Solar Storms and You!

Satellites and Kepler's Third Law

Introduction

Objective

To show that Earth-orbiting satellites obey Kepler's Third Law. Kepler's Third Law relates the time it takes a satellite to orbit a planet, to the diameter of the satellite's orbit. Students will graphically plot the orbital times and distances for a number of earth satellites, and show that on a 'log-log' plot, they all fall along a straight line...or nearly so.
Materials You will need to visit an archive of satellite data and extract the orbital period and orbit elements. You can visit the Monthly Satellite Situation Report which lists the orbital elements for hundreds of satellites, or you can use the attached, edited data file at the end of this page containing a smaller number of satellites. The table entries are as follows:
Column 1  = satellite name
Column 2  = satellite designation number 
Column 3  = country of origin
Column 4  = orbital period in minutes
Column 5  = orbital inclination to the equator in degrees
Column 6  = Orbit apogee in kilometers
Column 7  = Orbit perigee in kilometers
Column 8  = RCS tag
Note: the satellite number tells you how many objects have been tracked around the earth so far and exceeds 24,000! This includes tools, large water droplets and pieces of rockets!

Procedure

1) Assign each student one or two satellites.

2) Have each student look up 'perigee' and 'apogee' as new words! To the apogee number, given in kilometers, add the radius of the earth ( 6378 kilometers ) to get the satellite's distance from the center of the earth.

3) Using a calculator, have each student compute the base-10 logarithm of the orbital time and the apogee distance.

4) On log-log graph paper, plot each satellite's period and apogee distance.

5) With a ruler, draw a single straight line that passes through the distribution of the points.

6) From the 'rise divided by the run' of this straight line, determine its slope. If you plotted the orbital time on the horizontal axis and the apogee on the vertical axis, the rise/run should equal about 0.66 or 2/3. Since this is a log-log plot, this means that

                                               2/3
               distance  = Constant x    Period 

or that
                        3                      3
               distance    =  Constant x Period
This is Kepler's Third Law!

Key Terminology

Conclusions

The points when plotted should come out very nearly on a single straight line, however, there may be slight differences due to orbits being very elliptical.

Related Web Resources

Have the students look up on the internet or elsewhere what each of the satellites does. Have the students try the same procedure with the periods and orbital distances of the planets, or the satellites of Jupiter or Saturn.

Monthly Satellite Situation Report Part 1


                          SATELLITE SITUATION REPORT
                             VOLUME 38, NUMBER 01
                               JANUARY 31, 1997  
        THIS REPORT CONSISTS OF DATA COMPUTED AT UNITED STATES SPACE 
        COMMAND, GODDARD SPACE FLIGHT CENTER, OR PROVIDED BY SATELLITE
              OWNERS.  THE REPORT IS COMPILED AND PROVIDED BY: 
                      MISSION OPERATIONS AND SYSTEMS
                      DEVELOPMENT DIVISION, CODE 510
                     NASA/GODDARD SPACE FLIGHT CENTER
                    GREENBELT, MARYLAND,  U.S.A  20771

    The Satellite Situation Report is a listing of those satellites
    (objects) currently in orbit and those which have previously orbited the
    Earth.  Some objects are too small or too far from the Earth's surface
    to be detected; therefore, the Satellite Situation Report does not
    include all manmade objects orbiting the Earth.

    Generally, satellites are classified as follows:

    a.  Payloads may contain one or more functioning or nonfunctioning
        experiments.  Usually only the owners of the satellites know if the
        experiments are functioning, and there is no one source which
        indicates the operational status of all payloads and/or experiments.
        Payloads are normally the first listed in the Satellite Situation
        Report, i.e., 1982 087A, unless there are multiple payloads for the
        launch.  In which case, the first objects cataloged are usually all
        payloads, unless a subsequent payload is later identified after
        objects other than payloads have been cataloged.

    b.  Platforms are used to support a payload while it is being placed
        into orbit.  A platform may remain in orbit long after its purpose
        is served, usually longer than rocket bodies.  It is usually the
        first object identified in the Satellite Situation Report listing
        after the payload(s), i.e., 1982 087B (when a platform is not used,
        the first object after the payload(s) is usually the rocket body).

    c.  Rocket bodies are used to place the payload and platform (if one is
        used) into orbit. Some launches may have more than one rocket body
        because of the payload weight or the type of orbit or experiment.
        Most rocket bodies decay within a short time after the payload (and
        platform) have achieved orbit.  Rocket bodies are usually the third
        object listed in the Satellite Situation Report after the
        payload(s), i.e., 1982 087C.

    d.  Debris in orbit occurs when parts (nosecone shrouds, lens or hatch
        covers) are separated from the payload, when rocket bodies or
        payloads disintegrate or explode, or when objects are placed into
        free space from manned orbiting spacecraft during operations.
        Debris is detected by its size and distance from the Earth.  Debris
        objects are the last objects after payload(s), platform, and rocket
        body(s) listed in the Satellite Situation Report, i.e., 1982 087D,
        1982 087E, 1982 087F.

    The Satellite Situation Report does not attempt to classify payloads by
    experiment or function, such as geosynchronous satellites,
    communications satellites, Earth resources, and others. Certain groups
    of satellites, by the nature of their function, have similar
    inclinations, periods, and apogees.

    Geosynchronous satellites have almost equal apogee and perigee,
    inclinations close to 0 degrees, and a period of orbit approaching 1,440
    minutes.  These satellites are located almost directly above the Equator
    because they orbit at approximately the same speed that the surface of
    the Earth moves in relation to the Sun. Elements for these satellite
    types vary little.

    Communications satellites are usually geosynchronous. Although some are
    in geosynchronous orbit, most weather satellites have almost equal
    apogee and perigee, inclinations approaching 90 degrees, and a 90-minute
    period of orbit (they orbit the Earth once for each 22.5 degrees of
    Earth rotation).

    Weather satellites are only one type of Earth resources satellite.
    Others in the Earth resources category map the location of minerals,
    water, and vegetation.  These satellites may have apogees and perigees
    that are very divergent, and the period of orbit can range from 400 to
    700 minutes.

Certain terms used in the Satellite Situation Report are defined as follows:

AEROCENTRIC ORBIT       Object was launched from Earth and was last known to
                        be in orbit around Mars, but its orbit cannot be
                        confirmed.

BARYCENTRIC ORBIT       Object was launched from Earth and was last known to
                        be orbiting around a mass in space at a point of
                        equal Earth and Moon or Earth and Sun gravitational
                        pull, but its orbit cannot be confirmed.

ELEMENTS NOT AVAILABLE  Object was launched from Earth and elements are not
                        available.

HELIOCENTRIC ORBIT      Object was launched from Earth and was last known to
                        be in orbit around the Sun, but its orbit cannot be
                        confirmed.

NO INITIAL ELEMENTS     Object was launched from Earth but was not in orbit
                        long enough to establish elements before it decayed
                        into the Earth's atmosphere.

MARS ORBIT              Object was launched from Earth and was last known to
                        be in orbit around Mars, but its orbit cannot be
                        confirmed.

NO CURRENT ELEMENTS     Object was launched from Earth and current elements
                        are not available.

SELENOCENTRIC ORBIT     Object was launched from Earth and was last known to
                        be in orbit around the Moon, but its orbit cannot be
                        confirmed.

SOLAR SYSTEM ESCAPE     Object was launched from Earth and was last known to
TRAJECTORY              be in a trajectory that would allow the object to
                        escape the gravitational pull of any body in the
                        solar system.

VENUS IMPACT            Object was launched from Earth and was last known to
                        be in a trajectory that would have caused the object
                        to impact on Venus, but its impact cannot be
                        confirmed.

VENUS ORBIT             Object was launched from Earth and was last known to
                        be in orbit around Venus, but its orbit cannot be
                        confirmed.



                Satellite Situation Report Objects in Orbit part A
-------------------------------------------------------------------------------
 INT-ID/Name  CATALOG#  SOURCE   PERIOD    INCL   APOGEE    PERIGEE     RCS
-------------------------------------------------------------------------------
1996-073G       24710   CIS        88.5    62.8      229       173      N/A
BION 11 DEB                            Launched (12/24/96)
1996-073F       24709   CIS        87.5    62.8      164       133      N/A
BION 11 DEB                            Launched (12/24/96)
1996-073E       24708   CIS        91.3    62.8      390       288      N/A
BION 11 DEB                            Launched (12/24/96)
1996-073D       24707   CIS        91.9    62.8      435       302      N/A
BION 11 DEB                            Launched (12/24/96)
1996-073C       24706   CIS        89.9    62.8      332       211      N/A
BION 11 DEB                            Launched (12/24/96)
1996-072B       24681   US           NO ELEMENTS AVAILABLE              N/A
TITAN 4 R/B                            Launched (12/20/96)
1996-072A       24680   US           NO ELEMENTS AVAILABLE              N/A
USA 129                                Launched (12/20/96)
1996-071B       24678   CIS       104.9    82.9     1010       970    8.5630
SL-8 R/B                               Launched (12/20/96)
1996-071A       24677   CIS       105.0    82.9     1014       978    2.8144
COSMOS 2336                            Launched (12/20/96)
1996-070B       24675   US        647.6    22.5    35821      1013    1.2775
CENTAUR R/B                            Launched (12/18/96)
1996-070A       24674   IM       1434.5     2.6    35784     35727      N/A
INMARSAT 3-F3                          Launched (12/18/96)
1996-069A       24670   CIS        92.8    65.0      418       404   20.2589
COSMOS 2335                            Launched (12/11/96)
1996-068C       24669   US          HELIOCENTRIC ORBIT (SUN)            N/A
DELTA 2 R/B(2)                         Launched (12/04/96)
1996-068B       24668   US        116.1    36.4     2833       179   13.9519
DELTA 2 R/B(1)                         Launched (12/04/96)
1996-068A       24667   US          HELIOCENTRIC ORBIT (SUN)            N/A
MARS PATHFINDER                        Launched (12/04/96)
1996-067B       24666   US        598.3    23.8    34148       137   63.9000
CENTAUR R/B                            Launched (11/21/96)
1996-067A       24665   EUTE     1436.1     0.0    35799     35774   19.9500
HOT BIRD 2                             Launched (11/21/96)
1996-066A       24663   CIS        92.3    51.7      394       378    6.3000
PROGRESS M-33                          Launched (11/19/96)
1996-064A       24656   CIS        82.4    51.7      176      -385      N/A
MARS 96                                Launched (11/16/96)
1996-063D       24655   ESA       630.0     3.8    35662       267   61.1039
ARIANE DEB (SPELDA)                    Launched (11/13/96)
1996-063C       24654   ESA       646.0     3.7    36390       364    0.0503
ARIANE 44L R/B                         Launched (11/13/96)
1996-063B       24653   MALA     1436.1     0.0    35791     35782    7.4667
MEASAT 2                               Launched (11/13/96)
1996-063A       24652   AB       1435.6     0.1    35799     35756    3.8889
ARABSAT 2B                             Launched (11/13/96)
1996-062D       24651   US        132.7    25.3     4243       233   10.0827
DELTA 2 DEB                            Launched (11/07/96)
1996-062C       24650   US          HELIOCENTRIC ORBIT (SUN)            N/A
DELTA 2 R/B(2)                         Launched (11/07/96)
1996-062B       24649   US        133.6    25.3     4373       183   13.5031
DELTA 2 R/B(1)                         Launched (11/07/96)
1996-062A       24648   US          HELIOCENTRIC ORBIT (SUN)            N/A
MGS                                    Launched (11/07/96)
1996-061A       24645   US         95.1    38.0      556       487    3.6754
PEGASUS                                Launched (11/04/96)
1996-060D       24643   CIS       732.7    62.9    40426       663      N/A
SL-6 R/B(2)                            Launched (10/24/96)
1996-060A       24640   CIS       717.8    62.9    39697       660    6.3339
MOLNIYA 3-48                           Launched (10/24/96)
1996-058F       24503   CIS       571.1    47.1    32685       160    1.0112
SL-12 R/B(AUX MOTOR)                   Launched (09/26/96)
1996-058E       24454   CIS       631.3    47.2    35793       205    0.9217
SL-12 R/B(AUX MOTOR)                   Launched (09/26/96)
1996-058D       24438   CIS      1437.2     0.1    35856     35759      N/A
SL-12 R/B(2)                           Launched (09/26/96)
1996-058A       24435   CIS      1436.1     0.1    35793     35781      N/A
EXPRESS 12                             Launched (09/26/96)
1996-056C       24321   US        345.1    35.0    19630       207    1.9073
DELTA 2 R/B(2)                         Launched (09/12/96)
1996-056B       24323   US         95.4    35.5      608       471   12.9285
DELTA 2 R/B(1)                         Launched (09/12/96)
1996-056A       24320   US        718.0    54.7    20322     20041    7.1608
NAVSTAR 39 (USA 128)                   Launched (09/12/96)
1996-055B       24314   ESA       640.2     7.2    36238       217   19.3093
ARIANE 42P R/B                         Launched (09/11/96)
1996-055A       24313   US       1436.1     0.0    35796     35776   15.8030
ECHOSTAR II                            Launched (09/11/96)
1996-054B       24316   US       1059.2    25.1    55920       163   24.2058
CENTAUR R/B                            Launched (09/08/96)
1996-054A       24315   US       1436.1     0.0    35795     35779  485.7600
GE 1                                   Launched (09/08/96)
1996-053A       24307   IM       1436.1     2.5    35807     35767      N/A
INMARSAT 3-F2                          Launched (09/06/96)
1996-052C       24306   CIS       104.8    82.9     1003       966    9.2106
SL-8 R/B                               Launched (09/05/96)
1996-052B       24305   MEX       104.9    82.9     1010       967    0.1425
UNAMSAT                                Launched (09/05/96)
1996-052A       24304   CIS       104.9    82.9     1010       968    4.3271
COSMOS 2334                            Launched (09/05/96)
1996-051G       24303   CIS       102.3    71.1      920       818    0.5397
SL-16 DEB                              Launched (09/04/96)
1996-051F       24302   CIS       105.2    71.0     1161       846    0.1242
SL-16 DEB                              Launched (09/04/96)
1996-051E       24301   CIS       105.1    71.0     1158       842    0.1038
SL-16 DEB                              Launched (09/04/96)
1996-051D       24300   CIS       105.0    71.0     1141       843    0.1224
SL-16 DEB                              Launched (09/04/96)
1996-051C       24299   CIS       104.8    71.0     1130       844    0.0986
SL-16 DEB                              Launched (09/04/96)
1996-051B       24298   CIS       102.0    71.0      864       838   27.4124
SL-16 R/B                              Launched (09/04/96)
1996-051A       24297   CIS       101.9    71.0      855       846   14.3349
COSMOS 2333                            Launched (09/04/96)
1996-050F       24296   CIS       347.0    62.8    19159       796    6.8108
SL-6 R/B(2)                            Launched (09/04/96)
1996-050E       24295   CIS        95.3    62.8      851       210    4.3202
SL-6 PLAT                              Launched (08/29/96)
1996-050D       24294   CIS        96.7    62.8      961       238   13.6368
SL-6 R/B(1)                            Launched (08/29/96)
1996-050C       24293   CIS       347.3    62.8    19170       808   13.0651
INTERBALL AURORA                       Launched (08/29/96)
1996-050B       24292   CZCH      347.3    62.8    19180       799    0.7577
MAGION 5                               Launched (08/29/96)
1996-050A       24291   ARGN       97.9    62.8     1076       241    0.3965
MICROSAT                               Launched (08/29/96)
1996-049G       24646   US        133.0    83.0     4122       383    0.1071
PEGASUS DEB                            Launched (08/20/96)
1996-049F       24325   US        131.7    83.0     4056       335    0.0135
PEGASUS DEB                            Launched (08/21/96)
1996-049E       24319   US        131.9    83.0     4087       327    0.0914
PEGASUS DEB                            Launched (08/21/96)
1996-049D       24318   US        132.9    83.0     4150       349      N/A
PEGASUS DEB                            Launched (08/21/96)
1996-049C       24317   US        132.9    83.0     4148       349    0.0055
PEGASUS DEB                            Launched (08/21/96)
1996-049B       24286   US        133.1    83.0     4160       351    1.8098
PEGASUS R/B                            Launched (08/21/96)
1996-049A       24285   US        133.1    83.0     4164       352    1.8665
FAST                                   Launched (08/21/96)
1996-048B       24283   PRC       304.8    27.3    17030       220    9.9080
CSL-3 R/B                              Launched (08/18/96)
1996-048A       24282   PRC      1350.1    26.3    46491     21682    5.6123
CHINASAT 7                             Launched (08/18/96)
1996-047A       24280   CIS        92.3    51.7      394       378      N/A
SOYUZ TM-24                            Launched (08/17/96)
1996-046C       24279   JPN       107.0    98.7     1311       861   36.0147
H-2 R/B                                Launched (08/17/96)
1996-046B       24278   JPN       106.5    98.6     1324       801    0.2102
JAS 2                                  Launched (08/17/96)
1996-046A       24277   JPN       100.9    98.6      801       799   61.7786
ADEOS                                  Launched (08/17/96)
1996-045D       24276   CIS       732.3    62.9    40382       684    4.8191
SL-6 R/B(2)                            Launched (08/14/96)
1996-045A       24273   CIS       717.7    62.9    39657       691   19.6393
MOLNIYA 1-89                           Launched (08/14/96)
1996-044D       24211   ESA       621.1     5.7    35235       235   31.9672
ARIANE DEB (SPELDA)                    Launched (08/08/96)
1996-044C       24210   ESA       631.1     5.4    35770       216    0.4528
ARIANE 44L R/B                         Launched (08/08/96)
1996-044B       24209   FR       1436.1     0.2    35802     35770      N/A
TELECOM 2D                             Launched (08/08/96)
1996-044A       24208   IT       1436.1     0.0    35795     35779    3.8196
ITALSAT 2                              Launched (08/08/96)
1996-042B       23968   US        473.2    26.8    27134       338   20.2196
ATLAS 2 CENTAUR R/B                    Launched (07/25/96)
1996-042A       23967   US       1436.2     4.9    35800     35776   20.3373
UFO 7 (USA 127)                        Launched (07/25/96)
1996-041C       23955   US        344.6    35.0    19619       188    3.4400
DELTA 2 R/B(2)                         Launched (07/16/96)
1996-041B       23954   US         94.9    35.3      562       462   14.8189
DELTA 2 R/B(1)                         Launched (07/16/96)
1996-041A       23953   US        718.0    55.1    20235     20130    3.2083
NAVSTAR 38 (USA 126)                   Launched (07/16/96)
1996-040D       23951   ESA       611.5     7.2    34759       214   30.1737
ARIANE DEB (SPELDA)                    Launched (07/09/96)
1996-040C       23950   ESA       658.3     7.2    37081       299   26.4458
ARIANE 44L R/B                         Launched (07/09/96)
1996-040B       23949   TURK     1436.0     0.1    35793     35778   76.7928
TURKSAT 1C                             Launched (07/09/96)
1996-040A       23948   AB       1436.0     0.1    35799     35771   46.9547
ARABSAT 2A                             Launched (07/09/96)
1996-039B       23944   PRC       751.3    27.3    41770       223  999.0000
CZ-3 R/B                               Launched (07/03/96)
1996-039A       23943   AC       1436.2     0.0    35792     35784      N/A
APSTAR 1A                              Launched (07/03/96)
1996-037B       23941   US         97.4    97.4      927       342    0.4889
PEGASUS R/B                            Launched (07/02/96)
1996-037A       23940   US         94.6    97.4      508       492    4.7632
TOMS EP                                Launched (07/02/96)
1996-035A       23915   ITSO     1436.1     0.1    35805     35769  115.6595
INTELSAT 709                           Launched (06/15/96)
1996-034F       23887   CIS       550.2    46.6    31597       130    0.9013
SL-12 R/B(AUX MOTOR)                   Launched (05/25/96)
1996-034D       23883   CIS      1470.2     1.0    36587     36315      N/A
SL-12 R/B(2)                           Launched (05/25/96)
1996-034A       23880   CIS      1436.0     1.0    35842     35727      N/A
GORIZONT 32                            Launched (05/25/96)
1996-033C       23879   US        682.0    23.3    36671      1904    4.1579
DELTA 2 R/B(2)                         Launched (05/24/96)
1996-033B       23878   US        104.0    25.8     1560       338   10.7097
DELTA 2 R/B(1)                         Launched (05/24/96)
1996-033A       23877   US       1436.1     0.0    35790     35782    3.1221
GALAXY 9                               Launched (05/24/96)
1996-031A       23868   US         93.1    97.1      434       419    0.2475
MSTI 3                                 Launched (05/17/96)
1996-030D       23867   ESA       633.6     4.3    35761       356   28.4644
ARIANE DEB (SPELDA)                    Launched (05/16/96)
1996-030C       23866   ESA       637.1     4.5    35973       325   19.6882
ARIANE 44L R/B                         Launched (05/16/96)
1996-030B       23865   ISRA     1436.1     0.1    35802     35771    6.5584
AMOS                                   Launched (05/16/96)
1996-030A       23864   INDO     1436.1     0.0    35793     35781      N/A
1996-019A       23833   US        718.0    54.7    20260     20104    5.3023
NAVSTAR 37 (USA 117)                   Launched (03/28/96)
1996-009F       23792   CIS       114.2    82.6     1428      1412    3.3586
COSMOS 2330                            Launched (02/19/96)
1996-003A       23768   KOR      1436.5     0.1    35802     35788      N/A
KOREASAT 2                             Launched (01/14/96)
1996-002B       23765   MALA     1436.2     0.0    35794     35783   16.5252
MEASAT 1                               Launched (01/12/96)
1995-073C       23756   PRC       613.8    23.9    34851       244    8.3316
CSL-5 PKM                              Launched (12/28/95)
1995-067A       23730   FR       1436.1     0.0    35801     35771    6.1436
TELECOM 2C                             Launched (12/06/95)
1995-062C       24700   ESA      1435.2     1.5    70527      1012    9.5700
ISO DEBRIS                             Launched (11/17/95)
1995-059B       23711   US        109.7   100.6     1494       935   22.4623
SURFSAT                                Launched (11/04/95)
1995-049A       23670   US       1436.1     0.0    35793     35782  160.4536
TELSTAR 402R                           Launched (09/24/95)
1995-042A       23642   CIS       717.7    63.1    39181      1168   32.0794
MOLNIYA 3-47                           Launched (08/09/95)
1995-039F       23646   CZCH     5469.2    71.4   178122     14778      N/A
MAGION 4                               Launched (08/02/95)
1995-033E       23994   FR         98.1    98.1      675       664    0.0706
CERISE DEB                             Launched (07/07/95)
1995-033D       23608   ESA        98.1    98.1      686       648    7.0875
ARIANE 40 R/B                          Launched (07/07/95)
1995-033C       23607   SPN        98.2    98.1      675       667    0.7617
UPM/LBSAT                              Launched (07/07/95)
1995-033B       23606   FR         98.1    98.1      674       665    0.7082
CERISE                                 Launched (07/07/95)
1995-033A       23605   FR         98.4    98.1      682       680   20.2668
HELIOS 1A                              Launched (07/07/95)
1995-023A       23571   ITSO     1436.1     0.0    35802     35772   24.3597
INTELSAT 706                           Launched (05/17/95)
FAISAT                                 Launched (01/24/95)
1995-002B       23464   SWED      105.0    82.9     1027       963    0.3273
1994-070A       23331   LUXE     1436.0     0.0    35792     35779    0.3125
ASTRA 1D                               Launched (11/01/94)
1994-065B       23314   THAI     1436.2     0.1    35816     35761    0.3125
THAICOM 2                              Launched (10/08/94)
1994-065A       23313   MEX      1436.1     0.0    35796     35776    6.5876
SOLIDARIDAD 2                          Launched (10/08/94)
1994-049B       23200   TURK     1436.0     0.1    35796     35773    0.3125
TURKSAT 1B                             Launched (08/10/94)
1994-049A       23199   BRAZ     1436.1     0.0    35793     35781    8.6901
BRASILSAT B1                           Launched (08/10/94)

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This activity was developed by the NASA, IMAGE/POETRY 
Teacher and Student Consortium. 
For more information, and a list of other resources, visit 
the IMAGE/POETRYweb site.