3 ms·

Hmmm, interesting analysis, but 12,000km is 3x wider than continental US. Based on the plot from ESA's projection, the track over the +-10m period is much small

Hmmm, interesting analysis, but 12,000km is 3x wider than continental US. Based on the plot from ESA's projection, the track over the +-10m period is much smaller than France. I think the issue with your reasoning is that when you are dealing with orbits, you cannot really talk separately about position and (relative) velocity. Instead, for a given orbital trajectory, the position completely defines the speed. Moreover, your estimate might tell us how far _in space_ the impact would be given +/- 10min, but since both earth and asteroid are moving though space that doesn't really tell us much about how far apart it would be in an earthbound reference frame. In practice, I don't think they can accurately measure the position OR speed of an object like this... Instead, they make multiple observations over time and can fit the "shape" of the orbit, which can be done even with a fair amount of noise since we know all orbits are elliptical. If the object's orbit doesn't intersect Earth's, there's no impact. If the orbits do interest, there _may or may not_ be an impact event. To determine this, you have to figure out if both the object and the earth will be at that intersection point, _at the same time_. I'm guessing this is why the quoted uncertainty is given in minutes.

dredmorbius 4y ago
The 12,000 km estimate is straight maths assuming a (fairly typical) relative orbital velocity of ~20,000 km/s for the meteroid, and looking at distance travelled in 10 minutes. Mind that the geometry of the collision might truncate that considerably. Again, I'm not claiming expertise here, and the "straight maths" rubric isn't a justification for correctness so much as explaining how I arrived at the number.
- cshimmin 4y ago
  Understood! My point was that, while dimensional analysis almost always works (including for this problem), you have to make sure you are using the right dimensionful quantities. In this case that there are constraints here due to orbital mechanics that were not respected, and hence the 12,000km is way off. To successfully apply DA in this problem, we should start by noting that since we are talking about impact, it is a foregone conclusion that the earth and the asteroid will be in the same place at the same time (your application instead was related to figuring out where earth and asteroid would be in relation to each over at a given time). Once you've specified that they will be at the same place, asking where it lands _on earth_ amounts to asking which part of the earth will be facing the asteroid at that time. Since there is a quoted uncertainty of +- 10min, the range of outcomes is almost entirely defined by the angular distance that the earth with travel in those 20min -- about half a time zone! This gets us much closer to the actual projection from ESA. The actual central location at the nominal time is defined almost entirely by the direction the asteroid is approaching from -- i.e. the relative inclination and phase anomaly of the orbits. So, the rest of the projected range can be chalked up to uncertainty on the geometric fit of the object's orbit based on astrometric observations. Which we can't apply DA to without further information.
  - dredmorbius 4y ago
    Thanks, appreciate the clarifications.

dredmorbius 4y ago

The 12,000 km estimate is straight maths assuming a (fairly typical) relative orbital velocity of ~20,000 km/s for the meteroid, and looking at distance travelled in 10 minutes. Mind that the geometry of the collision might truncate that considerably. Again, I'm not claiming expertise here, and the "straight maths" rubric isn't a justification for correctness so much as explaining how I arrived at the number.

cshimmin 4y ago
Understood! My point was that, while dimensional analysis almost always works (including for this problem), you have to make sure you are using the right dimensionful quantities. In this case that there are constraints here due to orbital mechanics that were not respected, and hence the 12,000km is way off. To successfully apply DA in this problem, we should start by noting that since we are talking about impact, it is a foregone conclusion that the earth and the asteroid will be in the same place at the same time (your application instead was related to figuring out where earth and asteroid would be in relation to each over at a given time). Once you've specified that they will be at the same place, asking where it lands _on earth_ amounts to asking which part of the earth will be facing the asteroid at that time. Since there is a quoted uncertainty of +- 10min, the range of outcomes is almost entirely defined by the angular distance that the earth with travel in those 20min -- about half a time zone! This gets us much closer to the actual projection from ESA. The actual central location at the nominal time is defined almost entirely by the direction the asteroid is approaching from -- i.e. the relative inclination and phase anomaly of the orbits. So, the rest of the projected range can be chalked up to uncertainty on the geometric fit of the object's orbit based on astrometric observations. Which we can't apply DA to without further information.
- dredmorbius 4y ago
  Thanks, appreciate the clarifications.