[VA] SRC #011 - April 1st, 2022 Bizarro Special

[ijabbott]

(04-03-2022 01:25 AM)Valentin Albillo Wrote:  

(04-02-2022 08:31 PM)ijabbott Wrote:  TBH, I don't get why that is not the correct answer!

Because a cube doesn't have spherical symmetry. cf. Wikipedia:

"[...] an object with a spherically symmetric distribution of mass exerts the same gravitational attraction on external bodies as if all the object's mass were concentrated at a point at its center. (This is not generally true for non-spherically-symmetrical bodies.)"

V.

Indeed, splitting each cube into 8 cubelets and summing the gravitation forces between each pair of cubelets (one from Htrae 1 and one from Htrae 2) using the point mass assumption produces an answer that differs from 1 (actually about 1.09217), which means that cubes of uniform density cannot be replaced with point masses.

EDIT: As pointed out to me by Albert Chan, I forgot to resolve the vectors, so my sum is wrong. It should be less than 1.