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Question
How does one utilize the 2/5 in the formula for calculating a planet's sphere of influence. I found the formula at http://en.wikipedia.org/wiki/Sphere_of_influence_(Astrodyamics) I understand a, (m/M) but not how to apply the 2/5 above and to the right of the (m/M). 9.27 e 8 meters is listed as the Earth's sphere of influence but it seems neither I nor my coworkers understand the 2/5 part of the formula.

Answer
For the Earth, specifically, the Hill sphere is more accurately what you want.  http://en.wikipedia.org/wiki/Hill_sphere  It's also better derived, but it's an approximation.  It basically can be approximated at a minimum by the radius of the L1 point of the Earth orbiting the Sun (see here: http://en.wikipedia.org/wiki/Lagrangian_point ).  There are many descriptors for it, but the wikipedia is accurate.  The technical solution is indeed (read the details) the solution to a quintic function, so I can see why using 2/5=0.4 as an approximation will get you close...but someone on the Hill sphere page and the Lagrangian point page gave the perhaps more accurate approximation of R(m/3M)^1/3.  Keep in mind that the Hill sphere is not a sphere, but rather an oblate spheroid with a complex and asymmetric shape in three dimensions.  This is especially true for the Earth, with our relatively large moon.  These are approximations for a kinda-spherical volume of space which changes as the Earth orbits the Sun.

Excellent question, by the way.

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Dr. Stephen O. Nelson

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I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

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I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

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Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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