How fast does Smart-1 go?

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bobw

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I have been looking for a while now and haven't found an answer. It is dumb but I have been wondering if Smart-1 got up to escape velocity and when? I know that in an elliptical orbit an object sweeps out equal areas in equal times making it fast at perigee and slow at apogee. I was thinking that it got up to ~25000 mi/hr on it's last close approach to earth, but when I look at the charts of its orbits it seems that the perigee has been getting higher and higher; the orbit looks almost circular now which would make the change in velocity during the orbit small(er). I can't figgure out why, if it got to escape velocity a long time ago, it is still spiraling out; and I can't figgure out how they are going to slow it down now if it is going really fast. <br /><br />I've never done anything but simple orbital calculations (circular) so this spiral thing has my head spinning. Can anybody help me out? I'm confused. How fast does Smart-1 go? <div class="Discussion_UserSignature"> </div>
 
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mrmorris

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<font color="yellow">"It is dumb but I have been wondering if Smart-1 got up to escape velocity and when?"</font><br /><br />No it didn't and it's not going to. It will achieve a velocity and orbit sufficient for 'lunar capture'. This then is the point at which the gravity from moon exerts a larger force on the craft than that of earth. The velocity involved is less than escape velocity, but I don't know the exact value.<br /><br />Once SMART-1 has been captured in a lunar orbit -- it will undergo a 4.5 day long burn to reduce the height of the orbit.
 
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remcook

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The concept of escape velocity and Kepler's laws are set up in a problem where there is one big body (the Earth for instance) and one very small body (the satellite). SMART-1 is now at a point where the Moon and the Earth are roughly equally important for determining the motion of the satellite (at first, when it was still close to the Earth, the Earth was by far the most important body; it was just an Earth-orbiting satellite, like many others). You could say that it is orbiting both the Moon and the Earth. Soon (tomorrow I think), the Moon will be the most important body: it will pull SMART-1 towards itself and hence it will start orbiting the Moon.<br /><br />Another point: escape velocity varies with distance to the Earth (one over the square root of the distance). So, the farther you go out, the smaller your escape velocity is. And so, it doesn't need to go fast at all! In the theoretical case where a satellite is at infinite distance, it only needs a very small, non-zero, velocity to escape the body.<br /><br />Another thing. SMART-1 keeps 'accelerating' when having the thrusters on. But accelerating is really a strange of words in orbital mechanics. Because what actually happens, is that, by giving thrust, the orbit will be raised, and hence the velocity will go down. Constant thrust will give a constant raising of altitude, hence the spiral-shape.<br /><br />so..some of your questions:<br />"I can't figgure out why, if it got to escape velocity a long time ago..." it didn't!<br /><br />"..., it is still spiraling out; and I can't figgure out how they are going to slow it down now if it is going really fast. " it isn't!<br /><br />hope i was of some help <img src="/images/icons/smile.gif" />
 
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bobw

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mrmorris and remcook<br /><br />Ok, thanks a lot. I guess you only need escape velocity if your propulsion is a one-shot thing. We don't get a lot of moon shots so I've got Apollo-on-the-brain. Now, knowing it didn't get that fast, I looked around some more. I found the play-by-play narration of the launch on spaceflight now. The upper stage of the Ariane 5 burned out at about 27 minutes and they started dumping satellites when it was about 1200 miles high. They were going about 19200 miles/hour in the elliptical geosynchronous transfer orbit 400/22000 miles.<br /><br />Lately I've been imagining the "rubber sheet" model of gravity with Smart-1 climbing up the dent and the moon, with its own dent in the dent, coming along from behind and Smart-1 falling over the hill into the little dent. Lunar orbital velocity (the moon around the earth) is about 2300 miles/hr. I guess Smart-1 is probably not going much faster than that right now.<br /><br />Thanks for your time and effort, I think I have a better handle on it now than I did.<br /> <div class="Discussion_UserSignature"> </div>
 
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bobw

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<font color="yellow">Another thing. SMART-1 keeps 'accelerating' when having the thrusters on. But accelerating is really a strange of words in orbital mechanics. Because what actually happens, is that, by giving thrust, the orbit will be raised, and hence the velocity will go down.</font><br /><br />Imagine my surprise when I clicked on today's front page story about Smart-1 on Space dot com and found:<br /><br />"Take a look at the path of SMART-1 as it gradually increased its speed, spiralling further and further from Earth before breaking free of Earth's gravity and heading toward the moon."<br /><br />I guess I'm not the only one who is confused. <div class="Discussion_UserSignature"> </div>
 
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remcook

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another thing that adds to the confusing is the representation of energy raise by "delta-V", i.e. an increase in velocity. <br /><br />all things are just messed up in orbital mechanics, really.
 
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