The discussion revolves around calculating the gravitational force on a small mass located at the center of a spherical cavity within a larger spherical planet. The planet has a defined radius and density, while the cavity has a specific radius and is positioned at a certain distance from the planet's center.
There are multiple attempts to derive the gravitational force, with some participants expressing confusion over the results and seeking clarification on the methods used. Guidance has been offered regarding the treatment of the cavity and the gravitational effects of the surrounding mass.
Participants are required to show their working and provide relevant equations as per forum rules. There is an emphasis on understanding the gravitational field within spherical shells and the implications of the cavity on the overall gravitational force.
As per forum rules, you should quote any relevant standard equations of which you are aware and must show some attempt at a solution. If totally stuck, you should at least be able to provide some thoughts.anshuman3105 said:A large spherical planet of radius R made of a material of density d, has a spherical cavity of radius R/2, with center of cavity a distance R/2 from the centre of the planet. Find the gravitational Force on a small mass m at the centre of the cavity
I get ##\frac 23 G\pi d r m## (I'm guessing the "/2" in what you posted is a typo).anshuman3105 said:using the formula F = Gm1m2/r^2, i am getting 16Gpidrm/3 but the solution is 2Gpidrm/2
That formula is essentially for point masses. It also works if one mass is a uniform spherical shell (or assembly of concentric uniform spherical shells) and the other (point) mass is outside all the shells.anshuman3105 said:I used Gm1m2/r^2
http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/sphshell2.htmlanshuman3105 said:Can you show it to me the solved part..?