calculation of trajectory of astroid collide with the earth with runge kutta.

Using second order differential equations,using gravitation law
of two objects m1=astroide,comet m2=earth


F=G*(m1*m2)/r^2, F=m*a=m*dv/dt ,v=dx/dt

when m1 near earth with some initial velocity.

How you can make simulation of position of m1 will collide with the earth.


(some info : can so implement kepler laws in the problem),
what I want to know is the position at each moment in time.

what is influence of the moon in the problem.

can also easy implemented in the simulation.

"loebasken" wrote in message
om...
Using second order differential equations,using gravitation law
of two objects m1=astroide,comet m2=earth


F=G*(m1*m2)/r^2, F=m*a=m*dv/dt ,v=dx/dt

when m1 near earth with some initial velocity.

How you can make simulation of position of m1 will collide with the earth.


(some info : can so implement kepler laws in the problem),
what I want to know is the position at each moment in time.

what is influence of the moon in the problem.

can also easy implemented in the simulation.

You'll probably want at least four bodies in your
simulation:

Earth,
Moon,
Sun,
asteroid

Pick a starting time (epoch) and find the Cartesian
coordinates and velocities of the bodies. Sun-centered
ecliptic coordinates would probably be appropriate.
Commercial software such as MICA or the online
HORIZONS system will give you starting coordinates.
Or, just cook up some plausible scenario for demo
purposes.

Write the second order differential equations for the
four bodies as a system of coupled first order
equations. Code them into your RK software. Danby's
book, "Computer Modelling: From Sports to Spaceflight
...From Order to Chaos", provides an excellent RKF4(5)
implementation for these sorts of investigations.

Picking the starting parameters for the asteroid will
be the tricky bit. You'll want to play around. A
dynamic graphical display of the trajectories will be
helpful; perhaps an implementation in good old-
fashioned BASIC on a PC would be a good place to
start.