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Analyzing the Beresheet Impact
Analyzing the Beresheet Impact
Beresheet’s Last Image
Beresheet’s Last Image
This is the last image taken by Beresheet:
Estimated lunar coordinates for corners of this image:
In[]:=
coords=GeoPosition{41.53,20.67},,GeoPosition{42.54,20.23},,GeoPosition{42.01,22.28},,GeoPosition{41.5,22.25},;
Shown with lunar satellite imagery:
In[]:=
GeoGraphics[Style[Polygon[coords],White]]
Out[]=
Diagonal distance across picture:
In[]:=
GeoDistance@@GeoBoundingBox[coords]
Out[]=
Intended Landing Site vs. Impact Site
Intended Landing Site vs. Impact Site
The coordinates of the intended landing site:
In[]:=
intended=GeoPosition{33.03,19.45},;
Coordinates of the actual impact:
In[]:=
actual=GeoPosition{32.5956,19.3496},;
This shows the position of the last picture, together with the intended landing site (green) and the impact site (red):
In[]:=
GeoGraphics[{Style[Polygon[coords],White],GeoMarker[intended,"Color"Green],GeoMarker[actual]}]
Out[]=
50-mile image:
In[]:=
GeoGraphics{GeoMarker[intended,"Color"Green],GeoMarker[actual]},AspectRatio1,GeoRange->
Out[]=
Lightening the image:
In[]:=
GeoGraphics{GeoMarker[intended,"Color"Green],GeoMarker[actual]},GeoBackgroundGeoStyling["Satellite",GeoStylingImageFunctionImageAdjust],AspectRatio1,GeoRange->
Out[]=
Relief map:
10-mile image:
Relief:
3D visualization (with exaggerated height scale):
Impact Site
Impact Site
Zooming out from the impact site:
Corresponding position on Earth:
Direction of Travel
Direction of Travel
Assuming lander travels in a straight line from its last image to the impact site.
Center of last image:
Direction of travel:
Motion in the last second:
Image of motion:
Image of Impact Site
Image of Impact Site
Import images:
Inpaint to remove captioning:
Find the difference between the images:
Highlight the difference on the original image:
Smoothed difference:
Smoothed difference:
Find the pixel center of the smoothed difference:
Trimmed images:
Zoom apply a color map to the difference:
Make a Super-resolution Image
Make a Super-resolution Image
Neural net:
Define an evaluation function that prepares the image for this net:
Generate the upsampled image:
Highlight to generate the final image:
Make a comparison of images:
Telemetry Analysis
Telemetry Analysis
Dataset based on livestream (altitude is in meters, speeds are in meters per second):
Convert dates to time until impact:
Velocity
Velocity
Plot vertical speed:
Plot horizontal speed:
Find linear fit for vertical speed:
Find linear fit for horizontal speed:
Mean vertical acceleration:
Compare with lunar gravity due to acceleration:
Trajectory Plot
Trajectory Plot
Compute horizontal position from integrating the horizontal speed values:
Altitude
Altitude
Plot altitude:
Compare given altitudes with altitudes from integrating the vertical speeds:
The last graphic shows good agreement of the two datasets until about 60 sec before the impact.
This means between 60 sec and 15 sec before the impact some additional acceleration must have acted on the probe.
This means between 60 sec and 15 sec before the impact some additional acceleration must have acted on the probe.
Determine vertical accelerations
Determine vertical accelerations
The data fall naturally into two groups: the first 150 seconds and the last 10 seconds (with a point in the middle that is difficult to assign):
Relatively low-order fits seem to approximate the points well:
The corresponding vertical speeds:
The corresponding vertical accelerations: