If you search for questions like Do we weigh more at Death Valley than on top of Mount Everest and if we do would it be from gravity or from atmospheric pressure? They use use a sphere of radius. But if we are pulled in the direction of matter… Like there is more mass in a cone below me pulling on me on the top of a moutain than at sea level.
The mass of the mountain in relation to the mass of the Earth is so infinitesimally small as to be negligible when calculating your weight. The Moon overhead probably exerts more gravitational pull on you than the mountain.
There is a great deal more mass in the (pretty nearly) spherical Earth pulling me than in the mountain below me.
Even if you take into account that the gravitational force varies as the inverse square of the distance, all of that close-by mountain mass makes hardly any difference to the truly humongous quantity of mass represented by the earth. The effect of a mountain is enouigh (as Everest and the Great Arc surveyors found) to perturb your plumbline out of true, but if you were sent into space with a mountain, it’s gravitational attraction wouldn’t hold you to it. The gravitational attraction of the Earth keeps you and the air you breathe tethered by gravity.
Sure it would. Just very, very, very weakly. Just don’t fart.
Never fart in a EVA suit. Really.
It is much harder to do the calculation by integrating in three dimensons and even taking into account the oblate elipsoidal shape of the Earth. I have done it, in a course on mechanics, but it was quite the job, as I’m no mathematician.