Re: Satellite observing

Sue J. Worden (sjw@uts.cc.utexas.edu)
Fri, 10 Apr 1998 16:33:32 -0500 (CDT)

Fellow SeeSat'rs,

Below is a message that I just sent in response to an inquiry from
the folks at "Star Hustler", regarding satellite watching.  If I've
overlooked something, or didn't explain something quite right or
not clearly, or if you just want to clarify or expand upon what I
said -- whatever -- please contact Janis directly with your comments.

--Sue (worden@uts.cc.utexas.edu  a.k.a.  sjw@uts.cc.utexas.edu
                                 a.k.a.  s.worden@cc.utexas.edu
                                 a.k.a.  ad semi-infinitum :-)

----- Begin Forwarded Message ------------------------------------------------
> Date: Fri, 10 Apr 1998 16:18:49 -0500 (CDT)
> From: "Sue J. Worden"
> To: starhslr@netside.net
> Subject: Re: Satellite observing

> > Date: Thu, 09 Apr 1998 13:27:07 -0400
> > From: Star Hustler <starhslr@netside.net>
> > Subject: Satellite observing
> > [ ... ]
> > To:    Sue Worden
> >        University of Texas
> > From:  Janis Hernandez
> >        Miami Space Transit Planetarium
> > RE:    Satellite Observing

> > Our planetarium produces a five minute series on naked eye astronomy
> > (Star Gazer) distributed over PBS stations.  In researching the material
> > for our May scripts I came across this quote in the Old Farmer's Almanac
> > ..."This is also the time of year when space satellites are most
> > visible; you can see one crossing the sky every minute or two during
> > the first hour after nightfall..."

> > The position of the Sun with regard to our shadow must be a factor but
> > other than that I am not aware of why this is so. If this is, in fact,
> > an unusually good time of year for satellite observing could you please
> > let me know the reason? A simplified explanation would be most appreciated.
> > We would, of course, credit you on our program during the May show about
> > observing satellites. I am not sure how often you check your email, but
> > would really appreciate a response asap as we are currently writing the
> > scripts. Thanks so much and sorry to throw this on you so abruptly.
> > We will apreciate any help.

> > Thanks again and Keep Looking Up,
> > Janis Hernandez


> Dear Janis,

> I'm most curious to know how you came by my name and email address. :-)

> I'm not aware of anything "special" about the month of May in terms of
> watching satellites.  Many low earth orbit (LEO) satellites can be seen
> both morning and evening, every day of the year, in the middle latitudes.
> However, the late spring to early autumn months do afford longer periods
> after twilight for viewing satellites, compared to the winter months,
> with the maximum viewing period occurring at summer solstice.  Perhaps
> this is what the Old Farmer's Almanac is referring to.

> This seasonal effect, caused by the tilt of the Earth's axis of rotation,
> is due to the rate at which the Earth's shadow climbs into the sky after
> sunset.  As long as satellites remain outside the Earth's shadow, they
> are illuminated by sunlight and can reflect that sunlight back to your
> eyes and thus be visible to you.  We often think of this in terms of the
> "shadow height", how high the shadow extends above your location, versus
> the satellite's height above you in its orbit.  If a satellite is "above"
> shadow height, it can be visible.  If the satellite is "below" shadow
> height, it is being eclipsed by the Earth and cannot be visible.

> Let me simplify things greatly for a moment and ignore effects such as
> the apparent angular extent of the sun and the refraction of sunlight
> through the atmosphere.  Imagine that you are standing outside right at
> sunset, i.e., you are standing exactly on the terminator.  The Earth's
> shadow, at that instant, is tangent to the Earth at your location; it
> is at ground level, so the shadow height is zero.  As the Earth rotates
> you away from the sun, and twilight deepens, the height of shadow above
> you increases.  At some point, the shadow reaches a height where the sky
> becomes dark enough to provide sufficient visual contrast for you to be
> able to see satellites passing overhead.  This marks the beginning of
> the viewing period.  At some later point, the shadow height becomes so
> great that no LEO satellites remain above it.  This marks the end of the
> viewing period.

> The length of the viewing period depends on how quickly the shadow height
> increases after sunset.  If the shadow height grows rapidly, the viewing
> period is shorter.  If the shadow height grows slowly, the viewing period
> is longer.

> The rate at which the shadow height increases varies throughout the year
> and also depends on your latitude.  This seasonal effect is minimal at
> low latitudes near the equator, whereas it is dramatic at high latitudes
> in the arctic and subarctic regions.  At middle latitudes in the northern
> hemisphere, there is not very much change in the rate of shadow height
> growth from roughly August through April (autumn -> winter -> spring).
> However, beginning in May, the change becomes noticeable, as the shadow
> height grows slower and slower, until it grows at the slowest rate at
> summer solstice, then the shadow height begins to grow faster and faster
> again through the end of July, at which point the daily change becomes
> less noticeable again.

> So, roughly speaking, starting in May, at middle latitudes in the northern
> hemisphere, the satellite viewing period after sunset (and before sunrise)
> begins to noticeably lengthen from day to day.  As we approach the summer
> solstice, the daily change itself increases, i.e., there is a noticeable
> acceleration, until at summer solstice, the viewing period reaches its
> maximum.  In the days immediately following summer solstice, the satellite
> viewing period rapidly becomes shorter, with noticeable day-to-day decrease
> in the daily change (i.e., the deceleration is noticeable).  By mid-July,
> this deceleration is no longer noticeable, but the viewing period itself
> is still noticeably growing shorter, until by the end of July, the day to
> day change in the viewing period also has become too small to be noticed
> by the casual observer.

> With a longer viewing period, you have a better chance of seeing greater
> numbers of satellites.  So from that perspective, the May-through-July
> period is the best time to look for satellites from middle latitudes in
> the northern hemisphere.  At middle latitudes in the southern hemisphere,
> the corresponding best time is November through January.

> As mentioned earlier, this seasonal effect is very small at low latitudes
> near the equator.  At high latitudes, in arctic and subarctic regions,
> the effect is quite dramatic but somewhat different than what occurs at
> the middle latitudes.  At high latitudes, the shadow height never gets
> very far above ground level during local summer, if it gets above ground
> level at all, so you might think that the satellite viewing period would
> be extremely long.  However, without any shadow at all, or with the shadow
> never growing above some minimum height, the location is perpetually in
> sunlight or bright twilight, so the sky never grows dark enough for you
> to be able to see satellites passing overhead.

> In a way, this effect is reminiscent of Goldilocks and the three bears.
> When the shadow height is too small, the sky is not dark, and satellites
> cannot be seen.  When the shadow height is too big, shadow engulfs all of
> the LEO satellites and, again, they cannot be seen.  To see satellites,
> the shadow height has to be "just right".  This happy medium can occur
> all night at moderately high latitudes during local summer.  For example,
> at 50 degrees North latitude, at summer solstice, the shadow height grows
> very slowly, taking about two hours following sunset to reach the 60 mile
> height, which marks the end of twilight and start of the viewing period.
> However, for the rest of that night, the shadow height never grows beyond
> about 160 miles.  Since almost all satellites orbit the Earth at altitudes
> greater than 160 miles, the viewing period effectively lasts all night in
> this case.

> References

> 1. Kaler, James B.  The Ever-Changing Sky.  Cambridge University
>    Press, Cambridge, 1996 (with special note of Figure A1.3 on
>    page 433 and Figure A1.7 on page 437).

> 2. King-Hele, Desmond.  Observing Earth Satellites.  MacMillan
>    and Company, London, 1966 (with special note of Figure 14
>    on page 57).

> -------------

> I don't know whether there are other effects that could make May "special"
> in terms of watching satellites.  I'm forwarding a copy of this message
> to the SeeSat-L mailing list (international group of satellite observers),
> with a request that list members contact you directly, if they know of any
> other effects or if they want to correct, clarify, or expand upon something
> I've said here.

> As for giving credit, if you decide to use any material in this message,
> I would prefer that you give credit to the SeeSat group, rather than to me
> personally.  If you generate a printed or Internet version of the script(s),
> I also ask that you include a reference to our group's web site:

>    Visual Satellite Observer's Home Page
>       http://www.satellite.eu.org/satintro.html   (Germany site)
>       http://www2.satellite.eu.org/satintro.html  (England site)

> Best Regards,

> Sue J. Worden, PhD
> Mathematical Services
> Academic Computing & IT Services
> University of Texas at Austin
> email: s.worden@cc.utexas.edu
> voice: (512) 475-9259
> fax:   (512) 475-9382
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