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I'm trying to understand how much a small reduction in orbital velocity can affect the orbital decay rate of space debris. I understand that there are multiple factors to consider, such as debris in lower orbits are subject to higher levels of atmospheric drag and the lower the density of the debris debris the more it is affected by drag (such as a cube of plastic should re-enter more quickly than same cube of lead).

But assuming all other factors are equal, how much would you have to slow the debris to have it make a substantial increase in the rate of orbital decay. As a thought experiment, assume as a piece of debris flew by your spaceship you could apply a magic "tractor beam" to slow it (maybe using a magnet?)?

So my direct question is how much sooner would the orbit of a typical piece of space junk decay in a circular orbit roughly at ISS level (as suggested by @uhoh, a 400 km altitude), from a 1/10th of 1% reduction in velocity?

From a 1% reduction?

A 2% reduction?

The main purpose to this question is to understand how practical subtle effects could be at de-orbiting uncontrolled space debris. How minor a force could we apply to debris to clear them from orbital space?

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    $\begingroup$ A 1% reduction in speed from a 225 km orbit brings your periapsis to -32 km, very soon! $\endgroup$ Commented Feb 2, 2022 at 23:26
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    $\begingroup$ A simple answer to your question is "it depends bigly on the initial orbit". because apart from the orbital mechanics, atmospheric density varies exponentially with distance from Earth's surface (with different rates above and below the knee) Can you constrain your question somewhat? A popular low Earth orbit for these kinds of discussions would be the ISS' circular orbit near 400 km altitude, but you can choose another if you like. $\endgroup$
    – uhoh
    Commented Feb 2, 2022 at 23:44
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    $\begingroup$ @BrendanLuke15 Meanwhile, at GSO, you would have to burn retrograde 1017.7 meters per second, almost 33 percent of your velocity! Meanwhile a 2% reduction of speed at GSO would bring your periapsis down by about 10%, not a lot. $\endgroup$
    – WarpPrime
    Commented Feb 3, 2022 at 14:02
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    $\begingroup$ @BrendanLuke15 something along the lines of "Which is more likely in GEO, a billion atoms per second for a petasecond or a yotta atom all at once?" but more quantitative. $\endgroup$
    – uhoh
    Commented Feb 3, 2022 at 14:21
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    $\begingroup$ Asking how much force is needed doesn't make physical sense. To deorbit stuff, you need some amount of velocity change (delta-v), no matter how you induce it. An arbitrarily small force can deorbit anything from any orbit if applied for a long enough time. $\endgroup$
    – TooTea
    Commented Feb 8, 2022 at 14:49

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