- #1
visio
- 3
- 0
Homework Statement
We have given coordinates on the Earth from where we are shooting to the Moon (bullet has really small mass). The Moon orbit and therefore Moon position in time t is known. The task is to compute the initial velocity vector (the angle and velocity of the bullet), so the bullet will reach the Moon.
Homework Equations
Maybe we can use this equations?
[itex]\frac{d^2x}{dt^2} = 2\Omega \frac{dy}{dt} +\Omega^2x-\frac{GM_e(x-x_e)}{r^3_e}-\frac{GM_m(x-x_m)}{r^3_m} [/itex]
[itex]\frac{d^2y}{dt^2} = -2\Omega \frac{dx}{dt} +\Omega^2y-\frac{GM_e(y_e)}{r^3_e}-\frac{GM_m(y_m)}{r^3_m} [/itex]
Ω is angular system velocity
G is gravitational constant
[itex]M_e, M_m[/itex] is mass of the Earth, Moon
[itex]r_e, r_m[/itex] is distance between Earth, Moon and the bullet
[itex]x_e, x_m[/itex] coordinates of the Earth, Moon centre of mass
The Attempt at a Solution
I know that I need to solve it numerically with shooting method, but the problem is, how the differential equation describing bullet trajectory looks like. I found the ones above, but I am not physicist (the main problem is to find the numeric solution of that equation), I do not know, if I can use them or not.
If anyone can give me some reference to the literature about this problem or something (the equations can be simple - no need to include all the influences, just the main ones as gravity field and rotation), I would be very happy. Thank you
Last edited: