SPEDAS training course- ERG orbit Chae-Woo Jun, Y. Miyoshi, T. Hori, M. Shoji, S. Nakamura and M. Kitahara(ERG Science Center, ISEE, Nagoya University)

SPEDAS training session, Oct. 13, 2021
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Before this training course• This course will use ERG plug-in tool based on
IDL SPEDAS.
• Please update your ERG plug-in as the latestversion.
• ERG Science center provides lectures for thebeginners of IDL SPEDAS on our Youtube
channel.(url:https://www.youtube.com/channel/UCukIaSJ1l-KbZnVzYNmglVg)

Check the latest version!

• If you utilize ERG orbit data for your study,
please cite ERG orbit DOI on your publication.
• If you have any questions, please feel free tocontact “ergsc-help at isee.nagoya-u.ac.jp”.
2Goal of this training• We are going to learn how to load, and plot orbit data of theERG satellite, with a special focus on plotting satellite
trajectories in space and ionospheric footprints on the worldmap.

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Contents of this course• Information of ERG orbit dataset• Plot orbit data
1. Time series using “tplot”
2. Satellite trajectory in XY or XZ plane
3. Ionospheric footprints on the world map• Appendix
1. Information of coordinate system
2. Meaning of Lm and L*
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ERG orbit dataset

Web data repository Level

Datatype or model

Load procedure

L2(IGRF)Definitive

erg_load_orbPredict (pre, spre, mpre, lpre)

erg_load_orb_predict, datatype = ‘pre, spre, mpre, lpre’

L3(IGRF +externalfields)

OP77Q model using quiet time model
T89 model using Kp index

erg_load_orb_l3, model=‘op or t89 or ts04’

TS04 model using IMF + Dst index* Note: the information of L* and invariant is only provided by l3 orbit data set.

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Plot ERG orbit data:1. Time series using “tplot”; Set the time range to 9-18 UT on Sep. 21, 2019
IDL> timespan,'2019-09-21/09:00:00',9,/hour; Load Arase l2 def orbit data
IDL> erg_load_orb; Plot Arase orbit in the SM coord.
IDL> tplot,'erg_orb_l2_pos_sm'

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2. Satellite trajectory in XY or XZ plane; Set the time range to 9-18 UT on Sep. 21, 2019
IDL> timespan,'2019-09-21/09:00:00',9,/hour; Load Arase l2 def orbit data
IDL> erg_load_orb; Plot Arase orbit on the SM X-Y plane
IDL> tplotxy,'erg_orb_l2_pos_sm'

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2. Satellite trajectory in XY or XZ plane (cont’d); Plot Arase orbit on the X-Y plane of - 6 Re < x,y < 6 Re
IDL> tplotxy,'erg_orb_l2_pos_sm',versus='xy',xrange = [-6,6],yrange = [-6,6]; The same but on the X-Z plane
IDL> tplotxy,'erg_orb_l2_pos_sm',versus='xz',xrange = [-6,6],yrange = [-6,6]

8Additional information for “tplotxy” and “plotxy”
tplotxy, tplot_variable_name$ ; (e.g., ‘position_sm’), versus='xy'; choose axis (e.g., xy or xz), multi= 'n_col n_raw’ ; make multi plots (‘# of colum # of raw’), over = over; overplot on the current window, add = add; add plot
, additional plot options ; (e.g., title, xrange, color, linestyle, etc.)

plotxy, variable$; position array ([time,#_of_axis]), versus='xy'; choose axis (e.g., xy or xz), multi= 'n_col n_raw’ ; make multi plots (‘# of colum # of raw’), over = over; overplot on the current window, add = add; add plot
, additional plot options ; (e.g., title, xrange, color, linestyle, etc.)93. Ionospheric footprints on the world map; Initialize the map2d environment and Set
the coordinate system to geographicalcoordinate
IDL> map2d_init & map2d_coord, 'geo'; Generate an empty window
IDL> window, 0, xsize=800, ysize=640 &erase; Draw the grid (10 deg in lat & 15 deg inlog) on the window and Draw the coast lines
IDL> map2d_set & overlay_map_coast10

3. Ionospheric footprints on the world map (cont’d); get l2 data for ionospheric footprints on thenorthern hemisphere
IDL> erg_load_orb
IDL> get_data, 'erg_orb_l2_pos_iono_north',
data=data_foot; Store latitude and longitude separately.
IDL> store_data,'IGRF_ifoot_glat',data={x:data_foot.x,y:reform(data_foot.y[*,0])}
IDL> store_data,'IGRF_ifoot_glog',data={x:data_foot.x,y:reform(data_foot.y[*,1])}; Overplot Arase footprint on the map
IDL> overlay_map_sc_ifoot, 'IGRF_ifoot_glat','IGRF_ifoot_glog'

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Comparison of footprints using different models; get l3 OP77Q orbit data for ionospheric footprints
IDL> erg_load_orb_l3,model = 'op' & get_data, 'erg_orb_l3_pos_iono_north_op', data=data_foot_op
IDL> store_data, 'OP77Q_ifoot_glat',data= {x:data_foot_op.x, y:reform(data_foot_op.y[*,0])}
IDL> store_data, 'OP77Q_ifoot_glog',data= {x:data_foot_op.x, y:reform(data_foot_op.y[*,1])}; get l3 T89 orbit data for ionospheric footprints
IDL> erg_load_orb_l3,model = 't89' & get_data, 'erg_orb_l3_pos_iono_north_t89', data=data_foot_t89
IDL> store_data, 'T89_ifoot_glat',data= {x:data_foot_t89.x, y:reform(data_foot_t89.y[*,0])}
IDL> store_data, 'T89_ifoot_glog',data= {x:data_foot_t89.x,y:reform(data_foot_t89.y[*,1])}; get l3 TS04 orbit data for ionospheric footprints
IDL> erg_load_orb_l3,model = 'ts04' & get_data, 'erg_orb_l3_pos_iono_north_TS04',
data=data_foot_ts04
IDL> store_data, 'TS04_ifoot_glat',data= {x:data_foot_ts04.x, y:reform(data_foot_ts04.y[*,0])}
IDL> store_data, 'TS04_ifoot_glog',data= {x:data_foot_ts04.x,y:reform(data_foot_ts04.y[*,1])}
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Comparison of footprints using different models (cont’d); Generate a new map window
IDL> window, 0, xsize=800, ysize=640 & erase
IDL> map2d_set,glonc = 280,glatc=60,scale = 1e7 &overlay_map_coast; Overplot Arase footprints using different models
IDL> overlay_map_sc_ifoot, 'IGRF_ifoot_glat','IGRF_ifoot_glog'
IDL> overlay_map_sc_ifoot, 'OP77Q_ifoot_glat','OP77Q_ifoot_glog',trace_color=2
IDL> overlay_map_sc_ifoot, 'T89_ifoot_glat','T89_ifoot_glog',trace_color=4
IDL> overlay_map_sc_ifoot, 'TS04_ifoot_glat','TS04_ifoot_glog',trace_color=613

Additional information for “map2d_set” and“overlay_map_sc_ifoot”
Map2d_set, glatc=value, glonc=value, scale=value, coord=‘…’, /set_time, /nogrid
Keywords:- glatc (glonc): geographical latitude (longitude) at which a plot region is centered.
(both glatc and glonc should be given, otherwise ignored)- scale: same as the keyword "scale" of map_set- coord: name of the coordinate system.
('geo' or 0 for Geographic coordinate. 'aacgm' or non-zero numbers for AACGM coordinate.)- set_time: this is used to calculate MLT when coord is 'aacgm'- mltlabel: set to draw the MLT labels every 2 hour.
- nogrid: set to suppress drawing the lat-lon mesh
- dlat(dlong)_grid: set grid steps for latitude (longitude) (default: 10 deg in lat & 15 deg in log)

Overlay_map_sc_ifoot, tplot_variable_lat, tplot_variable_lon $, [‘YYYY-MM-DD/hh:mm’,’ YYYY-MM-DD/hh:mm’]; time range, trace_color = integer ; Set a color of the line
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Summary• Load procedure of ERG orbit data erg_load_orb  l2 definitive orbit data erg_load_orb_predict  l2 predicted orbit data (datatype: pre, spre,mpre,lpre)
 erg_load_orb_l3  l3 definitive orbit data (model: OP77Q, T89, TS04)• Plot ERG orbit
 Time-series plot  tplot
 Projection of orbit trajectories on 2D plane  tplotxy (or plotxy)
 Projection of ionospheric footprints on the map
1. Initialize map setting
2. Draw the map on the window
3. load and store ionospheric footprint information
4. Plot ionospheric footprints using “overlay_map_sc_ifoot”

15Appendix

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1. Information of geomagnetic coordinate system
Coord. System
Geocentric Equatorial
Inertial
Geographic
Geomagnetic
Geocentric Solar
Ecliptic
Geocentric Solar
Magnetospheric
Solar Magnetic

Aberration

UsageGEI

Astronomy, satellite orbits

GEOMAG

Position of ground stations
Position of geomagnetic observations

GSE

Satellite trajectories, Solar windGSM
SM

Magnetospheric fields in the outermagnetosphere
Magnetospheric fields in the innermagnetosphere

References:
1. Introduction to Space Physics, 531-543, 1995.(edited by M. G. Kivelson and C. T. Russell)
2. http://sscweb.gsfc.nasa.gov/
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Geocentric Equatorial Inertial (GEI) Coord.
• X: Pointing from the earth toward thefirst point of Aries (the position of theSun at the vernal equinox). This
direction is the intersection of the Earth’s
equatorial plane and the ecliptic plane.
• Z: Parallel to the rotation axis of theEarth.
• Y: Completes the right-handedorthogonal system. (𝑌 = 𝑍 × 𝑋)

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Geographic (GEO) Coord.
• X: In the Earth’s equatorial plane, but
fixed with the rotation of the Earth So
passes through the Greenwich meridian(0˚ longitude).
• Z: Parallel to the rotation axis of theEarth.
• Y: Completes the right-handedorthogonal system. (𝑌 = 𝑍 × 𝑋)
(Longitude: eastward, 0 UT = 0 LT at
Greenwich meridian)19

Geomagnetic (MAG) Coord.
• X: Perpendicular to the Z direction.
• Z: Parallel to the geomagnetic dipole
axis, positive northward.
• Y: Completes the right-handedorthogonal system. (𝑌 = 𝑍 × 𝑋)

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Geocentric Solar Ecliptic (GSE) Coord.
• X: Points from the center of the Earth
towards the Sun.
• Z: Parallel to the ecliptic north pole.
• Y: Completes the right-handedorthogonal system. (𝑌 = 𝑍 × 𝑋)

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Geocentric Solar Magnetospheric (GSM) Coord.
• X: Points from the center of the Earth
towards the Sun (same as GSE).
• Y: Perpendicular to both X-axis and theEarth’s dipole axis.
• Z: Completes the right-handedorthogonal system (𝑌 = 𝑍 × 𝑋).

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Solar Magnetic (SM) Coord.
• Z: Points from the center of the Earth tothe magnetic north pole.
• Y: Perpendicular to both Z-axis and theSun-Earth line.
• X: Completes the right-handedorthogonal system. (𝑌 = 𝑍 × 𝑋)

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2. LMcIlwain VS L*• L-shell, L-value, or McIlwain L-parameter: the set of magnetic
field lines which cross the Earth's magnetic equator at a numberof Earth-radii equal to the L-value.
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𝐿=, 𝑤ℎ𝑒𝑟𝑒 𝜆: 𝑖𝑛𝑣𝑎𝑟𝑖𝑎𝑛𝑡 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 (= 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒)
2𝑐𝑜𝑠 (𝜆)• For example, “L=4" indicates the set of the Earth's magnetic
field lines which cross the Earth's magnetic equator at 4 Re.
• L*: the magnetic drift variant, known as the Roederer Lparameter (Roederer, 1970).
′2𝜋𝑘 0∗𝐿 = Φ𝑅 ,𝑤ℎ𝑒𝑟𝑒 ቊ 𝑘0 : 𝑡ℎ𝑒 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝐸𝑎𝑟𝑡ℎ 𝑠 𝑑𝑖𝑝𝑜𝑙𝑒𝑒

Φ:𝑡ℎ𝑒 𝑡ℎ𝑖𝑟𝑑 𝑎𝑑𝑖𝑎𝑏𝑎𝑡𝑖𝑐 𝑖𝑛𝑣𝑎𝑟𝑖𝑎𝑛𝑡 𝑖𝑛 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑣𝑎𝑙𝑢𝑒• In plain language, L-shell  same field line
L*  same drift shell
Reference:Roederer, J. G. (1970), Dynamics of Geomagnetically Trapped Radiation, pp. 84–106, Springer, New York.
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