I personally think it is incorrect to say "the speed of" in this context.
I'm sure you understand that "the" is the definite article which would denote that there is only one of something, or you are referring to a specific example of something.
a rocket has to accelerate the satellite to the speed of 8 kilometers a second
This just sounds wrong. The rocket won't be the only thing traveling at 8km per second, so how can that speed be the definite article?
I can see why some people might think it might be okay. Let's look at a sentence that uses "to the" in a similar way:
Several songs are sung to the tune of 'Twinkle Twinkle Little Star'.
This means that more than one song can be sung to "the tune" (like lots of rockets accelerating to the same speed) but the sentence also makes it very clear that "the tune" belongs to one particular named song.
The only time I can think of "the speed" being used correctly is the speed of light (or sound, but that varies depending on air temperature so lets keep it simple). But by saying something is traveling (or accelerating to) the speed of light you are actually comparing it to something specific which is why the definite article is required. The speed 299,792 kilometers per second is the same speed as light travels.
So back to your example, and saying:
the speed of 8 kilometers a second
..is in effect saying that the speed of 8km/s is the speed that belongs to 8km/s. That makes no real sense.
In the latter part of your example, where it goes on to compare the speed to "the speed of a jet aircraft" - this is a specific, defined speed, and is also a comparison. There may be many jet aircraft, but they all have the same maximum speed. So the speed of a jet aircraft is a comparison to the specific speed shared by all jet aircraft.