I'd think that in relation to a stationary observer on the planet, the satellite would travel slowly across the sky, in reverse direction of the sun, for 5 local days, then disappear below the horizon for another 5.  Assuming that the periods in question are exactly 18 and 20 hours. 

It would be an interesting basis for a local week or month, much like the lunar calendars of Earth. However if the orbit of the body around it's star isn't evenly divisible by the weekly or monthly periods there would be a procession of lunar periods through the year.

Dave
Your 'reality', sir, is lies and balderdash,
and I'm delighted to say that I have no
grasp of it whatsoever.
                      - Baron Munchausen

On Sat, Mar 5, 2016 at 4:39 PM, Richard Aiken <xxxxxx@gmail.com> wrote:
On Sat, Mar 5, 2016 at 5:07 PM, Freelance Traveller <xxxxxx@freelancetraveller.com> wrote:
What would I see, in terms of satellite-rise, satellite-set, movement
across the sky, et cetera?

Just a WAG (since for me math stops at beginning algebra), I'd say that you'd see the satellite appear to slowly travel backwards (relative to the sun) across the sky throughout the day/night cycle (since it moves about 10% slower than the planet rotates).

BTW, I notice that you didn't specify whether (and by how much) the satellite's orbit is inclined to the planet's plane of rotation. 

--
Richard Aiken

"Never insult anyone by accident."  Robert A. Heinlein
"I studied the Koran a great deal. I came away from that study with the conviction there have been few religions in the world as deadly to men as Muhammed." Alexis de Tocqueville (1843)
"We know a little about a lot of things; just enough to make us dangerous." Dean Winchester
"It has been my experience that a gun doesn't care who pulls its trigger." Newton Knight (as portrayed by Matthew McConaughey), to a scoffing Confederate tax collector facing the weapons held by Knight's young children and wife.
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