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  1. Priyadi

    Priyadi New Member

    Claim:

    That's a recurring claim within the flat-Earth community, usually followed by concluding the ISS and other satellites are fake, and all the pictures are made by CGI.

    But the photos are real, and satellites are not visible because they are too far spaced apart from each other.

    (Disclaimer: this is originally posted on FlatEarth.ws, my FE debunking web site, modified to comply to Metabunk's policy)

    Let’s break down our facts one by one.
    1. In the LEO orbit, there is one satellite for every 175,000,000 km³ of volume of space. The average distance to the closest satellite is about 700 km. 700 km is more than the distance from New York City to Cleveland.
    2. According to simulation, the average distance from the ISS to the nearest satellite is 304 km. It is about the same distance from New York City to Boston.
    3. The ISS is about 400 km above the surface of the Earth. Neither cars, buses and even football fields are visible on general pictures taken from the ISS.
    4. General photography on the ISS is usually done using wide-angle lenses. 24 mm lenses and GoPros are popular. Wide angle means it is harder to recognize a distant object.
    5. Satellites come in different sizes. From small cubesats that fit in our palms, to the size of a football field. But it is safe to say there are not many satellites bigger than a school bus. All of the calculation done here includes everything. Cubesats and space debris that practically have no hope of being visible from the ISS are included as well.
    6. The probability of any satellite being within 5 km from the ISS at any random time is about 0.017%. Not to mention they actively steer the ISS to avoid collision.
    7. We can’t rule out satellites appearing in photos taken from the ISS. But it will be an extraordinary occurrence. And most of the time, satellite will appear as a dot, indistinguishable from background stars.
    8. To determine if a dot in a photo taken from the ISS is really a satellite, one needs to be familiar with the position of the stars. It would also be a tedious exercise, and pointless too.
    To sum it up: it is expected that satellites not appearing in general photos taken from the ISS, and if a satellite is visible, it would be an extraordinary occurrence.

    Calculations are detailed below.

    Photographic Calculation
    A common lens focal length used by the crew of the ISS appears to be 24mm. 24 mm focal length in a full frame body means a horizontal angle of view of about 74°.

    Let’s assume the very best case scenario that they are using the camera with very high megapixel count, let’s say 50 megapixel, or about 8712 pixel horizontally.

    Using these numbers, we can calculate that a single pixel represents about 0.0085° of angular size. (74°/8712 pixel = 0.0085°/pixel)

    Let’s assume the size of a satellite is 10 m; a very generous number, as very few satellites are over this size. What is the maximum distance a satellite can be represented by a single pixel in the camera? About 67 km. (10 m / tan(0.0085°) =67.4 km).

    If we want the satellite to be represented by 10 pixel, then we can simply divide by 10. So, a satellite needs to be 6.7 km from the ISS before it can be represented by 10 measly pixels on the camera.

    In real world situations, the satellite has to be much closer than that to be recognizable as a satellite. Otherwise, satellite will appear as a bright dot, indistinguishable from the background stars.

    Orbital Calculations
    First we calculate how much space is occupied by the Low Earth Orbit (LEO). Low Earth Orbit is defined as an orbit around Earth with altitude up to 2000 km. Let’s say the lower bound is 100 km, as anything below this will experience too much atmospheric drag to effectively orbit the Earth.

    Volume of LEO = volume of sphere with radius of 6371 km + 2000 km , subtracted by volume of sphere having the radius of 6371 km + 100 km.

    Vo = ((4 / 3 × π × (6371 km + 2000 km)³) – (4 / 3 × π × (6371 km + 100 km)³)) = 1.32206941 × 10¹² km³

    How many satellites are in LEO? According to SpaceBook, there are about 7500 satellites in LEO. Let’s find out the density of satellites in LEO; or in other words: if space in LEO is divided equally to each satellite, then how much space each satellite will have to themselves?

    Vs = Vo / 7500 = 1.32206941 × 10¹² km³ / 7500 = 176 275 921 km³

    Now let’s find out the average distance from any satellite to the ‘border’ of its ‘territory’:

    Vs = 4 / 3 × π × d³
    d = (176 275 921 km³ × 3 / (4 × π)) ^ (1/3) = 347.830874 km

    The average distance from a satellite to nearest one in LEO is twice that amount, or about 700 km.

    Simulation
    The calculation above results in the average distance to the nearest satellite in LEO. But, LEO extends to 2000 km above Earth’s surface, and there are far more satellites in the lower portion of LEO, where the ISS resides. So, I ran a simulation to get a number closer to reality.

    There are several parties maintaining the list of satellites orbiting the Earth. For this simulation I used satellite data from space-track.org. Orbit of a satellite is described in the standard TLE format (two-line element). To parse this data, I used the excellent pyephem library for Python. The library also provides routine to calculate the position of satellites, so I don’t have to do the grunt work myself.

    The TLE data from space-track.org contains 16481 entries. This list also includes space debris and various ‘micro satellites’ that practically have no hope of being visible from the ISS. But for the purpose of this simulation, I’ll include all 16481 entries in my calculation.

    I'm designing my simulation as follows:
    • Iterate every minute from 3 months in the past to 3 months to the future, for a total of about 6 months.
    • For each minute, calculate the position of every satellite in the TLE database, excluding the ISS, parts of the ISS itself, as well as supply and transport missions to the ISS.
    • Calculate the distance of each satellite to the ISS using the law of cosine, and determine which satellite is the closest.
    • At the end, tabulate the list and display the list of top 100 nearest satellite close pass, as well as calculate the mean distance to the closest occurrences.
    It took almost a day to complete the simulation. The result:
    • Mean: 304330 m
    • Standard deviation: 97810 m
    Source code of the simulation is available on my Github repository: github.com/flatearthws/nearest-satellites

    Raw simulation output

    Code:
    RESULTS:  
    start of procesing:  2018-01-13 08:13:05.986785
    end of procesing:  2018-01-14 03:44:43.360232
    start of simulation:  2017-10-15 08:13:05.986761
    end of simulation:  2018-04-13 08:13:05.986761
    sampling rate:  0:01:00
    mean:  304330.3076855794
    stddev:  97810.32808479421
    pstddev:  97810.13940800974
    variance:  9566860280.055082
    pvariance:  9566823371.0143
    n:  259201
    total satellites:  16480
    list of nearest satellites:
    6004.473765712113: 0 FENGYUN 1C DEB, 2017/12/15 16:01:05
    9675.567206403199: 0 PEGASUS DEB, 2018/02/10 06:46:05
    9770.109213661584: 0 SL-8 R/B, 2017/11/11 05:00:05
    11665.381203586961: 0 COSMOS 2251 DEB, 2017/11/29 16:52:05
    11728.94818587221: 0 DELTA 1 DEB, 2018/01/29 01:51:05
    14297.047401146328: 0 ALTAIR PATHFINDER, 2017/10/24 13:12:05
    14398.960036231783: 0 COSMOS 2098, 2017/10/24 17:29:05
    14933.69989267144: 0 ATLAS D R/B, 2018/01/05 03:00:05
    14988.063698740409: 0 CZ-6 R/B, 2017/12/22 22:17:05
    15634.989205904492: 0 NSIGHT-1, 2017/11/10 18:50:05
    15975.659913502008: 0 SHARC, 2017/11/19 09:39:05
    17344.80970186038: 0 COSMOS 1437, 2017/11/10 21:59:05
    18638.91195146259: 0 AOXIANG-1, 2017/10/18 02:05:05
    18719.305505112898: 0 SNUSAT-1B, 2017/11/13 13:58:05
    18863.407342739672: 0 CZ-4B R/B, 2018/02/11 10:29:05
    19309.717707753396: 0 XCUBESAT, 2017/10/16 23:04:05
    20060.427978282893: 0 SL-12 DEB, 2017/11/15 00:34:05
    20106.57488896667: 0 SPACECUBE, 2017/10/20 10:25:05
    20174.652361472057: 0 ZA-AEROSAT, 2017/10/29 03:33:05
    20641.878555424042: 0 NJUST-1, 2017/11/06 02:10:05
    21301.925760215905: 0 COSMOS 1174 DEB, 2018/02/12 10:58:05
    21307.87966560141: 0 SUMBANDILA, 2018/03/31 10:10:05
    21444.970594086855: 0 TK-1, 2017/10/28 18:09:05
    21785.791025918705: 0 CXBN-2, 2017/10/19 22:04:05
    22349.228559463187: 0 LILACSAT-1, 2017/11/19 04:15:05
    22534.083478214176: 0 SOMP 2, 2017/11/30 03:23:05
    22660.257328360152: 0 CSUNSAT 1, 2017/11/14 08:30:05
    22868.99767152028: 0 SNUSAT-1, 2017/10/19 04:19:05
    23061.30941032512: 0 BREEZE-M DEB (TANK), 2018/01/31 00:55:05
    23328.976481111426: 0 BEEAGLESAT, 2018/01/10 16:17:05
    23491.64806971299: 0 I-INSPIRE II, 2017/11/03 10:07:05
    23732.981803744657: 0 STSAT 2C, 2018/01/30 07:21:05
    23984.41753253558: 0 QBITO, 2017/11/23 23:13:05
    24574.29710146864: 0 PSLV R/B, 2017/12/27 00:36:05
    25275.109185595025: 0 CHALLENGER, 2017/11/04 04:38:05
    25363.843445813767: 0 HAVELSAT, 2017/10/28 22:09:05
    25574.220444497423: 0 TERRIERS, 2018/01/13 23:02:05
    25617.12894450459: 0 SUSAT, 2017/12/10 13:23:05
    25795.576215942532: 0 UNSW-ECO, 2017/11/19 01:56:05
    25801.657101579734: 0 QBEE50-LTU-OC, 2017/12/10 04:54:05
    25878.348255588106: 0 TET-1, 2017/10/28 01:36:05
    26710.30404842624: 0 PEGASUS R/B, 2018/01/07 03:51:05
    26715.90884016956: 0 TIANGONG-2, 2017/12/23 01:49:05
    27559.120028302335: 0 HOOPOE, 2017/11/24 16:12:05
    27605.05793130355: 0 CZ-4C R/B, 2017/12/31 05:02:05
    27704.535705762602: 0 CZ-3C DEB, 2018/02/05 05:11:05
    27895.782265761074: 0 PHOENIX, 2018/01/02 23:53:05
    28026.378733090456: 0 ICECUBE, 2017/12/06 05:13:05
    28547.749927752626: 0 EXALTA-1, 2017/12/20 21:51:05
    28920.865018021592: 0 UPSAT, 2017/11/19 05:47:05
    29844.906298541966: 0 FLOCK 2EP 14, 2017/10/16 02:59:05
    29895.865973094842: 0 RESURS P2 DEB, 2018/03/27 12:16:05
    29959.401250379655: 0 SL-4 R/B, 2018/01/26 08:27:05
    30027.076479248277: 0 FLOCK 2EP 15, 2017/11/30 19:34:05
    30580.73324185303: 0 XINYAN 1 (XY-1), 2017/10/29 19:45:05
    31166.04156419692: 0 LINK, 2017/11/20 06:29:05
    31171.687547807305: 0 MTI, 2017/10/29 05:39:05
    31347.652743816005: 0 COSMOS 1275 DEB, 2018/04/05 10:13:05
    31856.247547576913: 0 POLYITAN-2-SAU, 2017/11/08 10:30:05
    32243.907303841916: 0 SENSE SV2, 2017/12/25 06:14:05
    32274.775644795347: 0 COSMOS 252 DEB *, 2017/12/16 02:01:05
    32496.767985928233: 0 LEMUR 2 REDFERN-GOES, 2017/11/04 16:59:05
    32690.15599223832: 0 DELTA 2 R/B(1), 2017/11/07 00:10:05
    32994.52458481748: 0 AALTO-2, 2017/11/23 22:27:05
    33596.421043812465: 0 CZ-2C DEB, 2018/03/11 01:14:05
    33870.4203703246: 0 LEMUR 2 AUSTINTACIOUS, 2017/11/01 16:26:05
    34209.36917945506: 0 LEMUR 2 TRUTNAHD, 2017/10/30 01:09:05
    34730.75119220717: 0 PSLV DEB, 2017/10/17 21:50:05
    35453.97764752567: 0 IUS R/B(2), 2017/10/28 07:43:05
    35642.64874022061: 0 IRIDIUM 33 DEB, 2018/04/08 09:29:05
    36079.60335689162: 0 TIANWANG 1B (TW-1B), 2018/02/10 05:25:05
    36849.018377783825: 0 DUTHSAT, 2017/10/27 07:34:05
    36904.603918413755: 0 AAM/PSLV, 2018/03/04 16:52:05
    36966.40180940492: 0 AOBA-VELOX 3, 2017/11/09 11:11:05
    38070.21820719905: 0 BREEZE-M DEB, 2017/10/24 00:06:05
    38083.25574686663: 0 FLOCK 2EP 18, 2017/11/28 00:26:05
    38092.03038386934: 0 DIWATA-1, 2017/11/01 06:23:05
    38094.887387655115: 0 IRIDIUM 43, 2017/11/24 17:14:05
    38972.7506142112: 0 GPM, 2018/01/23 08:05:05
    39008.43691654249: 0 ITF-2, 2017/12/13 14:41:05
    39728.693220785026: 0 FLOCK 2EP 17, 2017/10/27 10:38:05
    39842.501844371545: 0 XW-2A, 2017/11/07 18:24:05
    40197.95365652181: 0 SGSAT, 2017/11/11 17:13:05
    40210.919596897125: 0 ERBS, 2017/11/06 07:15:05
    40364.688775238625: 0 SL-3 R/B, 2017/12/01 08:45:05
    40869.091456365284: 0 COSMOS 1263, 2018/04/05 11:23:05
    41277.28116879187: 0 DMSP 5D-2 F13 DEB, 2018/02/06 23:51:05
    41398.516186422676: 0 DELTA 2 DEB, 2018/04/09 20:51:05
    41748.18458964713: 0 COSMOS 1508, 2017/11/17 03:11:05
    42476.291990908: 0 FLOCK 2EP 13, 2017/10/23 04:00:05
    43128.62037412048: 0 HO'OPONOPONO 2, 2018/03/04 21:16:05
    43141.24597361845: 0 SL-23 DEB, 2017/11/26 21:08:05
    43205.024637260074: 0 OPTUS B3 PKM, 2018/03/22 15:23:05
    43367.62273484535: 0 COSMOS 807, 2018/02/20 09:02:05
    43872.41578376013: 0 TIANWANG 1C (TW-1C), 2018/02/07 04:49:05
    43997.84735749864: 0 ASAP-S, 2018/02/07 19:33:05
    44314.39863492452: 0 FLOCK 2EP 16, 2017/10/23 17:07:05
    44501.16876871045: 0 WASEDA-SAT3, 2017/11/11 14:53:05
    44661.64679023407: 0 LEMUR 2 TRUTNA, 2017/10/19 21:17:05
    44751.586278449395: 0 CZ-2C R/B, 2017/11/16 09:52:05
    45010.422727512516: 0 YAOGAN 28 DEB, 2017/10/30 11:32:05
    

    Reference
     
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  2. Whitebeard

    Whitebeard Senior Member

    Nice post.

    Every year I go to the Solarsphere music and astronomy festival in Wales, UK* and if the skies are clear (and the festival is held in mountains with very little light polution), you can sit outside your tent, look up and watch the satellites tracking across the sky, and there are loads of them, you see them every 10 minutes or so. So they are most certainly up there!!

    *This years festival is August 10th - 13th, tickets on sale £45 for the weekend, including camping and acess to all lectures, workshops and music performances.
     
    • Like Like x 1