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The following paragraph is from a wired.com article:

When I visited this past fall, SpinLaunch employees were still unpacking from the move. As we walked among giant sheets of steel, Yaney explained how his launcher will work. A centrifuge large enough to contain a football field will whip a rocket around in circles for roughly an hour, its speed steadily ramping up to more than 5,000 mph. The vehicle and its payload—up to 200 pounds’ worth of satellite—will experience forces that, at their peak, will be ten thousand times stronger than gravity. Once it’s spinning at launch speed, the centrifuge will release the rocket and send it screaming into the stratosphere. At the threshold of the cosmos, it will fire its engine for a final nudge into orbit.

However, Wikipedia says:

The mean orbital velocity needed to maintain a stable low Earth orbit is about 7.8 km/s (28,000 km/h; 17,000 mph), but reduces with increased orbital altitude.

So, even ignoring the inevitable loss of speed as it travels from the launch site on the ground to the edge of space, and assuming it is still going at 5000 mph, it will surely take more than a 'nudge' to place it in even low earth orbit, because an increase of speed to 17,000 mph is an increase of 12,000 mph. This seems more than just a 'nudge'.

So my question is, what does 'a nudge' mean in the context of rocketry?

Matthew Christopher Bartsh
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"Nudge" is not being used here in the rocketry context, but rather in a marketing context.

There's no way to throw a rocket from ground level into orbit without making a significant burn once in space. Even if you could throw it fast enough to maintain something like 7700 m/s once outside the atmosphere, you'd still be in a closed orbit that would bring you back to ground level; you need to do a "circularization burn" in order to reach a stable orbit.

In the case of Spinlaunch, as you note, the lion's share of orbital speed still needs to be provided by a conventional rocket. The sole function of the word "nudge" here is to obscure this point to make SpinLaunch's proposal look more attractive.

Russell Borogove
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    "At the threshold of the cosmos"! – Organic Marble Apr 26 '21 at 16:17
  • Why would Wired care whether SpinLaunch's proposal looks more attractive? – Matthew Christopher Bartsh Apr 26 '21 at 18:19
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    @MatthewChristopherBartsh It gets more clicks/views, more such stories in the future, and it's quicker and easier than an objective dissection of the claims and explaining the technical issues to the readers. – Christopher James Huff Apr 26 '21 at 19:22
  • @OrganicMarble Actually, the cosmos doesn't start at an altitude of sixty kilometers. The entire earth is part of the cosmos. Using a thesaurus can be risky. – Matthew Christopher Bartsh Apr 26 '21 at 19:45
  • @MatthewChristopherBartsh Agreed, it's a dumb thing to say. Just like the nudge. – Organic Marble Apr 26 '21 at 19:46
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    @MatthewChristopherBartsh many science journalists have absolutely no clue about the topic they are writing about and just regurgitate whatever they are being told. – eps Apr 27 '21 at 15:02
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    Daniel Oberhaus is a staff writer at WIRED, where he covers space exploration and the future of energy. He is the author of Extraterrestrial Languages (MIT Press, 2019) and was previously the news editor at Motherboard. They must fill their magazine up every month with new stuff. When not enough new stuff happens in a month... Anyway, at least they didn't accidentally invent a new particle! – uhoh Apr 27 '21 at 15:11
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    @eps I wonder why that is? Is it not a very sought-after job? – Matthew Christopher Bartsh Apr 28 '21 at 17:58
  • @MatthewChristopherBartsh There are excellent science writers, but there are also positions that they don't want, and are therefore filled by excellent (or good) writers that are can't necessarily instantly morph into expert mode on each topic they are assigned. It's a hard job; demanding editors, deadlines, potentially slow-to-respond sources. I guess they just do their best, get their copy submitted under the deadline and quickly move on to the next assignment. Publishing has changed a lot since the internet; goal now is advertisement views and clicks, revenues have dramatically dwindled. – uhoh Apr 28 '21 at 23:42
  • @uhoh I keep reading that writers get one USD per word. You'd think they could do better. I mean, you don't need to be an expert to realize that getting from 5000 mph to 17000 mph requires more than a nudge. Nor that the intelligent layman is likely to want to know in which direction the payload will be going when it is thrown at 5000 mph, and what speed it will be going when it is due for a 'nudge'. lol. – Matthew Christopher Bartsh Apr 29 '21 at 18:14
  • There’s a lot of stuff about space flight that isn’t obvious or intuitive (in particular, “orbit is about going fast more than getting high up”); I wouldn’t expect a general science writer to get it. – Russell Borogove Apr 29 '21 at 19:46
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    @RussellBorogove True, I guess, but it's actually a bit of both. The higher you are, the less fast you need to be going. If the the SpinLaunch rocket were thrown high enough, a nudge really would be all that would be needed. For example, if it were thrown to an altitude of 400,000 km (the same altitude as the moon) it would only need to be given a nudge of 1 km/s to put it into a circular orbit. And much less to put it into a highly elliptical orbit. – Matthew Christopher Bartsh Apr 29 '21 at 20:55