7. TUTORIAL NR.1: RENDEZ-VOUS WITH SPACE STATION GEO 7.1 Introduction If you have loaded "Default.orb" you are ready to start this journey. It is January 1, 2000. You (the little blue-white cross on the display) are now in a almost circular orbit at 800 km from Earth' surface or 7178 km from Earth's center. Slightly below you, at a height of 500 km, are the two low orbit space stations MIR (URSS) and Freedom (USA/EUR/JAP). You want to reach the GEO space station in geostationary orbit (this a circular orbit with a period of 24 hours). GEO is the orange dot in the upper part of the space display. Start by analysing the situation. Select "Pause" from the Simulation menu in order to "freeze" the time while you decide your action. Get an "Object Data" window from the Inquiry menu. Type GEO in the "Object ->" gadget and you get the orbital parameters of your objective GEO: note that its orbit is circular (e = 0) and the radius is 42248 km. Get now a "Transfer Orbit" window from the Enquiry menu. Make sure the right side gadget is toggled on "Radius" and input 7178 (your present radius) and 42248 (GEO's) respectively in r1 and r2. You will get the orbital parameters for a very elliptic orbit (e = 0.71) with perigee [r-] (nearest point to Earth) at 7178 km and apogee [r+] at 42248 km. Note now the speed at perigee [v-] for the transfer orbit: 9.746k m/s. The difference from your present speed (7.454 km/s) is 2.292k m/s: this is the increase (kick) which you must give to your spacecraft to bring it on the transfer orbit. Another kick will be required when you have reached the apogee at 42248 km: the apogee speed [v+] is 1.656 km/s while GEO on its circular orbit has a higher speed (3.072 km/s) which you will have to match. Now you know how to get to the same orbit as GEO. However, you also want that when you have reached it, GEO happens to be at the same location. For this, you must wait for a certain relative position between you and GEO before starting on the transfer orbit. An available tool program, called "Hohmann" can give you the next optimum transfer time. Get a NEWCLI with the appropriate menu, enlarge the window and type: > Hohmann Ship GEO This will give you the all the data for transfer to GEO. In particular, the next oppurtunity for insertion in the transfer orbit: this should be at time 4966 sec. By the way, flight times in this tutorial will be in seconds, so you may wish to select ' seconds' from the Time menu. 7.2 Getting on the transfer orbit We are now ready to send the first commands. Get the Command window from the 'Spacecraft Control' menu. See the pop-up menu (right mouse button), then: - Select 'Tangential Kick' from the pop-up menu. - Type in the first opportunity time, as obtained from the Hohmann program, in the time gadget: in this case 6337 seconds. - Just below, in the gadget following 'Delta-Vt (km/s) type in the value of DVš, that is 2.292 km/sec, which is the speed increase that will insert you on the transfer orbit. - Click [OK], note that the command DVT has been recorded. Do NOT close the Command window. You may wish, however, to close the Transfer Orbit and the Object Data windows in order to clean the display and make sure you do not run out of memory (if you do the program will crash, sorry). Now continue the simulation by selecting 'Continue' from the Simulation menu. Wait until the command time. Try the '10* faster' selection from the Simulation menu to let flight time pass quicker. In the meantime select 'Auto-draw Orbit' from the Display menu. At 6337 sec flight time, an acoustic signal will tell you that the ship will accelerate. In the present case the acceleration phase will be almost instantaneous and will put you on a transfer orbit (see the new orbit parameters in the upper right window) with apogee at 42278 km to be reached at time 27866 sec. You may load this situation as file 'ApproachGEO.orb'. This orbit is very closed to the theoretical you were aiming at: in fact the differences are due to the rounding error due to using only three decimals in the Delta-V command. 7.3 Apogee kick into geostationary orbit Now back to the Command window: input the expected apogee time (25688 sec) and the apogee kick given by 'Hohmann' (1.416 km/s). Click [OK], note that the command DVT has been recorded. At the apogee, then the spacecraft will increase its speed as programmed and set on a almost circular orbit very close to GEO. 7.4 Final approach to GEO If for any reason you did not get here as told above, you may load this situation from file 'ApproachGEO2.orb'. Now the final approach. Make sure that the simulation time step is small (a few seconds) by means of the ' * slower' menus. Get the Approach window by selection 'Approach guide ON' from the Spacecraft Control menu. Reply GEO the "Object:" prompt. Observe the window display: GEO is the orange spot at the centre, you are the white cross. The numeric data near the window top tell you how far you are from GEO in radial (Delta-r) and tangential (Delta-n) direction as well as the relative velocity. Important: the reference system of the window is fixed with the GEO-Earth line. If you have followed the instruction up to now you should be at about 220 km fro GEO, the spacecraft will appear in the approach window to the right of its objective. The maneuver jets are operated with the cursor keys; each time you press one a small velocity increment is given and you hear the short blast of the jets: Cursor up: positive radial (will move you toward the window top). Cursor down: negative radial. Cursor left: positive (counterclockwise) tangential (to the left). Cursor right: negative tangential. The amplitude of the velocity increment is initially set at 2 m/s. This will generally be too small when you are so far from the objective. Therefore select 'Change maneuver dV' from the Control menu and input 20 at the prompt. Now each kick will be of 20 m/s. A couple of kicks left and one down will bring you rapidly (you may increase the time step at about 40 sec) near the objective. You should re-scale the approach display regularly during the approach by means of the 'Re-scale display' menu, which will apply to the approach window when this is active (otherwise it will act on the main display). When the display scale is of a few kilometers GEO will be surrounded by a circle: the docking limit. In the final approach phase you should decrease the simulation time step and also the kick dV, down to a few meters per second, in order to reduce the velocity difference with GEO. When you are within the "docking circle", select the 'Dock' menu, which will automatically dock you beside GEO. Press q to quit and then left-Amiga_M to return to the ORBIT screen.