# What is the typical relative impact velocity of orbital debris in low Earth orbit?

We all know that space is about going really fast. We also know that what matters in a collision isn't really absolute speed, but relative velocity. (Two cars with matched speeds on a highway touching each other doesn't necessarily lead to large damage, but if one of them was standing still, it probably would.) A large fraction of the orbiting spacecraft are in prograde orbits, simply because it's easier and, if not actively helpful, at least doesn't hurt; that also reduces the relative velocity between the two.

Yet people keep saying that in-orbit collisions happen at such extreme velocities.

What is the typical relative impact velocity of a piece of orbital debris to an operational spacecraft in low Earth orbit? What are the vector component values of this velocity?

Bonus points for answers that include citations.

Also bonus points for answers that include the data from which the "typical" is derived.

• What this question deserves is an answer that analyzes the different orbital planes of satellites in LEO as that should also be representative of debris. Most satellites in LEO are not at 0 inclination it's not even possible (as such) to launch into 0 inclination from the major space ports, so nearly all LEO satellites are in differently inclined orbits - some like sun synchronous even being slightly retrograde. So there should be plenty of scope for collisions at a significant fraction of, or even higher than, orbital speed. – Blake Walsh Jun 12 '17 at 9:23
• @BlakeWalsh You will notice that I very specifically did not assume any particular orbital inclination in the question, only that "a large fraction" of orbiting spacecraft in LEO are in prograde orbits. – a CVn Jun 12 '17 at 9:30
• There is a partial answer and some helpful links, but a more complete answer would be great, although I'd like to see an actual distribution, not just something reduced to a single "typical" velocity. I would not stop wearing my seatbelts even if a "typical" car-car event were a fender-bender. – uhoh Jun 12 '17 at 9:33
• @uhoh Indeed; the discussion in the comments to Tristan's answer was largely what inspired me to ask this question. I also edited the question slightly to try to address your concern without making the question entirely too broad. – a CVn Jun 12 '17 at 11:49
• Because you want detailed data and citations, I will not provide an answer, as the underlying data products are export controlled. It depends on the altitude and inclination of your orbit, but for ISS, the typical velocity for orbital debris is 11 km/s. Feel free to dig around ntrs.nasa.gov with the search term ORDEM for corroboration. – Tristan Jun 12 '17 at 13:45

Take a look at this answer by Mark Adler. As you can see, a small panel over a 15 years endured many impacts. I would expect there have been multitudes of impacts over all. I doubt anyone knows what the average impact velocity has been.

I'll attempt to give you some tools to examine different scenarios, though.

Given a triangle with lengths a, b, c:
$c^2 = a^2 + b^2 - 2ab * cos(\alpha)$
where $\alpha$ is the angle between a and b.

The Law of Cosines may look hard. But if you remember cos(90º) is zero, you can see the Pythagorean theorem drop out when alpha is 90º. So if you just memorize the $-2 ab * cos(\alpha)$ part, the rest is the Pythagorean theorem you learned in high school.

And when you do vector subtraction, the third side of the triangle is the delta v between the first two velocity vectors.

Below is a series of 7.7 km/s velocity vectors forming different angles with the original 7.7 km/s velocity vector. These are vectors from 300 km altitude circular low earth orbits:

• Why would you assume most satellites and debris are in inclinations 30º or less? For USA and to an even greater extent Russia the plane change would be very expensive to get into a low inclination orbit, furthermore an equatorial LEO orbit would only be useful for servicing (spying on) countries on the equator while I'd expect USA and Russia are/were mainly interested in themselves or each other so favoring higher inclinations (after all high inclination can also service (spy on) the equator). All references I can find have most LEO satellites between 30 and 110 degrees. – Blake Walsh Jun 12 '17 at 20:56
• @BlakeWalsh It was just a guess on my part. Googling around it seems you're correct. I deleted the last two paragraphs of my answer. – HopDavid Jun 13 '17 at 2:16
• Most LEO assets are highly inclined. Huge number between 70 and 98 degrees. – Tristan Jun 13 '17 at 2:16
• There is a simpler formula when a and b are equal: c = 2 * a * sin(α/2). – Uwe Jun 13 '17 at 11:21

Not sure how precise you need the answer, but just thinking about the first cosmic velocity and the escape velocity, it can only be a value between that. So Something between ~7.8 km/s - 11.2 km/s.

Of course as you mentioned the relative velocity matters. The orbits of the debris could be opposed to the orbit of the spacecraft so the theoretical max relative velocity would be 11.2 km/s + ~7 km/s = ~ 18 km/s (since you're talking about a LEO and not a HEO or something). Since most launches take place in a prograde orbit I'd imagine that most of the debris would be in a prograde orbit as well so most impacts probably take place at a relative velocity of the perigee speed of a HEO (9-11 km/s depending on the orbit) and the speed of the spacecraft in LEO (~7-7.5 km/s). Worst case is about 19 km/s as mentioned before though.

All speeds below that are possible though, as the inclinations between the spacecraft can vary, resulting in very different relative velocities.

• Looks like a good answer to me. Who voted it down and why? I gave this an upvote. – HopDavid Jun 12 '17 at 16:15

I calculated a simple example. Two objects are in a circular low orbit but in different planes. The impact velocity depends on the angle between the orbit planes. I use 7.8 km/s for the speed in orbit.
For an angle of 5° the vectorial velocity difference is 0.68 km/s, for 10 ° 1.36 km/s, for 15 ° 2.04 km/s, for 30 ° 4.04 km/s, for 45 ° 5.96 km/s and for 90 ° 11.04 km/s.
Two orbits with an angle difference of 45 ° to the equatorial plane in oppositional directions have an angle difference of 90 ° between them.
Impact velocities of 1 to 11 km/s are possible.

• I think you are missing out on elliptical debris. In cases such as a Molniya orbit, it could be around 10km in LEO. – Antzi Jun 12 '17 at 11:06
• @Antzi The difference between 7.8 and 10 km/s is not that large. You may add a calculation for elliptical orbits. – Uwe Jun 12 '17 at 11:15
• Better double check the math. I did it wrong the first time also. At 90 degrees the relative velocity is $\sqrt{2} \times v_0$ or 1.414 times 7.8 km/s See this link. – uhoh Jun 12 '17 at 12:05
• Two objects both at 30 degrees inclination, but with opposite LANs, should collide at exactly orbital velocity as the velocity component that doesn't cancel out should be 2 x sin(30) – Blake Walsh Jun 12 '17 at 13:35
• @HopDavid Yes, numbers were wrong. But your value for 90 ° is wrong too, 7.8 * 1.4142 is 11.03 – Uwe Jun 12 '17 at 19:48