1ASEN 3200 Orbit Mechanics and Attitude Dynamics Spring 2006 LABORATORY O-1 Assigned January 27, 2006 Due February 7, 2006 I. Using STK 6.2 generate the ground track for one orbit of a circular orbit with an inclination of 60°, a semimajor axis of 6878 km and longitude of the ascending node = 0. Do not use the orbit wizard but create the satellite using properties Browser. Use a start time of 1 Jan, 2006 00hr 00min 00s and an end time one orbit period later. Note that you must set the times in the properties/basic of both the scenario and satellite. Use a two-body propagator. Now create a second satellite with the same orbit parameters except that it is in a retrograde orbit with the same maximum latitude. Note that the initial longitudes of the nodes are identical but that the retrograde orbit has gone through more than 360° of longitude in one orbital period while the prograde orbit has gone through less than 360°. Why is this? From the groundtrack map, compute the approximate orbital period. Include the groundtrack map in your report. Use a dotted line for the retrograde orbit. Also, you should use a white map background to reduce printer time. II. You have been assigned to develop a surveillance orbit, which flies directly over the Engineering Center (EC) on an ascending pass once every day (EC geodetic lat = 40.008°, lon = -105.262°, alt = 1.61 km). Create a facility representing the EC. In order to simplify the preliminary design process you are to use a two-body orbit propagator. Further restrictions are that the satellite should have an inclination of 66 deg, an eccentricity of 0.001, an argument of perigee of 0.0 deg, and make exactly fourteen orbits every sidereal day (23h 56m 04.091s of solar time). Use an epoch time of Jan 1, 2006 00h 00m 00s and have the satellite at perigee at this time. Specific tasks are: 1. Determine the orbit period and choose the longitude of the initial ascending node so that the first ascending pass goes directly over the Engineering Center (see Pre-Lab assignment). 2. Using STK generate and plot the ground track for one solar day using a 60sec step size. 3. Generate an access report for the EC for all orbits with elevation angles over 20 deg (set the min elevation using “constraints” on the left hand side of the facilities properties browser). 4. Plot the orbits during this access period using the zoom feature of STK. 5. Identify the start and stop times to the nearest minute for the ascending orbit that passes directly over the Engineering Center (use a 20 deg elevation mask). 6. Generate a report of azimuth, elevation and range (AER) of the satellite from the facility for this pass during the time elevations are greater than 20 deg. Write a Matlab program to verify the following results from STK: 1. Propagate the orbit for this same day using two-body classical Keplerian elements (,,, , ,a e i andωθΩ). Convert the classical elements to Earth Centered Inertial (ECI)2Cartesian coordinates (you may use software on the web handouts page to do this) and compare with those from STK (create a J2000 ECI position and velocity report) by plotting the difference in the position and velocity magnitudes and in the X coordinate. 2. Transform the ECI Cartesian position coordinates (X, Y, Z) from your program into Earth Centered and Fixed (ECF) position Cartesian coordinates and compare your results with STK (create an ECF position velocity report) by generating the X-coordinate and position magnitude difference plots as above. The Greenwich Hour Angle for Jan 1, 2006 00h 00m 00s is 100.43878° and the Earth rotation rate is 2Pi/(23h 56m 04.091s) = 0.72921158553x10-4 rad/sec (you need this to compute ECF coordinates). 3. Compute the longitude and geocentric latitude (λ, φ) using your ECF coordinates and plot the groundtrack for one solar day. Also include coastal outlines on your plot (the coastline file can be found at http://rimmer.ngdc.noaa.gov/coast/ ). See page 4 for the equations for λ and φ. Note that you must use both cos λ and sin λ to obtain the proper quadrant for λ. Write a report summarizing your results for problems I and II following the guidelines in the syllabus. Do not include large tabular reports but summarize your results and express them graphically to the extent possible. Be sure to Include and discuss all requested plots and reports. In your conclusions, discuss what you learned from this experiment and how it could be improved. Please imbed you figures in the text. Total page count for your report, not counting cover page or table of contents, should not exceed 11 pages. Pre-Lab Assignment for Problem II. Prior to the lab on Friday compute the value of the initial longitude of the ascending node that will send the first orbit of your satellite directly over the Engineering Center (EC). In order to do this, you will need to use the spherical trig handout that is on the class web page. Because these equations apply to spherical triangles, you must convert the geodetic latitude (see the web handout on geodetic and geocentric latitude) for the EC to geocentric latitude. You should find the geocentric latitude to be to be 39.819°. You will need to compute the amount of time it takes your satellite to go from its initial position over the equator to the EC. By accounting for Earth rotation during this time, you can compute the longitude of the first ascending node so that your satellite flies directly over the EC. If you have done this calculation correctly, you can use STK to zoom in on the EC and see that your first orbit goes through the center of the EC Icon. Put this calculation in your Lab report. Instructions for putting coastline into a MATLAB file • Get coastline data file from http://rimmer.ngdc.noaa.gov/coast Latitude range: 90 –90 Longitude range: -180 180 Database: WCL Select: ZIP, MATLAB, GMT Plot3• Make sure the preview looks good and download, be sure that it is a .dat file. This file is 2 columns of latitude and longitude. For MATLAB the file must be either .dat or .txt • On the code; %load coastline data name = load (‘filename.dat’) o Make sure the file is in the same directory as your program o Sometime this works without the parenthesis, it depends on the MATLAB version. The version in the ITLL works just like stated. %separate coastline