By Duncan Steel 22/02/2019

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The International Space Station (and many other satellites) can easily be viewed passing overhead using the naked eye, so long as you know when to look, and where. But why  can we see it, and how does it return so often? 

In a blog post a few days ago I presented tables of times when the International Space Station (ISS ) could be spotted from fourteen different towns/cities in New Zealand through until the last day of the month, and it should be easy enough for anyone to estimate the viewing opportunities from anywhere else in NZ using those tables. The calculations were made using the Heavens-Above website, and I also mentioned a NASA website from which email alerts can be obtained automatically, telling you when the ISS can be seen from your location. Since then David Gibb has kindly pointed out to me a website from which a smartphone app can be downloaded and ISS viewing opportunities obtained.

Seeing the ISS is simple. On the evening of Tuesday 19th February my old friend Dr John Campbell was giving a talk about Ernest Rutherford to the Nelson Science Society. He finished giving his presentation and fielding questions about 20:50. Along with several other attendees we then retired to the Free House to further our discussions over refreshments. Stood on the pavement outside on Collingwood Street, under the street lamps, we could see the ISS rising in the northwest over Abel Tasman National Park just after 21:06 (NZDT; this is UTC plus 13 hours). We alerted the people sat outside the pub having a drink (and some others walking along the street) what they had the opportunity to monitor as it was passing across the sky, and then emptied the building of customers by telling them too. A few minutes and it was gone. Led in bed later, through the window my partner Jan and I saw the ISS on its next pass, at 22:43. From Nelson two passes are potentially visible every evening until the 28th. These ISS overpasses are generally brighter, longer, and higher in the sky the further south you are in NZ.

In that preceding post I finished by writing that a visualisation of the ISS in its orbit, and these passes over NZ, would likely be of interest to some people. So, here is my follow-up post. As background: the ISS orbits at an altitude of about 408 km (as it crosses the equator), that orbit being near-circular, and in a plane that is tilted by 51.64 degrees to the equator (that tilt or inclination being set by the location of the Russian Space Agency’s launch site at Baikonur in Kazakhstan). The speed of the ISS in that orbit is close to 7.66 km/sec (27,600 kph).

First, here is a link to a movie (10MB, WMV file, 61 seconds duration) that shows the passes by the ISS on 19th February mentioned above. In making that movie I have held the Earth still, and consequently you will see that the stellar background is moving, and the orbital plane of the ISS also appears to rotate. In reality there is a small shift of the satellite’s orbital plane (precession caused by the fact that the Earth is neither spherical nor homogeneous, so that its gravitational field is not spherically-symmetric), but the main effect causing that plane to appear to swivel around is that the planet is spinning beneath it. Various graphics below will help develop an understanding of what is occurring.

Here is a simulation that shows the pass over the North Island that we witnessed soon after 21:06 on the 19th from Nelson (and I hope many other people elsewhere gazed at it too):


As can be seen above, the ISS was over the night-side of the Earth, and NZ was in darkness. So how could we have viewed the ISS as a bright object crossing the sky, given that it emits little or no light of its own? The answer is that it was still illuminated by sunlight, reflecting some of that to us down below. This next graphic shows what I mean:


In the above image (made using the wonderful STK tool) we are looking back from above the night-side of the Earth (which I have artificially brightened up so one can see the landforms) and the ISS has just passed over NZ, coming to the end of its visibility from the North and South Islands (though still in sight from the Chathams). That bright splodge is the Sun. I have also put in an atmospheric model, resulting in a bright rim to the planet around the lower left in this simulated view.

At its altitude of 408 km the ISS is still exposed to the Sun, having yet to enter eclipse. Being fully illuminated by sunlight, it scatters a substantial amount downwards (remember that the ISS is about the size of a rugby field, being about 73 metres by 108 metres in extent) and so it is an obvious thing to see moving across a dark, clear sky. It surely scatters a great deal of sunlight.

As I wrote, this was a simulation on my laptop. The photograph at the head of this blog post shows the situation in reality: the ISS near to the camera (I imagine this photo was taken from a manned capsule approaching to dock with the station), the limb of the Earth at the top of the frame, and the Sun in the distance. Note that the ISS is in direct sunlight, but is also above the dark, night-side of the planet.

In essence this is how all satellites may be observed from the ground: they are sufficiently high up that soon after dusk or before dawn the surface of the Earth below is shielded from the Sun but the orbiting object is still in sunlight.

Moving along another 97 minutes on the evening of 19th February, the next nearby pass by the ISS occurred just south of Stewart Island, as depicted below:


From Nelson we could see the ISS low in the sky, starting close to due west of us and passing to the south and then south-east. Obviously enough, looking at the above graphic, from Queenstown, Invercargill and Dunedin the ISS would have appeared higher in the sky; and the period of visibility would have started slightly earlier.

Now let me add something to the preceding graphics, for the NZ passes by the ISS starting at around 21:06 and 22:43. The following picture is identical to that immediately above, but now the ground track of the ISS is also shown. The ground track is the line figuratively drawn across Earth’s surface by the point directly below the ISS. Now you can see how the path of the ISS over the Earth has appeared to swivel around, that being mostly due to the planet itself spinning about its rotation axis (i.e. the line joining the North and South Poles).


What about the next pass, 97 minutes later? The orbital path for that occasion is shown in the next graphic:


Now the path taken is further south again, crossing the Auckland and Campbell Islands. From Nelson this pass was below the horizon; however, from Queenstown, Invercargill and Dunedin the ISS might have been seen at about twenty-five minutes past midnight (the start of 20th February), barely more than 10 degrees above the south-western horizon and only visible for up to twenty seconds; I did not include such brief and inconvenient passes amongst the opportunities that I tabulated in my previous post.

The trend – the rotation of the orbital plane relative to the planet below – apparent in the three ISS passes near NZ late on 19th February/early on 20th February continues. In the following graphic, covering the interval from about 20:00 NZDT on the 19th through to 08:00 on the 20th, the ground tracks for eight orbits by the ISS are shown. By the evening of 20th February that process resulted in the ISS again passing over NZ and being visible after dark. To look at it another way, the Earth has spun once beneath that large orbiting satellite.


Just to ensure that readers can follow what is going on, let me present the ground tracks of the ISS as 2D maps, rather than the 3D views above. The next graphic shows a world map of the ISS ground track beginning at 20:00 NZDT on 19th February, when the orbiter was over southern Brazil/to the north-east of Uruguay. Its path then took it over the north-west of Africa and the Mediterranean before reaching a furthest-north point over Russia and then coming southwards over central Asia and China before passing over the Coral Sea and then NZ’s North Island. We had the chance to see it soon after 21:00 (again NZDT). On its next orbit it passed over the middle of Australia and then crossed the Tasman Sea so as to pass just south of NZ at around 22:45.


Let me next add a representation of the night-time to such a map. The graphic on the left below shows the dark part of the Earth’s surface as a grey region, with a black border indicating where sunset is occurring at that instant in time (21:06 on 19th February), which is when the visible pass over NZ begins. The graphic on the right is similar, but shows the situation for the following pass, at 22:43; now the ISS is deeper into the dark region, and so one might anticipate (correctly) that the visible part of the ISS path is reduced, and so the period of visibility is less.




















These phenomena can be sketched out in other ways. In the diagram that follows I have shown these two passes by the ISS over/near NZ with yellow ground-tracks indicating when the satellite was in direct sunlight, and black lines showing when it was in Earth’s shadow/in eclipse. The total time covered is three hours, just short of two complete orbits.


The final map shows all three passes that might have been seen from somewhere in New Zealand on the 19th (or shortly after the midnight beginning the 20th), with the dark side hatched in below as it was at the time of that final pass (00:25 on 20th February). As can be seen, for this final chance someone in Fiordland might have witnessed the ISS briefly in the low, south-western sky; at that time it was closer to Tasmania than to NZ.


I started this blog post with a movie, and will finish it with another. The movie available here (WMV file, 4.2 MB, 37 seconds duration) shows the first visible pass over NZ by the ISS on 21st February. I have put in the positions of Auckland, Wellington, Christchurch and Dunedin. Within the minute after 21:00 NZDT (08:00 UTC, as shown in the movie) each of those cities acquired line-of-sight to the ISS, which was also required to be at an elevation angle of more than ten degrees above the horizon from each of those four locations so that it was high enough in the sky to be seen. This condition of visibility is depicted by each city being connected to the ISS by a differently-coloured line in the movie. There is a far-away viewpoint, and then a close-up repeat of the pass, for clarity.