OK, so aftermost night I acquaint about satellites that collided in orbit. I mentioned that the activity created in the blow was about the aforementioned as atomic a ton of TNT. I got asked how I did that math. That’s no botheration (well, a little one), but a bigger botheration is that I busted up the physics of the orbits. As commenter Marco Langbroek acicular out, the bend of appulse I acclimated was wrong. I forgot about the bend of the nodes.
Let me explain.
Both satellites were in arctic orbits, added or less. One had an affection (tilt) of about 86 degrees to the Equator — in added words, it anesthetized 4 degrees (90 – 86 = 4) from actuality anon over the Earth’s poles, and the added had an affection of 74 degrees from the Equator. I affected that meant that the bend of access was 12 degrees. FYI, a arch on blow would be an bend of access of 180 degrees (they are affective in adverse directions, against anniversary other), one communicable up to the added would be 0 degrees, and a battery “T-bone” blow is an bend of 90 degrees.
So area did I spiral this up? The affection is not the alone important angle. What’s additionally important is what’s alleged the bulge of an orbit, or the bend about the Earth. Here’s an illustration:
The chicken and red advance represent two arctic accessory orbits. You can see that a accessory in either apogee will canyon absolute aing over the Earth’s pole (the south pole is apparent here), so the inclinations of both orbits is high, a 90 degrees. But you can see they are rotated with account to anniversary other, in this case by about 60 degrees. That agency that area they intersect, over the Earth’s poles, the bend amid them is about 60 degrees.
That has a huge appulse (har har) on the blow speed. If they had the aforementioned bulge and the aforementioned inclination, the blow acceleration would be zero; they’d be on the aforementioned orbit. But if the nodes are rotated by 90 degrees, the blow would be a broadside, one slamming anon into the ancillary of the other.
That’s what happened with the Cosmos and Iridium satellites. The affection aberration was about 12 degrees, but the bulge bend aberration was about 83 degrees (according to Mr. Langbroek, whose chat I’ll acquire actuality back he’s an abecedarian accessory tracker). So the appulse bend was about a absolute broadside.
How does that affect the activity of the impact? Well, it’s accessible to get a appealing asperous idea. What follows is basically a back-of-the-envelope calculation, meant to be appealing loose. BotE calculations aren’t declared to be absolutely accurate; they’re meant to accord you an abstraction of the consistent number. So I wouldn’t be afraid if the accurate cessation I ability actuality as far as atomic crop is anxious is off by a agency of 2 or more, but the affair is I don’t care. We’re aloof aggravating to the consequence of the armament involved, not their exact measurements.
The blow activity depends on the about velocities of the satellites. Imagine two cars aing an intersection. One car is in the average back the added slams into it at a 90 bulk angle. The alone important cardinal actuality is the acceleration of the impacting car; the acceleration of the added one doesn’t matter. It could be sitting there in the intersection, or affective at 100 kph; the acceleration of the blow absolutely alone depends on how fast the added car was affective back it hit.
In reality, with satellites, it’s added complicated. The absolute three dimensional trigonometry of the accident is a little fierce, but it turns out that an appulse at 83 degrees is mathematically absolute aing to a simple 90 bulk blow (the aberration in angles after-effects in aloof a baby allotment aberration in velocity). In added words, a car hitting you at an 83 bulk bend has about the aforementioned acceleration as if it were hitting you absolutely broadside.
Assuming the satellites were both affective at the aforementioned speed, the appulse acceleration afresh is artlessly the acceleration of one of the satellites, or about 8 kilometers per second.
The activity of appulse depends on the accumulation of the satellites, too. The Iridium accessory was about 700 kg, and the Cosmos was apparently about the same. I couldn’t acquisition a acceptable bulk for Cosmos, aloof estimates… but it’s aing enough. Remember, I’m aggravating to be absolute asperous here; I don’t affliction if I’m off in my numbers by a agency or two or not; I aloof appetite an approximation.
The active activity of an article is according to 1/2 x its accumulation x its velocity2. Again, because I’m actuality absolutely asperous here, it doesn’t bulk which accessory hits the other. We can accept they accept about the aforementioned mass, so the active activity (in ergs, which I’ll explain in a second) is
KE = 0.5 x 700,000 grams x (800,000 cm/sec)2 = 2 x 1017 ergs
An erg is a baby assemblage of energy, but 200,000,000,000,000,000 is a lot of them. Blowing up a ton of TNT releases about 4 x 1016 ergs, so this blow was almost the agnate of casting 5 bags of TNT at the satellites.
[FWIW, my aberration in the antecedent column was d the blow bend was 12 degrees, and the acceleration of blow depends on the sine of the bend amid the objects. Sin(12) = .20, so my cardinal was 1/5 as big as it should be.]
That’s why there’s a ample billow of accretion debris; anniversary allotment of burst accessory agitated abroad a allotment of that agitated activity release. The activity of blow afflicted the orbits of all those shards, so they are now orbiting the Earth on new paths that booty them college or lower over the surface, appropriate into the cartage lanes of added satellites.
So eventually, some may already afresh acquisition an article in their way. And because of the aerial velocity, the active activity of appulse alike from a low-mass allotment can be appealing fierce. A burglarize ammo does a huge bulk of accident back it hits something, and it has a accumulation of about 10 grams and moves at a paltry 1 km/sec. Now anticipate of the accident inflicted by a baby accessory block that masses about 1 kg (100 times as abundant as the bullet) and affective 8 times faster… the activity of appulse is 6400 times that of the bullet. Imagine accepting hit by six thousand burglarize bullets, and you alpha to get an abstraction of why accessory collisions are not aloof adverse for the two birds involved, but additionally a crisis to added altar in apogee as well.
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