- X 3 2 Ax H 6m X Ch Cxcl12 Hg4e132 Y T 6m Cale Y T 2 2 H 5 Let Vx T X T And Vy T Y 1 (26.02 KiB) Viewed 32 times
- X 3 2 Ax H 6m X Ch Cxcl12 Hg4e132 Y T 6m Cale Y T 2 2 H 5 Let Vx T X T And Vy T Y 2 (70.46 KiB) Viewed 32 times
5) Let vx(t) = x'(t), and vy(t) = y'(t), and turn each equation into a system of two first- order differential equations. Collect these into a system of four first-order differential equations (the order should be x(t), vx(t), y(t), vy(t)). The four unknowns are the x and the y coordinate, and the velocities in the x and the y directions of each celestial object orbiting the Sun. This system of four first-order differential equations will separately model the orbits of Earth, Mars and the spacecraft, if we use the correct initial conditions for each orbiting object. In other words, if you use the four initial conditions for Mars in this system of equations, and solve them, you can get the x, and the y coordinates of Mars, and its velocity in the x and the y directions for a given time. 6) The four initial conditions for this system, for each orbiting object at 1 = 0 (Nov. 25th, 2011) are given below. The letter e is for Earth, m is for Mars, and c is for the curiosity spacecraft. Note that the initial positions for the spacecraft are the same as Earth's. That is because when the spacecraft is launched outside of Earth's strong gravitational field, it is about 200 miles above Earth, which is negligible compared to cosmic distances. xe(0) = 0,44503 AU vxe(0) = -5.71113 AU/y ye(0) = 0.88106 AU vye(0) = 2.80924 AU/y xm(0) = -0.81449 AU vxm(0) = -4.23729 AU/y ym(0) = 1.41483 AU vym(0) = -2.11473 AU/y - XC(O) = 0.44503 AU vxc(0) = Yours to find out AU/y. ye(O) = 0.88106 AU vyc(0) = Yours to find out AU/y vxc(O) = Yours to find out AU/y,