ASEN 6008: Interplanetary Mission Design Lab Spring, 2015

Transcription

1 ASEN 6008: Interplanetary Mission Design Lab Spring, 2015 Lab 4: Targeting Mars using the B-Plane Name: I d like to give credit to Scott Mitchell who developed this lab exercise. He is the lead Astrodynamicist at Ball Aerospace & Technologies Corporation here in Boulder. If Ball needs an interplanetary trajectory design, he is the one they call. I have taken out a few things and added a few things in order to make the lab a bit more challenging (and, of course, more of a learning experience. I know you love it!) Using the STK Astrogator Targeter to get to Mars February, 18, 2002 Scott Mitchell A real example I did this for our Mars Scout study/proposal effort. The RF and power engineers want to know things like the spacecraft to Earth range, the spacecraft to sun range, and the angle formed by the sun, Earth, and spacecraft (for antenna placement and range of motion). For all of these, we need to generate a trajectory from the Earth to Mars. Scott Mitchell Mission Design Parameters The pork chop plot shown in Figure 1, below, shows the mission design parameters for an Earth- Mars transfer in the opportunity. The nominal departure date (JD = ) is June 28 th, 2007 and the nominal arrival date (JD = 24544) is Jan 24 th, Determine the type of transfer, the departure and arrival dates, the launch C 3, the declination of the departure asymptote, and the right ascension of the departure asymptote that minimizes the value of the launch C 3. Record these values on the attached answer sheet. (It s hard to read, but the smallest C 3 contour near the middle of the plot has a value of about 12.8 km 2 /s 2 ). The right ascension and declination in the plot are with respect to the ecliptic (this is important later). Important! Please check your answers with me or the TAs before continuing to make sure that your parameters are correct (the following scenario might not work otherwise). 1

2 Days past Jan 24th, 2008 (JD = 24544) Pork Chop Plot for the 2007 Earth-Mars Transfer Opportunity Days past June 28th, 2007 (JD = ) C 3 (km 2 /s 2 ) L (deg) RA D L (deg) L Figure 1. A pork chop for the Earth-Mars transfer opportunity: Red lines show C3, green lines show DLA and red lines show RLA Introduction We will be using Astrogator s targeter to target a full mission from low-earth orbit to low-mars orbit. We will begin in LEO and target the best launch time to put us on the proper trajectory. Then we will add Trajectory Correction Maneuvers (TCMs) to improve the performance of our satellite s trajectory. These TCMs will be performed at launch +15 days, launch + days, and arrival 20 days. In reality there are typically four or five TCMs, but there are also many other perturbing effects that we will not be modeling. Finally, we will enter into a Mars Capture Orbit. STK Setup - Start an STK scenario. Save the new Scenario to its own new folder (new, clean folder!) - Under the Scenario s properties: - Set the starting epoch to your departure date and the ending epoch to your arrival date plus days. 2

3 - Under 2D Graphics, turn on Show Orbits for the planets and vehicles. Change whatever else you d like (It s recommended to turn off Ground Tracks). - Under the 2D Graphics Window s properties: - Set up Projection to orthographic, ECI, display height =,000 km, lat =. - Under the 3D Graphics Window s properties: - Hit Advanced; Change the Max Visible Distance to 1e15 km (so we can see the action from a long way off). - Make a new propagator using the Components Browser: Click on Utilities: Component Browser. Click on Propagators. Highlight Earth J2 and click Duplicate. Rename to Mars J2 and hit ok. Double-Click Mars J2, change central body to Mars, change gravity field to ZonalsToJ4, set degree to 2, hit OK. Hit OK to exit the Component Browser. - Create two planets: make one Earth, and the other Mars. Check to make sure that their 2D and 3D graphics properties are desirable (show orbit, show inertial position, etc.) Use the DE421 ephemeris for both. - Create a satellite - Change its name to Scout - View the basic properties, and select Astrogator as the propagator - Under 2D Graphics, select Pass and change the ground track lead type to None and the orbit track lead type to All. - Under 3D Graphics, select Pass and check the inherit from 2D Graphics option. - Under 3D Graphics, select Model and maximize the viewing distance for the spacecraft s Marker and Label (so we can see the spacecraft s marker and label from a long way off). Launch and outward trajectory - Delete the default initial state, but leave the default propagate segment. - Create a target sequence before the propagate segment. Inside of the target sequence put a launch, propagation segment, and impulsive maneuver. We will use this to target the outgoing C3, declination of the launch asymptote, and right ascension of the launch asymptote. - For the launch, put the time as 12:00 on your departure date. Leave the other items as the defaults. Check the Launch epoch bulls-eye. - Rename the propagate segment for DLA, RLA ; use the Earth J2 propagator; change the trip time to sec ( min, or roughly one orbit); check the trip duration bulls-eye; turn off maximum propagation time (under the Advanced button). - Rename the impulsive maneuver segment target C3, DLA, RLA, and select attitude control along velocity vector ; put in an initial guess (magnitude) of 3 km/s; check the magnitude bulls-eye. - With the impulsive maneuver highlighted, hit the Results button, and under target vector select C3 energy, outgoing asymptote declination, outgoing asymptote right ascension. Since the pork chop plot showed angles with respect to the ecliptic, change the Coordinate System 3

4 Value for the both the declination and the right ascension to the True Ecliptic of Date, TrueEclpDate. - With the target sequence highlighted, do the following: - Change the Action to Run active profiles - Change the Differential Corrector s Mode to Iterate - Hit the Properties button. Select the launch epoch, the trip duration, and the magnitude of the impulsive maneuver to be the active control parameters. The epoch and trip duration will target the proper launch asymptote and the impulsive maneuver will thrust only in the velocity direction (most efficient). Select C3, Dec, and RA as the Equality Constraints and set them to be the numbers that you obtained from the pork chop plot. - Run the targeter (hit the green go button). It may take a few runs (~?) to converge. You can watch the convergence process in the targeting profile window at the top. - Once the targeter has converged, set the targeter s Action to Run nominal sequence and hit the Apply Changes button. Finally, observe the trajectory in each view. - What are your new launch date, propagation trip duration, and impulsive ΔV magnitude? (Write your answers on the Answer Sheet) - Highlight the Propagate segment after the Targeter. Set the propagator to CisLunar and the Trip duration to 12 hours. Hit OK in the MCS window and view the trajectory in the 2D and 3D windows to make sure that you re on a hyperbolic escape trajectory. You should notice that the trajectory departs the Earth in the general direction of the Earth s velocity. - Change 2D map to heliocentric (hit the Graphics Window Central Body button on the top toolbar and change the central body to the Sun), orthographic projection with display height of 0,000,000 km and lat of deg. - Change 3D map central body to Mars (Graphics Window Central Body button). If you don t like getting dizzy, go to the View From/To button and change the Reference Frame to Mars Inertial Axes. - Add another propagate segment (change it to a different color). Set the propagator to Heliocentric and the Trip duration to 0 days. Make sure to click off the maximum propagation time (Hint it s best to do this all the time!). Now view the overall trajectory. The satellite should come very close to Mars! - Save your Scenario! 4

5 TCM 1 You may have noticed that the satellite came close to Mars, but did indeed miss the planet. Mission designers fully expect errors in the satellite s initial trajectory. Hence, they build in Trajectory Correction Maneuvers (TCMs) to re-target their ideal trajectory. - Remove the two propagate segments after the Target Sequence. - Add a new propagate segment and rename it to propagate to L+15 days. Set the propagator to Heliocentric. Set the Trip length to be 15 days. (Might as well get used to removing the maximum propagation time out of habit). - Add a target sequence after the propagate segment and rename it TCM1. We will now calculate the first TCM. - In the target sequence, put an impulsive maneuver and a propagate segment. Rename the impulsive maneuver to target B dot R, B dot T, time of arrival - With the impulsive maneuver highlighted, change attitude control to thrust vector, thrust axes to Mars VNC. Select all three velocity components as the varied parameters (put a check in the target next to each of them). - In the propagate segment, select the Heliocentric propagator. Hit the advanced button and turn off the maximum propagate time. Under stopping conditions, Insert a periapsis stopping condition and remove the duration stopping condition. With the periapsis condition highlighted, change the Central Body to Mars. The propagator will now propagate to the closest Mars approach. - With the propagate segment highlighted, hit the Results button. Select Epoch. From Multibody, select BDotR and BdotT. Change the target body for each of these to be Mars by double clicking on the target body in the bottom panel. Change the Reference Vector to Mars Ecliptic Normal. Use the planet Mars that you created. You should now have 3 selected components; hit OK. - Highlight the TCM1 target sequence, hit the Properties button under Profiles. - Select all three Control Parameters. - Select all three Equality Constraints. Set the Epoch Desired Value to your arrival date with a tolerance of 1 hour. Set the BdotT and BdotR Desired Values to be 6000 km (targeting for a near miss of Mars, but allowing for planetary protection considerations). Set the tolerance to km, allowing a large range of acceptable near-misses, which helps the targeter. Hit OK. - Highlight the TCM1 target sequence, change the Action to Run active profiles. Change the Differential Corrector s Mode to Iterate. - Run the targeter (hit green go button) until it converges (7 iterations?). - Once the targeter has converged, with the targeter highlighted, change the Action to Run nominal sequence and hit Apply All Corrections. The maneuver components should be on the order of m/s. What are the three components of your ΔV vector? (see answer sheet) - Hit OK in the MCS window. View the trajectory in the 2-D window to make sure that you re getting close to Mars. When the s/c gets close to Mars, view the s/c in the 3-D window and see just how close to Mars it really is getting. 5

6 - Add a return segment between the impulsive maneuver and the propagate segment inside of the TCM1 target sequence. We want to add further TCMs before reaching Mars, hence we don t want the propagate segment to be active, but we want to keep it in for error-checking in the future, in case something goes wrong. - Save your work! - TCM 2 - Add a propagation segment after the TCM1 target sequence. Rename the propagation segment to be propagate to L+ days. Set the propagator to Heliocentric. Set the trip length to be 75 days. - Add a target sequence after the propagate segment and rename it TCM2. We will now calculate the second TCM. - Perform the exact same actions as for TCM 1, but now reduce the tolerance on the constraints to 1 km for BdotT and BdotR and 1 minute for the Epoch. - Observe the converged maneuver. The maneuver should be small a few m/s at most. What are the three components of your ΔV vector? - Hit OK in the MCS window. View the trajectory in the 2-D window to make sure that you re getting close to Mars. When the s/c gets close to Mars, view the s/c in the 3-D window and see just how close to Mars it really is getting. - Add a return segment between the impulsive maneuver and the propagate segment. - TCM 3 - Add a propagation segment after the target sequence. Rename the propagation segment to be propagate to arrival-20 days. Set the propagator to heliocentric. Hit the advanced button and turn off the maximum propagate time. Set the trip length to be your total trip duration minus 1 days (20 days for arrival-20 plus because you are starting from L+). If my total trip duration were 374 days, I would enter 264 as the trip duration. - Add a target sequence after the propagate segment and rename it to TCM3. We will now calculate the third TCM. - Follow the same instructions as in TCM 1 and 2, however make these changes: - Instead of targeting BdotR, BdotT, and an Epoch, this time target Altitude of Periapsis (Mars Periapsis) and Epoch. - Target an altitude above Mars of 200 km with a tolerance of 0.1 km. - Target your Arrival Epoch with a tolerance of 0.1 sec. - Once the targeter has converged, observe the total ΔV. The maneuver should be small a few m/s at most. What are the three components of your ΔV vector? - Hit OK in the MCS window. View the trajectory in the 2-D window to make sure that you re getting close to Mars. When the s/c gets close to Mars, view the s/c in the 3-D window and see just how close to Mars it really is getting. 6

7 - Depending on how we targeted for Mars we could have entered into nearly any Martian orbit. In this case, let s find out what incoming orbit we have with respect to Mars. - Highlight the final propagate segment in the TCM3 Target Sequence (if you added a return segment, make sure you allow the Targeter to Bypass). - Double-click the propagate segment or otherwise go to its properties menu. Change the Coord. System to Mars Centered Inertial. - Now with the propagate segment highlighted, hit the Summary button. - What are the satellite s current orbital elements with respect to Mars? - Semi-major axis, eccentricity, inclination, and V - If you haven t done it already, add a return segment between the TCM3 impulsive maneuver and the propagate segment (and make sure that the targeter is not allowed to bypass). - Mars Orbit Insertion - Add a propagation segment after the TCM3 target sequence. Rename the propagation segment to be propagate to Mars periapsis. Set the propagator to Heliocentric. Under stopping conditions, select periapsis and remove duration. For central body, select Mars. The propagator will now propagate to the closest Mars approach. - Add a target sequence after the propagate segment and rename it MOI. We will now calculate the Mars Orbit Insertion (MOI) burn. - In the target sequence, put an impulsive maneuver and propagate segment. Rename the impulsive maneuver to MOI - With the impulsive maneuver highlighted, change attitude control to thrust vector, thrust axes to Mars VNC. Select only the X (along) velocity component as the varied parameters (put a check in the target next to X only). Start with an initial guess of 1 km/s for the X velocity. - With the propagate segment highlighted, change the Propagator to Mars J2. Change the Trip duration to 35 hours. - With the propagate segment highlighted, hit the Results button. From Keplerian Elements, select orbit period. Change the central body to be Mars by double clicking on the central body in the bottom panel. - Set the targeter to target an orbital period of 35 hours (targeting for a Mars capture orbit period of 35 hours). - Run the targeter (hit green go button). - Once the targeter has converged, observe the maneuver. What is the new ΔV? Draw what you see in the 3D window on the Answer Sheet. Your spacecraft should now be in an eccentric Mars orbit, with a period of 35 hours and a periapsis of 200 km. This is a typical Mars capture orbit. Aerobraking would then be used to circularize the orbit. We will learn how to target specific orbits about another planet next week. (P.S. Save your scenario!) 7

8 Lab 4: Targeting Mars using the B-Plane Spring 2014 ANSWER SHEET Name: / Earth to Mars mission design parameters (determined from the pork chop plot): Type: (4 pts) Launch Date: (4 pts) Arrival Date: (4 pts) Launch C 3 : (4 pts) Declination of departure asymptote: (4 pts) Right ascension of the departure asymptote: (4 pts) Launch Targeter Segment: New launch date and time (4 pts) New propagate trip duration: (4 pts) New impulsive ΔV magnitude: (4 pts) TCM 1: ΔV x : (4 pts) ΔV y : (4 pts) ΔV z : (4 pts) 8

9 TCM 2: ΔV x : (4 pts) ΔV y : (4 pts) ΔV z : (4 pts) TCM 3: ΔV x : (4 pts) ΔV y : (4 pts) ΔV z : (4 pts) sma: (4 pts) ecc: (4 pts) inc: (4 pts) V : (4 pts) MOI: ΔV: (4 pts) Draw the final Mars Orbit that you see in your 3D window: (8 pts) 9