I have just read this article and I need help. Accordingly when this little device needed to slow down when approaching Saturn it fires it's rocket engine to brake, and it says it (must) last 96 minutes. Less or more than that it would end in loss of the device. Anyone can shed a bit of light here?
But I remember I heard that the Apollo rocket fires 15 tons of fuel per second. If you don't believe me than here is the quote;
"The Saturn V rocket's first stage carries 203,400 gallons (770,000 liters) of kerosene fuel and 318,000 gallons (1.2 million liters) of liquid oxygen needed for combustion. At liftoff, the stage's five F-1 rocket engines ignite and produce 7.5 million pounds of thrust."
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Some points to think about:
I don't know what device you are talking about, but it seems like it is not trying to escape a powerful gravity well (like say the surface of the Earth), is just trying to slow down (relative to Saturn), and probably has a tiny mass compared to a Saturn V. Presumably it does not need to do this quickly so it makes sense it should do it with less power (greater time) to improve efficiency. Less power (more efficiency) typically means less fuel needed.
You do know that there are different types of engines. Saturn rocket engines are huge. Car engines are big. The engine in your electric toothbrush is small. Does this help you understand this 96 minute thing/?
I just found this site and it shows the two rocket engines are not small engines. And above it look like the fuel tank. But I don't know the reality of rockets so I have to take their statements as it is.
They are tiny as compared to the F-1. Do you see the step ladder in the background? That entire engine is about the size of 1 fat person.
Now look at the F-1 engine below (the Saturn V had 5 of these):
But all of that aside, I really don't understand the question. Can you rephrase the question explicitly.
@Nyarlathotep: "Can you rephrase the question explicitly"
Here a Youtube clip of rocket assisted drone launching. At the 35th seconds you will see it fires only for 4 seconds to lift the drone to such distance against the gravity. Jump into 2 minutes and 52 seconds and you will see the size of the rocket when a person is standing next to it.
Now imagine a rocket just of that size firing for 5760 seconds continuously. But the Cassini probe's engine is bigger. 5760 seconds non stop firing from it in an empty space not only would stop the probe, it would push it back to earth.
I don't know rocketry but I have seen lots of them in documentaries, at best they only fires for 3 or 4 minutes. In probes like this or on satellites they only used to steer the direction with split second burst. And the 96 minutes of continuous powering is truly mind boggling.
Given this data:
So what is the acceleration produced by the engines on Cassini? Easy:
F = m*a
-980 (Newtons) ≈ 2,150 (kilograms) * a (meters/second^2)
a ≈ -0.46 (meters/second^2)
To put that acceleration into perspective, an object dropped from your hand accelerates towards the Earth at about -10 (meters/second), so this is a rather mild acceleration.
What effect will this mild acceleration have after being applied for 5760 seconds (96 minutes)? Since the mass and force are constant, the acceleration is also constant. So the final velocity (Vf) is just a function of time (t), acceleration (a), and the initial velocity (Vi):
Vf(t) = a * t + Vi
Vf (meters/second) ≈ -0.46 (meters/second^2) * 5760 (seconds) + 44,000 (meters/second)
Vf ≈ 41,350 (meters/second)
Clearly it would not. The spacecraft was heavy, has a very low power engine(s), and had an enormous initial velocity. This is why it is dangerous to just making hand-waving statements about what will or will not happen; and better to just calculate it.
@Nyarlathotep: "I don't have the data of how much fuel it started and ended this burn with"
I found it - it started with 3132 kg of propellant. But the first link on the OP states something which you probably did not read.
By the time it arrived at Saturn in 2004 at the speed of 87709 kph when they decided to brake for continues 96 minutes the amount of fuel was only 20% left. So when it has only 643 kg that was when the 96 minute firing started. Once it has achieved the desired speed at 5760 seconds later - than the probe used whatever fuel it has left to work for the next 13 years.
At this video clip few times the scarcity of fuel was mentioned, at the lecture as well at question time. A question was posed like "why did not you do this manoeuvre or that manoeuvre?" and the answer was there was no enough propellant.
I have a feeling there is an error in reporting. But hey, who read it anyway, and who cares other than those on payroll? I read it out of curiosity only. Anyway thanks for the method of calculating the acceleration.