Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Modelling the motion of a meteor

  1. Dec 13, 2014 #1
    Hi!
    I am to model the motion of a meteor as it travels through the atmosphere, taking into account the loss of mass, which is 0.025 kg upon impact (height = 0). I also have to take into account the air resistance on the meteor, the fact that the air density is a function of height and that the orthographic projection of the meteor perpendicular the direction of movement (part of the air resistance equation) is a function of the mass of the meteor.
    I assume that gravitational field strength is constant.

    I have attached a picture of the equations I have been able to derive so far using standard formulas.

    I have to solve the differential equations for x(t) and y(t) numerically, however, I fail to see how and therefore seek help.

    This is for a very important school project and I'm running out of time, so I really need help. Even the smallest hint would be greatly appreciated!
     

    Attached Files:

    • Mat.jpg
      Mat.jpg
      File size:
      61.5 KB
      Views:
      108
  2. jcsd
  3. Dec 13, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Simply calculate it step by step in small time steps?
    You know the initial position and velocity at t=0, you can calculate the acceleration there and use this to estimate the position and velocity at t=0.01s (or whatever). Use the data there to estimate the values for t=0.02s and so on. There are better integration schemes, but start with the easiest one and improve that later if you like.

    Your equation for A can be simplified a bit.

    The atmospheric density does not follow an exponential law as the temperature depends on height, by the way.
     
  4. Dec 13, 2014 #3
    Newtonian gravity with atmospheric drag is not solvable analytically. Use an ordinary differential equation numerical solver. I prefer MATLAB.

    It would help if you tell us what exactly A(m), m(t), etc are. Also, what is that little squiggly variable for? Is it a constant?
     
    Last edited: Dec 13, 2014
  5. Dec 13, 2014 #4
    This is everything
     

    Attached Files:

    • Mat.jpg
      Mat.jpg
      File size:
      43.2 KB
      Views:
      124
  6. Dec 13, 2014 #5
    Mass as a function of time only
     

    Attached Files:

  7. Dec 14, 2014 #6

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I don't think that equation for m(t) makes sense, it has m(t) at the right side as well, but multiplied by t and other factors. Looks like a wrong differential equation.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook