From your question, you are looking for weight in grams.
in physics weight are united with Newton, not in grams. but in real world sometimes people call mass as weight.
Quote from: lili song on July 24, 2015, 08:00:46 AM
Centripetal_force 1 = centripetal_force 2
84,000 g * (464 m/2)^2 / 6,371,000 m = mass * (463.2 m/s)^2 / 6,371,000 m
mass = 84,290.4 g
and u claimed this answer as the winner. So the answer you are looking is mass not weight.
from this https://en.wikipedia.org/wiki/Weight is the description of weight physics
and this https://en.wikipedia.org/wiki/Mass is the description of mass in physics
if you are reading it carefully, in paragraph 2 of description of mass you will read "An object on the Moon would weigh less than it would on Earth because of the lower gravity, but it would still have the same mass".
so whenever you are, whatever the velocity or radius of the planet
your mass will still same, but your weight will change.
and I want to straighten our concept about centripetal force.
from lili song answer centripetal force 1 = centripetal force 2.
This is completely wrong! As far as i know centripetal force change as the related variable change.
Sorry, lili, i did not mean to blame you.
this for the reference of the centripetal force description http://www.regentsprep.org/regents/physics/phys06/bcentrif/default.htm
So, the answer should still same mass(weight) 84,000 grams
As ndnhc pointed out, and as I already said in my answer, I gave it in mass equivalent.
What do I mean by mass equivalent?
The weight is 826.59 N, but it is the same weight of an object with mass of 84,289.46 grams on the surface of the earth.
OP asked for it in grams, so I gave it in mass equivalent.
Read my answer, it is different from lili's answer, but straightens out a lot of things he said, better explaining them.
He has a valid reason for being unable to explain it too, as English is not his first language either.