Geometric Event Finding Hands-On Lesson (IDL) |
Table of ContentsGeometric Event Finding Hands-On Lesson (IDL) Overview Note About HTML Links References Tutorials Required Readings The Permuted Index Icy API Documentation Kernels Used Icy Routines Used Find View Periods Task Statement Learning Goals Approach Solution steps Solution Solution Meta-Kernel Solution Code Solution Sample Output Find Times when Target is Visible Task Statement Learning Goals Approach Solution steps Solution Solution Code Solution Sample Output Extra Credit Task statements Solutions Geometric Event Finding Hands-On Lesson (IDL)
Overview
In this lesson the student is asked to construct a program that finds the time intervals, within a specified time range, when the ExoMars-16 Trace Gas Orbiter (TGO) is visible from ESA's deep space station in New Norcia. Possible occultation of the spacecraft by Mars is to be considered. Note About HTML Links
In order for the links to be resolved, create a subdirectory called ``lessons'' under the ``doc/html'' directory of the ``icy/'' tree and copy this document to that subdirectory before loading it into a Web browser. ReferencesTutorials
Name Lesson steps/routines it describes --------------- ----------------------------------------- Time Time Conversion SCLK and LSK Time Conversion SPK Obtaining Ephemeris Data Frames Reference Frames Using Frames Reference Frames PCK Planetary Constants Data Lunar-Earth PCK Lunar and Earth Orientation Data GF The SPICE Geometry Ginder (GF) subsystemThese tutorials are available from the NAIF ftp server at JPL:
http://naif.jpl.nasa.gov/naif/tutorials.html Required Readings
Name Lesson steps/routines that it describes --------------- ----------------------------------------- frames.req Using reference frames gf.req The SPICE geometry finder (GF) subsystem kernel.req Loading SPICE kernels naif_ids.req Body and reference frame names pck.req Obtaining planetary constants data spk.req Computing positions and velocities time.req UTC to ET time conversion windows.req The SPICE window data type icy.req The Icy API The Permuted Index
This text document provides a simple mechanism by which users can discover which Icy routines perform functions of interest, as well as the names of the source files that contain these routines. Icy API Documentation
For example, the document
icy/doc/html/icy/cspice_str2et.htmldescribes the cspice_str2et routine. Kernels Used
1. Solar System Ephemeris SPK, subsetted to cover only the time range of interest: de430.bsp 2. Martian Satellite Ephemeris SPK, subsetted to cover only the time range of interest: mar085.bsp 3. ESA stations SPK: estrack_v01.bsp 4. ESA stations frame definitions: estrack_v01.tf 5. EARTH_FIXED/ITRF93 frame connection: earthfixeditrf93.tf 6. Binary PCK for Earth: earth_070425_370426_predict.bpc 7. ExoMars-16 TGO Spacecraft Trajectory SPK, subsetted to cover only the time range of interest: em16_tgo_mlt_20171205_20230115_v01.bsp 8. Generic LSK: naif0012.tls 9. Generic PCK: pck00010.tpc 10. ExoMars-16 TGO FK, containing the SPICE ID/name mappings for the TGO spacecraft: em16_tgo_v07.tfThese SPICE kernels are included in the lesson package available from the NAIF server at JPL:
ftp://naif.jpl.nasa.gov/pub/naif/toolkit_docs/Lessons/ Icy Routines Used
Name Function that it performs -------------- --------------------------------------------------- cspice_furnsh Loads kernels, individually or listed in meta-kernel cspice_gfoclt Solve for times of occultation or transit cspice_gfposc Solve for times when a position vector coordinate constraint is met cspice_rpd Return number of radians per degree cspice_str2et Converts a time string to ET seconds past J2000 cspice_timout Format a time string for output cspice_wndifd Find the difference of two d.p. windows cspice_wnfetd Fetch a specified interval from a d.p. window cspice_wninsd Insert an interval into a d.p. windowRefer to the headers of the various procedures listed above, as detailed interface specifications are provided with the source code. Find View PeriodsTask Statement
2018 JUN 10 TDB 2018 JUN 14 TDBwhen the ExoMars-16 Trace Gas Orbiter (TGO) is visible from ESA's New Norcia station. These time intervals are frequently called ``view periods.'' The spacecraft is considered visible if its apparent position (that is, its position corrected for light time and stellar aberration) has elevation of at least 6 degrees in the topocentric reference frame NEW_NORCIA_TOPO. In this exercise, we ignore the possibility of occultation of the spacecraft by Mars. Use a search step size that ensures that no view periods of duration 5 minutes or longer will be missed by the search. Display the start and stop times of these intervals using TDB calendar dates and millisecond precision. Learning Goals
ApproachSolution steps
Preparation:
SolutionSolution Meta-Kernel
KPL/MK This is the meta-kernel used in the solution of the tasks in the Geometric Event Finding Hands On Lesson. \begindata KERNELS_TO_LOAD = ( 'kernels/spk/de430.bsp' 'kernels/spk/mar085.bsp', 'kernels/spk/estrack_v01.bsp' 'kernels/fk/estrack_v01.tf' 'kernels/fk/earthfixeditrf93.tf' 'kernels/pck/earth_070425_370426_predict.bpc' 'kernels/lsk/naif0012.tls' 'kernels/spk/em16_tgo_mlt_20171205_20230115_v01.bsp' 'kernels/pck/pck00010.tpc' 'kernels/fk/em16_tgo_v07.tf' ) \begintext Solution Code
PRO viewpr ;; Find and display the window of times when the ExoMars-16 ;; TGO spacecraft is above a specified elevation limit in the ;; topocentric reference frame of ESA's New Norcia station. ;; ;; The meta-kernel: ;; META = 'viewpr.tm' ;; ;; Maximum number of intervals in any window: ;; MAXIVL = 1000 ;; ;; Time string length: ;; TIMLEN = 50 ;; ;; Format string for time output: ;; TDBFMT = 'YYYY MON DD HR:MN:SC.### (TDB) ::TDB' ;; ;; Load the meta-kernel. ;; cspice_furnsh, META ;; ;; Assign the inputs for our search. ;; ;; Since we're interested in the apparent location of the ;; target, we use light time and stellar aberration ;; corrections. We use the "converged Newtonian" form ;; of the light time correction because this choice may ;; increase the accuracy of the occultation times we'll ;; compute using cspice_gfoclt. ;; srfpt = 'NEW_NORCIA' obsfrm = 'NEW_NORCIA_TOPO' target = 'TGO' abcorr = 'CN+S' start = '2018 JUN 10 TDB' stop = '2018 JUN 14 TDB' elvlim = 6.0d ;; ;; The elevation limit above has units of degrees; we convert ;; this value to radians for computation using SPICE routines. ;; We'll store the equivalent value in radians in REVLIM. ;; revlim = cspice_rpd() * elvlim ;; ;; Since SPICE doesn't directly support the AZ/EL coordinate ;; system, we use the equivalent constraint ;; ;; latitude > REVLIM ;; ;; in the latitudinal coordinate system, where the reference ;; frame is topocentric and is centered at the viewing location. ;; crdsys = 'LATITUDINAL' coord = 'LATITUDE' relate = '>' ;; ;; The adjustment value only applies to absolute extrema ;; searches; simply give it an initial value of zero ;; for this inequality search. ;; adjust = 0.0d ;; ;; STEPSZ is the step size, measured in seconds, used to search ;; for times bracketing a state transition. Since we don't expect ;; any events of interest to be shorter than five minutes, and ;; since the separation between events is well over 5 minutes, ;; we'll use this value as our step size. Units are seconds. ;; stepsz = 300.0d ;; ;; Display a banner for the output report: ;; print, ' ' print, 'Inputs for target visibility search:' print, ' ' print, ' Target = ' + target print, ' Observation surface location = ' + srfpt print, ' Observer''s reference frame = ' + obsfrm print, FORMAT = '(A,F8.6)', $ ' Elevation limit (degrees) = ', elvlim print, ' Aberration correction = ' + abcorr print, FORMAT = '(A,F10.6)', $ ' Step size (seconds) = ', stepsz ;; ;; Convert the start and stop times to ET. ;; cspice_str2et, start, etbeg cspice_str2et, stop, etend ;; ;; Display the search interval start time and stop ;; times using the format shown below. ;; ;; 2004 MAY 06 20:15:00.000 (TDB) ;; cspice_timout, etbeg, TDBFMT, TIMLEN, timstr0 cspice_timout, etend, TDBFMT, TIMLEN, timstr1 print, ' Start time = ' + timstr0 print, ' Stop time = ' + timstr1 print, ' ' ;; ;; Create the "confinement" window; store in this window ;; the interval over which we'll conduct the search. ;; cnfine = cspice_celld( 2 ) cspice_wninsd, etbeg, etend, cnfine ;; ;; Create an empty search result window that can hold MAXIVL ;; intervals. ;; riswin = cspice_celld( MAXIVL ) ;; ;; In the call below, the maximum number of window ;; intervals cspice_gfposc can store internally is ;; set to MAXIVL. ;; ;; Now search for the time period, within our confinement ;; window, during which the apparent target has elevation ;; at least equal to the elevation limit. ;; cspice_gfposc, target, obsfrm, abcorr, srfpt, $ crdsys, coord, relate, revlim, $ adjust, stepsz, MAXIVL, cnfine, riswin ;; ;; The function cspice_wncard returns the number of intervals ;; in a SPICE window. ;; winsiz = cspice_wncard( riswin ) ;; ;; Display the rise and set times. ;; if winsiz EQ 0 then begin print, 'No events were found.' endif else begin ;; ;; Display the visibility time periods. ;; print, 'Visibility times of ' + TARGET + $ ' as seen from ' + SRFPT + ':' print, ' ' for i = 0, winsiz-1 do begin ;; ;; Fetch the Ith interval from the window. ;; cspice_wnfetd, riswin, i, intbeg, intend ;; ;; Convert the rise time to a TDB calendar string. ;; cspice_timout, intbeg, TDBFMT, TIMLEN, timstr ;; ;; Write the string to standard output. ;; if i EQ 0 then begin line = 'Visibility or window start time: ' endif else begin line = 'Visibility start time: ' endelse print, line + timstr ;; ;; Convert the set time to a TDB calendar string. ;; cspice_timout, intend, TDBFMT, TIMLEN, timstr ;; ;; Write the string to standard output. ;; if i EQ (winsiz-1) then begin line = 'Visibility or window stop time: ' endif else begin line = 'Visibility stop time: ' endelse print, line + timstr print, ' ' endfor endelse ;; ;; Unload kernels so they are not accidentally used by another ;; SPICE-based program during the current IDL session. ;; cspice_kclear END Solution Sample Output
After compiling the program, execute it. The output is:
Inputs for target visibility search: Target = TGO Observation surface location = NEW_NORCIA Observer's reference frame = NEW_NORCIA_TOPO Elevation limit (degrees) = 6.000000 Aberration correction = CN+S Step size (seconds) = 300.000000 Start time = 2018 JUN 10 00:00:00.000 (TDB) Stop time = 2018 JUN 14 00:00:00.000 (TDB) Visibility times of TGO as seen from NEW_NORCIA: Visibility or window start time: 2018 JUN 10 00:00:00.000 (TDB) Visibility stop time: 2018 JUN 10 02:11:17.355 (TDB) Visibility start time: 2018 JUN 10 13:19:58.777 (TDB) Visibility stop time: 2018 JUN 11 02:08:16.008 (TDB) Visibility start time: 2018 JUN 11 13:16:50.542 (TDB) Visibility stop time: 2018 JUN 12 02:05:12.548 (TDB) Visibility start time: 2018 JUN 12 13:13:38.573 (TDB) Visibility stop time: 2018 JUN 13 02:02:06.618 (TDB) Visibility start time: 2018 JUN 13 13:10:23.432 (TDB) Visibility or window stop time: 2018 JUN 14 00:00:00.000 (TDB) Find Times when Target is VisibleTask Statement
Display each of the intervals in the result window as a pair of start and stop times. Express each time as a TDB calendar date using the same format as in the previous program. Learning Goals
ApproachSolution steps
SolutionSolution Code
PRO visibl ;; Find and display the window of times when the ExoMars-16 ;; TGO spacecraft is above a specified elevation limit in the ;; topocentric reference frame of ESA's New Norcia station ;; and is not occulted by Mars. ;; ;; The meta-kernel: ;; META = 'viewpr.tm' ;; ;; Maximum number of intervals in any window: ;; MAXIVL = 1000 ;; ;; Time string length: ;; TIMLEN = 50 ;; ;; Format string for time output: ;; TDBFMT = 'YYYY MON DD HR:MN:SC.### (TDB) ::TDB' ;; ;; Load the meta-kernel. ;; cspice_furnsh, META ;; ;; Assign the inputs for our search. ;; ;; Since we're interested in the apparent location of the ;; target, we use light time and stellar aberration ;; corrections. We use the "converged Newtonian" form ;; of the light time correction because this choice may ;; increase the accuracy of the occultation times we'll ;; compute using cspice_gfoclt. ;; srfpt = 'NEW_NORCIA' obsfrm = 'NEW_NORCIA_TOPO' target = 'TGO' abcorr = 'CN+S' start = '2018 JUN 10 TDB' stop = '2018 JUN 14 TDB' elvlim = 6.0d ;; ;; The elevation limit above has units of degrees; we convert ;; this value to radians for computation using SPICE routines. ;; We'll store the equivalent value in radians in REVLIM. ;; revlim = cspice_rpd() * elvlim ;; ;; We model the target shape as a point and the blocking body's ;; shape as an ellipsoid. No body-fixed reference frame is ;; required for the target since its orientation is not used. ;; back = target bshape = 'POINT' bframe = ' ' front = 'MARS' fshape = 'ELLIPSOID' fframe = 'IAU_MARS' ;; ;; The occultation type should be set to 'ANY' for a point ;; target. ;; occtyp = 'any' ;; ;; Since SPICE doesn't directly support the AZ/EL coordinate ;; system, we use the equivalent constraint ;; ;; latitude > REVLIM ;; ;; in the latitudinal coordinate system, where the reference ;; frame is topocentric and is centered at the viewing location. ;; crdsys = 'LATITUDINAL' coord = 'LATITUDE' relate = '>' ;; ;; The adjustment value only applies to absolute extrema ;; searches; simply give it an initial value of zero ;; for this inequality search. ;; adjust = 0.0d ;; ;; STEPSZ is the step size, measured in seconds, used to search ;; for times bracketing a state transition. Since we don't expect ;; any events of interest to be shorter than five minutes, and ;; since the separation between events is well over 5 minutes, ;; we'll use this value as our step size. Units are seconds. ;; stepsz = 300.0d ;; ;; Display a banner for the output report: ;; print, ' ' print, 'Inputs for target visibility search:' print, ' ' print, ' Target = ' + target print, ' Observation surface location = ' + srfpt print, ' Observer''s reference frame = ' + obsfrm print, ' Blocking body = ' + front print, ' Blocker''s reference frame = ' + fframe print, FORMAT = '(A,F8.6)', $ ' Elevation limit (degrees) = ', elvlim print, ' Aberration correction = ' + abcorr print, FORMAT = '(A,F10.6)', $ ' Step size (seconds) = ', stepsz ;; ;; Convert the start and stop times to ET. ;; cspice_str2et, start, etbeg cspice_str2et, stop, etend ;; ;; Display the search interval start time and stop ;; times using the format shown below. ;; ;; 2004 MAY 06 20:15:00.000 (TDB) ;; cspice_timout, etbeg, TDBFMT, TIMLEN, timstr0 cspice_timout, etend, TDBFMT, TIMLEN, timstr1 print, ' Start time = ' + timstr0 print, ' Stop time = ' + timstr1 print, ' ' ;; ;; Create the "confinement" window; store in this window ;; the interval over which we'll conduct the search. ;; cnfine = cspice_celld( 2 ) cspice_wninsd, etbeg, etend, cnfine ;; ;; Create an empty search result window that can hold MAXIVL ;; intervals. ;; riswin = cspice_celld( MAXIVL ) ;; ;; In the call below, the maximum number of window ;; intervals cspice_gfposc can store internally is ;; set to MAXIVL. ;; ;; Now search for the time period, within our confinement ;; window, during which the apparent target has elevation ;; at least equal to the elevation limit. ;; cspice_gfposc, target, obsfrm, abcorr, srfpt, $ crdsys, coord, relate, revlim, $ adjust, stepsz, MAXIVL, cnfine, riswin ;; ;; Now find the times when the apparent target is above ;; the elevation limit and is not occulted by the ;; blocking body (Mars). We'll find the window of times when ;; the target is above the elevation limit and *is* occulted, ;; then subtract that window from the view period window ;; riswin found above. ;; ;; For this occultation search, we can use riswin as ;; the confinement window because we're not interested in ;; occultations that occur when the target is below the ;; elevation limit. ;; ;; Find occultations within the view period window. ;; occwin = cspice_celld( MAXIVL ) cspice_gfoclt, occtyp, front, fshape, fframe, $ back, bshape, bframe, abcorr, $ srfpt, stepsz, riswin, occwin ;; ;; Subtract the occultation window from the view period ;; window: this yields the time periods when the target ;; is visible. ;; viswin = cspice_celld( MAXIVL ) cspice_wndifd, riswin, occwin, viswin ;; ;; The function cspice_wncard returns the number of intervals ;; in a SPICE window. ;; winsiz = cspice_wncard( viswin ) ;; ;; Display the rise and set times. ;; if winsiz EQ 0 then begin print, 'No events were found.' endif else begin ;; ;; Display the visibility time periods. ;; print, 'Visibility times of ' + TARGET + $ ' as seen from ' + SRFPT + ':' print, ' ' for i = 0, winsiz-1 do begin ;; ;; Fetch the Ith interval from the window. ;; cspice_wnfetd, viswin, i, intbeg, intend ;; ;; Convert the rise time to a TDB calendar string. ;; cspice_timout, intbeg, TDBFMT, TIMLEN, timstr ;; ;; Write the string to standard output. ;; if i EQ 0 then begin line = 'Visibility or window start time: ' endif else begin line = 'Visibility start time: ' endelse print, line + timstr ;; ;; Convert the set time to a TDB calendar string. ;; cspice_timout, intend, TDBFMT, TIMLEN, timstr ;; ;; Write the string to standard output. ;; if i EQ (winsiz-1) then begin line = 'Visibility or window stop time: ' endif else begin line = 'Visibility stop time: ' endelse print, line + timstr print, ' ' endfor endelse ;; ;; Unload kernels so they are not accidentally used by another ;; SPICE-based program during the current IDL session. ;; cspice_kclear END Solution Sample Output
After compiling the program, execute it. The output is:
Inputs for target visibility search: Target = TGO Observation surface location = NEW_NORCIA Observer's reference frame = NEW_NORCIA_TOPO Blocking body = MARS Blocker's reference frame = IAU_MARS Elevation limit (degrees) = 6.000000 Aberration correction = CN+S Step size (seconds) = 300.000000 Start time = 2018 JUN 10 00:00:00.000 (TDB) Stop time = 2018 JUN 14 00:00:00.000 (TDB) Visibility times of TGO as seen from NEW_NORCIA: Visibility or window start time: 2018 JUN 10 00:00:00.000 (TDB) Visibility stop time: 2018 JUN 10 01:00:30.640 (TDB) Visibility start time: 2018 JUN 10 01:41:03.610 (TDB) Visibility stop time: 2018 JUN 10 02:11:17.355 (TDB) Visibility start time: 2018 JUN 10 13:28:28.785 (TDB) Visibility stop time: 2018 JUN 10 14:45:38.197 (TDB) Visibility start time: 2018 JUN 10 15:26:21.981 (TDB) Visibility stop time: 2018 JUN 10 16:43:32.192 (TDB) Visibility start time: 2018 JUN 10 17:24:17.290 (TDB) Visibility stop time: 2018 JUN 10 18:41:27.535 (TDB) Visibility start time: 2018 JUN 10 19:22:13.628 (TDB) Visibility stop time: 2018 JUN 10 20:39:21.785 (TDB) Visibility start time: 2018 JUN 10 21:20:08.856 (TDB) Visibility stop time: 2018 JUN 10 22:37:12.445 (TDB) Visibility start time: 2018 JUN 10 23:18:00.834 (TDB) Visibility stop time: 2018 JUN 11 00:35:01.034 (TDB) Visibility start time: 2018 JUN 11 01:15:50.883 (TDB) Visibility stop time: 2018 JUN 11 02:08:16.008 (TDB) Visibility start time: 2018 JUN 11 13:16:50.542 (TDB) Visibility stop time: 2018 JUN 11 14:20:09.789 (TDB) Visibility start time: 2018 JUN 11 15:01:08.370 (TDB) Visibility stop time: 2018 JUN 11 16:18:03.385 (TDB) Visibility start time: 2018 JUN 11 16:59:03.014 (TDB) Visibility stop time: 2018 JUN 11 18:15:58.739 (TDB) Visibility start time: 2018 JUN 11 18:56:59.199 (TDB) Visibility stop time: 2018 JUN 11 20:13:54.308 (TDB) Visibility start time: 2018 JUN 11 20:54:55.301 (TDB) Visibility stop time: 2018 JUN 11 22:11:47.045 (TDB) Visibility start time: 2018 JUN 11 22:52:48.925 (TDB) Visibility stop time: 2018 JUN 12 00:09:35.868 (TDB) Visibility start time: 2018 JUN 12 00:50:39.046 (TDB) Visibility stop time: 2018 JUN 12 02:05:12.548 (TDB) Visibility start time: 2018 JUN 12 13:13:38.573 (TDB) Visibility stop time: 2018 JUN 12 13:54:43.524 (TDB) Visibility start time: 2018 JUN 12 14:35:54.054 (TDB) Visibility stop time: 2018 JUN 12 15:52:36.256 (TDB) Visibility start time: 2018 JUN 12 16:33:47.502 (TDB) Visibility stop time: 2018 JUN 12 17:50:30.988 (TDB) Visibility start time: 2018 JUN 12 18:31:42.896 (TDB) Visibility stop time: 2018 JUN 12 19:48:26.827 (TDB) Visibility start time: 2018 JUN 12 20:29:39.039 (TDB) Visibility stop time: 2018 JUN 12 21:46:20.933 (TDB) Visibility start time: 2018 JUN 12 22:27:33.596 (TDB) Visibility stop time: 2018 JUN 12 23:44:11.473 (TDB) Visibility start time: 2018 JUN 13 00:25:24.992 (TDB) Visibility stop time: 2018 JUN 13 01:42:00.777 (TDB) Visibility start time: 2018 JUN 13 13:10:23.432 (TDB) Visibility stop time: 2018 JUN 13 13:29:19.789 (TDB) Visibility start time: 2018 JUN 13 14:10:38.985 (TDB) Visibility stop time: 2018 JUN 13 15:27:11.882 (TDB) Visibility start time: 2018 JUN 13 16:08:31.566 (TDB) Visibility stop time: 2018 JUN 13 17:25:06.068 (TDB) Visibility start time: 2018 JUN 13 18:06:26.219 (TDB) Visibility stop time: 2018 JUN 13 19:23:01.820 (TDB) Visibility start time: 2018 JUN 13 20:04:22.175 (TDB) Visibility stop time: 2018 JUN 13 21:20:57.296 (TDB) Visibility start time: 2018 JUN 13 22:02:17.650 (TDB) Visibility or window stop time: 2018 JUN 13 23:18:49.624 (TDB) Extra Credit
These ``extra credit'' tasks are provided as task statements, and unlike the regular tasks, no approach or solution source code is provided. In the next section, you will find the numeric solutions to the questions asked in these tasks. Task statements
2018 JUN 10 TDB 2018 JUN 11 TDB
2018 JUN 10 TDB 2018 JUN 11 TDB
2018 JUN 10 TDB 2018 JUN 11 TDB
Solutions
1. Inputs for the equator crossing search, using cspice_gfposc for the spacecraft latitude in the Mars body-fixed frame equal to 0: Target = TGO Observer = MARS Observer's reference frame = IAU_MARS Elevation limit (degrees) = 0.000000 Aberration correction = NONE Step size (seconds) = 300.000000 Start time = 2018 JUN 10 00:00:00.000 (TDB) Stop time = 2018 JUN 11 00:00:00.000 (TDB) TGO Mars' equator crossing times: Equator crossing time: 2018 JUN 10 00:14:08.836 (TDB) Equator crossing time: 2018 JUN 10 01:12:34.582 (TDB) Equator crossing time: 2018 JUN 10 02:12:00.375 (TDB) Equator crossing time: 2018 JUN 10 03:10:28.808 (TDB) Equator crossing time: 2018 JUN 10 04:09:53.955 (TDB) Equator crossing time: 2018 JUN 10 05:08:23.919 (TDB) Equator crossing time: 2018 JUN 10 06:07:48.630 (TDB) Equator crossing time: 2018 JUN 10 07:06:17.539 (TDB) Equator crossing time: 2018 JUN 10 08:05:42.659 (TDB) Equator crossing time: 2018 JUN 10 09:04:09.120 (TDB) Equator crossing time: 2018 JUN 10 10:03:34.270 (TDB) Equator crossing time: 2018 JUN 10 11:01:59.269 (TDB) Equator crossing time: 2018 JUN 10 12:01:22.866 (TDB) Equator crossing time: 2018 JUN 10 12:59:49.352 (TDB) Equator crossing time: 2018 JUN 10 13:59:13.289 (TDB) Equator crossing time: 2018 JUN 10 14:57:41.242 (TDB) Equator crossing time: 2018 JUN 10 15:57:07.576 (TDB) Equator crossing time: 2018 JUN 10 16:55:35.266 (TDB) Equator crossing time: 2018 JUN 10 17:55:02.773 (TDB) Equator crossing time: 2018 JUN 10 18:53:30.271 (TDB) Equator crossing time: 2018 JUN 10 19:52:56.383 (TDB) Equator crossing time: 2018 JUN 10 20:51:23.966 (TDB) Equator crossing time: 2018 JUN 10 21:50:47.729 (TDB) Equator crossing time: 2018 JUN 10 22:49:14.385 (TDB) Equator crossing time: 2018 JUN 10 23:48:37.583 (TDB) 2. Inputs for the periapsis search, using cspice_gfdist for the spacecraft distance from Mars at a local minimum: Target = TGO Observer = MARS Observer's reference frame = J2000 Aberration correction = NONE Step size (seconds) = 300.000000 Start time = 2018 JUN 10 00:00:00.000 (TDB) Stop time = 2018 JUN 11 00:00:00.000 (TDB) TGO periapsis times: Periapsis time: 2018 JUN 10 00:43:06.357 (TDB) Periapsis time: 2018 JUN 10 02:40:47.168 (TDB) Periapsis time: 2018 JUN 10 04:38:45.496 (TDB) Periapsis time: 2018 JUN 10 06:36:32.706 (TDB) Periapsis time: 2018 JUN 10 08:34:10.548 (TDB) Periapsis time: 2018 JUN 10 10:31:49.108 (TDB) Periapsis time: 2018 JUN 10 12:29:20.342 (TDB) Periapsis time: 2018 JUN 10 14:27:07.089 (TDB) Periapsis time: 2018 JUN 10 16:25:36.081 (TDB) Periapsis time: 2018 JUN 10 18:24:02.653 (TDB) Periapsis time: 2018 JUN 10 20:22:23.184 (TDB) Periapsis time: 2018 JUN 10 22:20:12.453 (TDB) 3. Inputs for the apoapsis search, using cspice_gfdist for the spacecraft distance from Mars at a local maximum: Target = TGO Observer = MARS Observer's reference frame = J2000 Aberration correction = NONE Step size (seconds) = 300.000000 Start time = 2018 JUN 10 00:00:00.000 (TDB) Stop time = 2018 JUN 11 00:00:00.000 (TDB) TGO apoapsis times: Apoapsis time: 2018 JUN 10 01:41:44.632 (TDB) Apoapsis time: 2018 JUN 10 03:39:31.106 (TDB) Apoapsis time: 2018 JUN 10 05:37:22.115 (TDB) Apoapsis time: 2018 JUN 10 07:34:59.674 (TDB) Apoapsis time: 2018 JUN 10 09:32:25.708 (TDB) Apoapsis time: 2018 JUN 10 11:29:47.945 (TDB) Apoapsis time: 2018 JUN 10 13:27:30.200 (TDB) Apoapsis time: 2018 JUN 10 15:26:02.524 (TDB) Apoapsis time: 2018 JUN 10 17:24:37.842 (TDB) Apoapsis time: 2018 JUN 10 19:23:11.265 (TDB) Apoapsis time: 2018 JUN 10 21:21:13.530 (TDB) Apoapsis time: 2018 JUN 10 23:18:56.796 (TDB) |