Asteroid Probabilities. How are they calculated?

[rogerinnh]

A recent news article states "Astronomers are monitoring an asteroid named Apophis, which has a 1 in 45,000 chance of striking Earth on April 13, 2036."<br />How can they possibly calculate a probability of it hitting Earth? What are the variables? What's the equation?

 

[MeteorWayne]

The variables are basically position measurement errors.<br />There is always some error in any position measurement. So, when an orbit is calculated from these measurements, with each one having an error, there is a range of possible solutions. In general you wind up with an ellipse of possible positions and times.<br /><br />In addition, there are other factors such as the variable strength solar wind, radiative factos such as the Yarkofsky and Poymtimg-Robertson effects causing a change in velocity.<br /><br />So you look at all the possible solutions, and figure out how many end with a bang <img src="/images/icons/smile.gif" /> <div class="Discussion_UserSignature"> <p><font color="#000080"><em><font color="#000000">But the Krell forgot one thing John. Monsters. Monsters from the Id.</font></em> </font></p><p><font color="#000080">I really, really, really, really miss the "first unread post" function</font><font color="#000080"> </font></p> </div>

 

[tony873004]

<i>"In addition, there are other factors such as the variable strength solar wind, radiative factos such as the Yarkofsky and Poymtimg-Robertson effects causing a change in velocity."</i><br /><br />I've never heard of the Poymtimg-Robertson effect. Do you have a link? I tried Googling it with no luck. Perhaps its spelled differently.<br /><br />I believe the Yarkovsky effect is negligable over short periods of time such as decades. Rather, it is used to explain long-term evolution of the orbits of small asteriods. The rotation of the asteriod, its mass, and its albedo must be known to compute the Yarkovsky effect.<br /><br />Solar light pressure is much more significant than the solar wind, but it tends to be rather constant. I believe both are negligable for an asteroid over a timespan of a few decades. These forces only have significant effects on very small particles such as the dust in a comet's tail. Over the course of an orbit, any amount you are pushed away from the Sun will be balanced by the push in the opposite direction you receive half an orbit later. That's why solar radiation doesn't cause objects to spiral outward from the Sun.<br /><br />JPL uses n-body integration to predict the future positions of asteroids. Their n-body routines account for non-spherical gravity and general relativity, which I believe are the most dominant influences after simple Newtonian propogation (which by itself works quite well). <br /><br />So in this case, they've computed the keyhole, which is a small area a few hundred meters wide that if the asteroid passes through it in its 2029 encounter with Earth, it will return to strike Earth in 2036. Then it's simply a matter of predicting the odds of it passing through the keyhole in 2029. They probably put a gaussian curve centered on their 2029 prediction and see how far from the mean the keyhole is... just my guess as to how they do it...

 

[MeteorWayne]

SOrry about typo; it's Poynting-Robertson. Not particularly relevant here since it's so small it produces velocity changes on meteoroid sized particles.<br />So negligible is a good word for that.<br /><br />Certainly the Yarkofsky effect is small, but depending on the rotation rate and radiative properties of the objects, it does accumulate, which addresses the question of how probabilities are determined.<br /><br />Calculations also include the top several hundred most massive solar system bodies, but of course not all, and more are discovered all the time. The net result is, AFAIK, a Gaussian curve centered on the best estimated position as you said.<br /><br /><br />The odds are not as precise as those that Mr Spock would deliver, but they're in the ballpark.<br /> <div class="Discussion_UserSignature"> <p><font color="#000080"><em><font color="#000000">But the Krell forgot one thing John. Monsters. Monsters from the Id.</font></em> </font></p><p><font color="#000080">I really, really, really, really miss the "first unread post" function</font><font color="#000080"> </font></p> </div>

 

[doubletruncation]

Just to add to the excellent answers so far - there is a really nice animation showing how the orbit of the asteroid gets narrowed down over time at:<br />http://spaceguard.esa.int/NScience/neo/neo-how/mea-orbit.htm<br /> <div class="Discussion_UserSignature"> </div>

 

[MeteorWayne]

Nice, thanx!! <div class="Discussion_UserSignature"> <p><font color="#000080"><em><font color="#000000">But the Krell forgot one thing John. Monsters. Monsters from the Id.</font></em> </font></p><p><font color="#000080">I really, really, really, really miss the "first unread post" function</font><font color="#000080"> </font></p> </div>