Quote of the Day
We live in a society exquisitely dependent on science and technology, in which hardly anyone knows anything about science and technology.
— Carl Sagan
Introduction
Figure 1: Philae Lander.
I have been following the Rosetta mission for years and I have been completely captivated by the Philae probe (Figure 1) landing on the surface of the comet C67P (Figure 2). In addition to watching the television coverage of the landing, I have been reading all the articles I could find. Most of the articles I have read quote information from the ESA website. There is quite a bit of information available on technical details like the battery capacity, lander mass, and power usage.
Figure 2: Rosetta Image of Comet_67P (Wikipedia).
In these articles, I have also seen a number of estimates for the weight of the Philae lander on comet 67P (here - equivalent to 1 gram of force on Earth, or here - 0.04 ounces). Let's do an approximate calculation of Philae's weight ourselves. I will use the same approach as described here for determining the acceleration due to gravity of the Earth, but I will use the comet's mass and the lander's distance from the "center" of the comet.
Analysis
Basic Parameters
I need a few pieces of information to estimate the weight of the Philae lander on comet 67P.
- Mass of the comet 67P: MC67P=1x1013 kg (Wikipedia)
- Mass of Philae lander: MProbe=100 kg (Wikipedia)
- Distance of the Philae lander from the centroid of the comet 67P: RC67 = 8057 feet (my estimate shown in Figure 3).
I grabbed the following image from the web and drew a line on it (blue) from my guess for the centroid of comet 67P to the lander site. I determined the range represented by the blue line by comparing it with the 9500 foot line on the original drawing.
Figure 2: My Centroid Distance Estimate.
Calculations
Figure 3 summarizes my weight calculations.
Figure 3: Philae Weight Calculation on Comet C67P.
I computed a weight of about 1/25th of ounce or about the weight of a gram mass on Earth.
Conclusion
I have verified the weight estimate of 1/25th of an ounce that I have read in several publications. I can see why ESA tried to use harpoons and screw-type landing feet to hold Philae on the surface – there is not much gravitational force to hold the probe down on the surface.