an error in this problem?

    I am currently working on problem 32-15 in Calculus by Spivak, and in question (b) in the bottom line there is a relation [\phi_1'(b)\phi_2(b) -\phi_1'(a)\phi_2(a)]+[\phi_1(b)\phi_2'(b)-\phi_1(a)\phi_2'(a)]>0 But I can only get it to work out if [\phi_1'(b)\phi_2(b)...
  25. M

    Uncertain about premise for proof.

    I am reading §22 of Topology by Munkres, in Theorem 22.2 the function g is said to be constant on each set p^(-1)({y}). However the only explicit property given in Corollary 22.3 to the function g is that it is continuous and surjective, but Theorem 22.2 to g in the proof. Is it implied that g...
  26. M

    Problem with basic sets proof.

    A \subseteq B means if x\in A then x\in B for all x\in A.
  27. M

    The meaning of different in Munkres' Topology

    The meaning of "different" in Munkres' Topology Hi, I'm working on problem 20.8(b) (page 127f) in Munkres' "Topology", the problem is to show that four topologies are "different". Does different in this context mean that they are unequal - in which case one can contain the other, or...
  28. M

    Which road to Special and General Relativity, and beyond?

    Hi Deluks, thank you very much for your suggestions! The books you suggested does indeed seem excellent. .. Mads
  29. M

    Which road to Special and General Relativity, and beyond?

    Hello, I am studying mathematics and physics on my own. However, it is the mathematical side of physics that intrest me. I would like some recommendations on which books would be beneficial for me to read, to gain an understanding of Special and General Relativity, and ultimatly string...
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