Bill Nye: An asteroid will hit Earth

Apophis Risk Assessment Updated    Apophis Earth Impact Risk Summary

Linearized Acceleration Fields

The linearized relative acceleration used to check the least squares fit of the 2012 DA14 observations was evaluated for a neighborhood centered on the Earth's position. One can derive the formula as follows,

GM is the gravitational constant for the Sun, X_E the Earth's position relative to the Sun and X is the position relative to the Earth where one wants to evaluate the acceleration. Beyond 500 R_E the error in the linear approximation is quite noticable. It might be better if one used the methods above to derive the linearized acceleration for a neighborhood about the position of the object at X_o.

The constraint that the two accelerations be the same is equivalent to requiring that the object follow a path determined by Newton's law, F=ma. The eigenvectors were used to search the neighborhood of the object for the point of best correspondence. All the eigenvectors can be used but the ones with smaller eignevalues tend to produce larger corrections. In the example given the change in both the position and velocity were along the line of sight.

Feb 20th MSL Press Telecon - Drilled Rock Samples

src: nasajpl
JPL had another MSL teleconference last Wed discussing the first rock drilling tests on Mars. The location was tagged "Drill" and the tailings that it produced helped remove some of the Earth's contaminants. The rock appears to be sedimentary based on its fine grained clay and silt composition. The chemical analysis still remains to be done.
telecon images  msl images  press release

A Reality Check For the Tracking Fit

The least squares fit for the tracking polynomial was in very good agreement with the observations but there was some disagreement between the gravitational acceleration and the fit acceleration. An examination of the eigenvalues for the matrix, Σ, revealed that there were some directions which were insensitive to changes.

These directions were used to adjust the fit to bring the two accelerations into better agreement. At the distances involved a linear approximation could be made to relative acceleration of 2012 DA14 to the Earth and a new set of polynomial coefficients was computed. An average value for the direction of the Sun, e_S, was used. I in the expression is the 3D identity matrix.

The relative deviation between the two accelerations was much smaller and the time at which the error was a minimum was used to compute a position and velocity for 2012 DA14.

These values for position and velocity could be used to compute the path of the asteroid and get the details of the close approach.

Some accuracy for the fit was sacrificed to produce a better correspondence with reality.

Russian Meteor

The meteor that landed near Chelyabinsk, Russia on Feb 15, 2013 03:20:26 UT (09:20:26 YEKT, 15.13919 UT) definitely wasn't 2012 DA14 which was observed later on the day at 15.875036 UT. In the 1951 movie, When Worlds Collide, the world is struck by a rogue planet, Bellus, which had a smaller companion, Zyra. The lesson that might be drawn from this is that even though the asteroid that we are focused on may miss the Earth another object can still strike it.

Amateur Astronomy, NEOs and Social Media

What should be the motivation for tracking NEOs on social media? As with many other things there is the potential for abuse of power. The uncertainty in predicting an Earth impact may expose amateurs to civil penalties if they post their information. Even civil authorities can be exposed to risk when making public statements that can be misinterpreted as the l'Aquila earthquake trial has recently brought to light. I don't think that amateurs or professionals should be restricted to just posting observations. The data needs to be processed to extract the three dimensional information contained within it. But observational and computational errors contribute to the uncertainty about subsequent events. Amateurs work out of a need to know and a desire to put their skills to the test. When posting results it may be best to culture a spirit of public service and step forward to help in the way that amateur radio operators do when there is a public emergency.

Close Approach Calculation Sensitive to Changes in Parameters Used

The calculation of the point of closest approach appears to be sensitive to small changes in the parameters used. This result used a step size of 0.0005 days and averaged the acceleration over the interval. A close approach point near the South Pole makes the positions difficult to determine precisely.

2012 DA14 on NASA JPL Live

src: nasajpl2

2012 DA14 Close Approach Details

I just got through recalculating today's close approach details for 2012 DA14. I used the fitted position and velocity of the asteroid on Feb 9.0 and subtracted the values for the motion of the Earth's center relative to the Earth-Moon barycenter to get the position and velocity relative to the Earth's center at that time. The gravitational attraction of the Sun, Earth and Moon were used to compute 2013 DA14's trajectory. Since the Earth and Moon are also accelerating due to the Sun's attraction the difference between the asteroid's acceleration and the Earth's was used to get the acceleration relative to the Earth. My computed time for close approach is Feb 15, 2013 23:46 UT (15:46 PST) at a distance from the Earth's center of 6.477 Earth radii. The JPL ephemeris gave a time of 19:20 UT and a radial distance of 5.492 Earth radii.

Supplemental (Feb 15): 2012 DA14 may not be visible at the time of close approach since it is likely to be passing through the Earth's shadow during the middle of the night.

2012 DA14 Track Anaglyph

To get a better picture of what 2012 DA14 is doing in 3D I used the previous set of observations and the corresponding fit to make an anaglyph. The horizontal axis is the RA in degrees and the vertical axis is the Decl in degrees so that both scales have the same unit of measurement. The separation of our "eyes" is the diameter of the Earth and our "vista point" is the Earth-Moon barycenter. The time span ranges from Feb 6.388 to Feb 11.496 and points further away occur earlier in time.

red-cyan 3D glasses required for viewing

Cubic Fit to the 2012 DA14 Observations

There was enough data to get a cubic fit to the 2012 DA14 observations. The results are shown in the image below. The positions are again given relative to the Earth-Moon barycenter.

The extrapolated close approach is Feb 15, 2013 19:54 UT.  There was little change in the minimum distance.

The Earth's gravitational attraction should change the results some.

2012 DA14 Tracking Update

 

  The MPC 2012 DA14 obsersvations for Feb 2013 are now showing signs of acceleration.

 

 

  The latest least squares fit for position, velocity and acceleration has an rms angular deviation of about 3 asec. I used MPC's longitude and parallax constants for the observatories for the first time.

 

 

  The fit now indicates a close approach at Feb 15, 2013 11:30 UT with a radial distance from the center of the Earth of 7.3 Earth radii. There may be more signs of acceleration as the asteroid approaches. The formula for the fitted position is X=X₀+V₀Δt+A₀Δt² with Δt=t-t₀ and t₀=6.388. Distance was measured relative to the Earth-Moon barycenter.

 

 

Tracking Results For 2012 DA14

 

  Some observations are now coming in at the Minor Planet Center for 2012 DA14. There is some deviation from where the 2012 predictions say 2012 DA14 will be. I used the observations from Feb 6 through Feb 8 to get an estimated position and velocity for the asteroid. A simple projection along the direction of the velocity indicates that the close approach will occur in early March.

 

 

  I merged the gravitational attraction of the Earth and Moon into a single body to get a better estimate of the close approach.

 

 

  This is also a rough estimate but it doesn't appear that 2012 DA14 will approach as closely as predicted a year ago. My fit wasn't particularly good with the asteroid at about 600 Earth radii away. The uncertainty in angular direction is magnified by this distance to increase the uncertainty in the asteroid's position. The uncertainty in the velocity also contributes to the uncertainty in the distance of close approach. One needs to take the Earth's motion and the Sun's gravitational field into account to get a better path for the asteroid's motion. The estimated position and velocity above are given relative to the Earth's center.