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update March 2018: I just saw this in Buzzfeed (Google sent me there, I don't normally read it): Rich People Will Soon Be Able To Buy Fake Meteor Showers On Demand


@Antzi mentioned below the question Why does all satellites seems to have the same color from earth? this June 8, 2017 Nikkei business profile On-demand shooting stars? Japanese startup dreams big.

The article mentions a 50 cm sized nanosatellite at about 500 km altitude that will launch "simulants" or small objects (looks like about 1 cm gum balls) that will then burn up in the atmosphere, likely laced with compounds or elements that will produce brighter emission in the process.

From a conservation of momentum point of view, how can a reasonably affordable micro or nano satellite in a stable LEO orbit of several hundred kilometers get a small object into the atmosphere at a predictable time. I mean it would be extremely hard to do it in a few minutes, but if it were to be days or years, then the uncertainty in reentry time would be unacceptable.

Perhaps the idea is to use some serious, expensive hardware, and rely on economies of scale? Millions of shooting-star orders? Or a substantial fraction of the budget for the "opening ceremonies of the 2020 Tokyo Olympics"?

Does this seem possible from the point of view of what is known about objects in stable LEO orbits? Or is it more of a "magic leap" of faith?

There is further information from CNN, a nice write-up about the company Ale at f6s.com, and I found this promotional video that illustrates the idea (little balls pooping popping out of the rear-end of the satellite) but does not handle momentum conservation that well:

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    $\begingroup$ Speaking from my role in protecting the ISS from orbital debris impact damage, here's what I have to say about the idea of releasing hundreds or thousands of 1cm objects from a 500 km orbit: NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! $\endgroup$ – Tristan Jun 9 '17 at 17:41
  • $\begingroup$ @Mark thanks but in this particular case the issue of distracting graphics is central. I suppose on a large monitor or tablet oriented vertically one can not avoid seeing the GIFs without resizing the browser temporarily, but for most viewers they will be or can easily be kept out of sight while reading the question. $\endgroup$ – uhoh Jun 10 '17 at 5:05
  • $\begingroup$ @Tristan they are supposed to remain for half an orbit. $\endgroup$ – Antzi Jun 10 '17 at 7:23
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    $\begingroup$ @Antzi have there ever been cases of things not happening the way they are "supposed to" in space? The more one looks into the reality of this, it's a nightmare. Look at the delta-v necessary to de-orbit each little ball from 500 km LEO, it's huge! What if the ball fragments during acceleration? What if the delta-v is only 90%? What if something hits this satellite and releases thousands of ball bearings into LEO? $\endgroup$ – uhoh Jun 10 '17 at 9:34
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    $\begingroup$ @RoryAlsop "... how could this possibly work (economically/technologically)?" Also "Does this seem possible from the point of view of what is known about objects in stable LEO orbits? Or is it more of a "magic leap" of faith?" I've addressed part of the (technologically) in my answer. The satellite must function as a gun, and deliver at a minimum about 121 m/s of delta-v to each "shooting star" in order to de-orbit it. If you can contribute to the "economically" aspect that would be great! $\endgroup$ – uhoh Jun 11 '17 at 19:44
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Now that I have my comment out of the way, I can't envision sending something up to a relatively high LEO would be either effective or efficient. It would make far more sense to do something on a suborbital trajectory -- this saves you a huge amount of delta-V and provides much finer control over the timing and dispersion of your reentering particles. It still would present hazards to assets on orbit to the point of coming close to violating international agreements, but it would be far more practical than the concept outlined in the question.

It's probably still a whole lot more bang for one's buck to just use plain old fireworks though.

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  • $\begingroup$ I think at least their initial idea would be to dispense a few at a time, on demand, or at least on a arranged schedule. Customers would 'order' one, or two, or a half-dozen on a certain orbital pass, and of course enter a credit-card number. So they'd want their satellite to remain safe and stable up there for a while, because it may take years to use up their payload. So I'm really asking how to de-orbit these 'droppings' on an individual basis - how much delta-v to get it to re-enter and burn up over a predicted site, every time. $\endgroup$ – uhoh Jun 9 '17 at 17:50
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    $\begingroup$ Since I'm back in comment land, I can be a little more opinionated: NO CENTIMETER-CLASS OBJECTS ANYWHERE ABOVE 300 KM FOR ANY REASON EVER! I would be happy to scream that over the phone to anyone considering doing it. $\endgroup$ – Tristan Jun 9 '17 at 17:52
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    $\begingroup$ Can you expand upon the issues related to the size of these projectiles at this follow-up question? $\endgroup$ – uhoh Jun 10 '17 at 6:02
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    $\begingroup$ Yes, it would take less delta-V to have it be suborbital, but you need the orbital-scale velocity to make it burn! Otherwise you're just dropping pebbles. $\endgroup$ – Deimophobia Jun 11 '17 at 21:58
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    $\begingroup$ You could save even more delta-V by taking my advice and NOT FREAKING DOING IT IN THE FIRST PLACE! $\endgroup$ – Tristan Jun 12 '17 at 1:46
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Economically:

Economic arguments and business plans can range in both honesty and subjectivity, but I'll outline a hypothetical estimate.

This quora post written by Peter Hand, VP of Western Pyrotechnic Association puts the cost of a 20 minute fireworks display anywhere from $20,000 to a million dollars, depending on the level of firework used:

For a professional display, you’re probably looking at $10,000 to 20,000. There’s a lot of work for a lot of people in the setup, and a lot of capital tied up in the mortars and firing systems. On the other hand, professional shells are relatively inexpensive compared to the retail consumer kind, with a case of 64 three inch shells often no more expensive than a box of two dozen consumer shells from a retailer. Most professional displays use larger shells, like six inches and higher, and these can cost upward of 300 [dollars] each. If you spend the money, you’ll get these in your display, otherwise it will just be 3 and 4 inch shells. It takes a lot of these small bursts fired at once to fill the sky, which is rather dismissively called “Chinese carpet bombing”. I wouldn’t call that a “decent quality” firework display.

Some really outstanding 20 minute displays have cost upward of a million dollars, but these often cover a huge area and use many custom shells, some 24 inches in diameter and needing 60 pounds of gunpowder to lift. (emphasis added)

The website ReactionFireworks.co.uk says in its faq (in part):

As a guide an organisation such as a Round Table or Parish Council typically spends between £3,000 to £6,000 for a 15 to 20 minute pyromusical.

Major Guy Fawkes displays as seen in many cities accross the UK over November would typically cost between £10,000 and £16,000 and often have audiences in excess of 20,000.

Larger displays seen in such places as Battersea Park, Edinburgh Castle and the London Eye can range from between £30,000 to £200,000. The record for the most expensive firework display is held by Kuwait for the 50th anniversary of the ratification of Kuwait’s Constitution in November 2012. The display cost a reported £10,000,000 !

So let's say the spacecraft carried enough "stars" to do 100 shows a year for ten years with one hundred 2 gram shooting stars per show. There are certainly that many fireworks displays happening on Earth, but the question of how many would shift to this new technology is... subjective.

Then suppose that they grossed on average $100,000 per show (ranging from personal single shooting stars to million dollar events) that's a gross income of one hundred million dollars, and that could at least conceivably pay for the design, construction, launch, control and orbital maintenance of a ~70 cm, maybe 500 kg nano satellite for ten years, considering the way costs and technology is evolving and beginning to standardize. It's in the right ballpark at least.


Technologically:

Let's try this using the vis-viva equation:

$$v^2 = GM_E\left(\frac{2}{r}-\frac{1}{a}\right),$$

the equatorial radius of the Earth 6378 km or $6.378\times10^6 \ meters$, and the Standard gravitational parameter of the Earth $GM_E = 3.986\times 10^{14} \ m^2s^{-3}$.

The semi-major axis of the satellite in a circular orbit with an altitude of 500 km is $a_0 = 6.878 \times 10^6 \ meters$. Using the vis-viva equation, that gives an initial velocity $v_0 = 7613 \ m/s$. As a check, the period would be $2\pi a_0 / v_0 = 5677 \ sec$ or about 94.6 minutes.

An educated guess would be that a targeted perigee somewhere between about 80 and 100 km would be guaranteed prompt, localized re-entry. This bars oddly or aerodynamically shaped objects or plane-shaped objects, but small spheres at this perigee and this kind of velocity will re-enter and burn up.

What delta-v is needed to do this? If we assume the orbit of the recently ejected ball has its apogee at 500 km altitude and its perigee at 80 km, then the new semi-major axis is now $a_1 = 0.5 \times (6.878 \times 10^6 + 6.458 \times 10^6) = 6.668 \times 10^6 \ meters$. Plugging the new semi-major axis $a_1$ and maintaining the apogee of 500 km into the vis-viva equation, the new velocity required for a re-entry orbit would be $v_1 = 7492 \ m/s$, a delta-v of 121 $m/s$.

This is a minimum. You may want substantially greater delta-v for improved re-entry targeting accuracy.

Using algebra, one can use $x=\frac{1}{2}at^2$ and $v=at$ to obtain $a=v^2/2x$. To get a velocity of 121 meters per second inside a 50 centimeter nano satellite, you need an acceleration of almost 1500 gees.

The satellite is a gun. It fires deer slugs with a muzzle velocity of at least 400 feet per second, ideally much more. It carries of order ten thousand rounds of ammunition or more, in order to be economically feasable. It can get at you, but it's darn hard for you to get back at it, unless you build a bigger gun, and we know how that story goes...

The projectile velocity relative to you and yours could easily be a few thousand meters per second or ten thousand feet per second depending on the inclinations of the two orbits, and so the impact energy would be enormous if one of these hit anything.

But don't worry, it's "not supposed to" do that.

Still, the fact that the spacecraft is effectively a gun with ten thousand rounds could conceivably make the whole project moot. If it were struck by space debris, it could release ten thousand radar-invisible projectiles into short-term stable LEO orbits above the orbit of the ISS and Taingong-1 and Tiangong-2, and this possibility could make this project highly objectionable to any country associated with any current or future manned space mission.

enter image description here

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  • $\begingroup$ A close look at the linked video brings a whole new meaning to the term range-safety. $\endgroup$ – uhoh Jun 11 '17 at 17:32
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    $\begingroup$ Anonymous down votes without comments don't help improve answers. $\endgroup$ – uhoh Jun 11 '17 at 19:41
  • $\begingroup$ @Hohmannfan OK I'll take my own question even more seriously and simply answer it fully myslef ;) It doesn't look like anyone else will. $\endgroup$ – uhoh Jun 12 '17 at 8:34
  • $\begingroup$ You also have the issue that throwing balls at that speed will actually be propelling tthe satellite (action/reaction). Thus the satellite will also accelerate. $\endgroup$ – Gp2mv3 Jun 16 '17 at 13:14
  • $\begingroup$ @Gp2mv3 it will gain angular momentum, but it won't accelerate. Sounds like a good follow-up question, why not ask it? $\endgroup$ – uhoh Jun 16 '17 at 15:04

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