Is it plausible that the explosion of a satellite in an orbit 65km above the ISS will not threaten the ISS?

Question

(Not sure if this is better-suited to the Astronomy SE or Space Exploration SE)

Recently in the news was Russia using an anti-satellite weapon to destroy a Soviet-era satellite. The destruction created over 1500 trackable pieces of debris that the US says threatens the International Space Station. AP says the destroyed satellite had an orbit 65 km higher than the ISS:

The defunct Russian satellite Cosmos 1408 was orbiting about 40 miles (65 kilometers) higher than the space station.

The article also includes this paragraph:

Russia's Defense Ministry on Tuesday confirmed carrying out a test and destroying a defunct satellite that has been in orbit since 1982, but insisted that “the U.S. knows for certain that the resulting fragments, in terms of test time and orbital parameters, did not and will not pose a threat to orbital stations, spacecraft and space activities.” It called remarks by U.S. officials “hypocritical.”

How plausible is Russia's claim? It seems implausible to me because one presumably cannot predict how the pieces of the satellite will move after destruction (system too chaotic), and 65 kilometers is not that far in space, especially when the ISS itself orbits at nearly 30,000 km/h. However, I am not an expert, so I would like to confirm.

Answer 1

To use an anti-satelite weapon on a (decommissioned) satellite that is in an orbit at higher altitude than the ISS is an act of abysmal stupidity.

When India used an anti-satellite weapon they destroyed a satellite that was orbiting at something like 300 km altitude. At that altitude the amount of atmosphere present causes an amount of drag that will cause the orbiting object to de-orbit in months.

My understanding is that the debris from this destruction event will take around a decade to lose the amount of altitude such that it de-orbits.

In low-Earth orbit everything is losing altitude, due to drag. The ISS needs a boost back to higher altitude from time to time. These boosts need to happen anyway, and there is some leeway, so they can be planned earlier or later. The boosts are timed such that there is maximal probability of not being hit by any of the known orbital debris. This addition to the orbital debris will reduce the margins.

Pieces of debris that have been sent into an eccentric orbit will lose altitude the quickest, since their perigee is comparitively close to the Earth. The debris that ended up in circular orbit will take the longest. Over time the debris-in-circular-orbit will spread out to a distribution over the entire circumference of the orbit.

See also: video by science communicator Scott Manley about the russian anti-satellite weapon.

[Later edit]
Satellites in low-Earth orbit have a dedicated propulsion system that is fired from time to time in order to maintain altitude. When the propellent is depleted the satellite can no longer maintain altitude, and over time it will de-orbit

(The satellites for the SpaceX Starlink system have such a propulsion system. SpaceX has made it clear that on decommisioning a Starlink satellite there will be a propellent reserve, enough to perform a rapid de-orbit, thus reducing the probability of causing orbital debris.)

Presumably the destroyed satellite was on a different orbital plane than the ISS. Over time the orbital debris will lose altitude, and each of the individual pieces will in its own time be orbiting within the altitude range of the ISS. The respective orbital planes are at an angle, so there will be two crossing points. The odds of a collision are small, but not zero.

Of course: once a piece of orbital debris has lost so much altitude that it orbits at lower altitude than the altitude range of the ISS it no longer poses a threat to the ISS.

The pieces of debris from the destruction event will lose altitude at different rates, so for many years pieces of orbital debris will be moving into the altitude range of the ISS.

Answer 2

I would like to consider just one aspect of the situation: does it really matter much if the satellite was destroyed above or below the ISS?

Let us consider a destruction of a satellite that initially moved in a circular orbit at the altitude of $h=200$ km (satellites at lower orbits would have a short lifetime (https://www.spaceacademy.net.au/watch/debris/orblife.htm)). The speed $V$ of the satellite can be calculated from the following equation:$$\frac{m V^2}{R+h}=\frac{\gamma m M}{(R+h)^2},$$ where $m$ is the mass of the satellite, $M$ is the mass of the Earth, $R$ is the radius of the Earth, $\gamma$ is the gravitation constant. We obtain $V\approx 7780$ m/s. Let us assume that after the satellite is destroyed the debris initially fly in all directions with speed $v$ with respect to the satellite (sorry, this sounds clumsy), so the fastest debris will have speed $V+v$, and the orbit of this debris will have perigee $h$ and apogee $h_2$. Let us assume that the apogee of this debris equals the perigee of ISS (418 km) and calculate $v$. We have an equation for energy conservation $$-\frac{\gamma m M}{R+h}+\frac{m(V+v)^2}{2}=-\frac{\gamma m M}{R+h_2}+\frac{m V_2^2}{2}$$ and the third Kepler's law $$(V+v)(R+h)=V_2(R+h_2).$$ We obtain $v\approx 63.2$ m/s, and I would suspect that the maximum relative speed of debris is significantly higher when a satellite is destructed. So, if I have not miscalculated, destruction of a satellite is dangerous for ISS if it happens below ISS orbit as well.