Gravity and Radius of the earth problem

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Homework Help Overview

The discussion revolves around a problem involving the measurement of gravity on different floors of a building using a gravometer, with the aim of calculating the radius of the Earth. The original poster mentions the challenge of accounting for the changing mass below as they move between floors, noting that the distance between floors is 0.5m, later corrected to 5m.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the accuracy of the floor height measurement and discussing how to estimate the impact of the mass below on gravity readings. There is a suggestion to calculate an upper bound on the effect of the mass change.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and raising questions about the assumptions made regarding floor height and mass distribution. Some guidance has been offered regarding estimating the mass per floor to assess its impact on the gravity measurements.

Contextual Notes

There is a correction regarding the height of each floor, which may affect the calculations. The original poster's initial radius estimate of 6500km is noted, but there is concern about the accuracy due to not accounting for the changing mass below.

J.Sterling47
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Homework Statement


Hey guys, I have a problem where we measured the gravity on separate floors of a building using a gravometer. It gave us values in mgals. So each floor has a distance of 0.5m. How do we take this into account as we move up and down the floors? As we move up, there's and increase of mass below us and vice versa as we go down. The goal is to calculate the radius of the Earth using this method.

Homework Equations


dg/g = -2(dr/r) where dg is the change in gravity per floor and dr is the height of each floor. We got the radius to be close at about 6500km, but without taking into account the changing of the mass below.

The Attempt at a Solution


Don't really know where to start
 
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J.Sterling47 said:
So each floor has a distance of 0.5m.
You sure about that?
 
DaveC426913 said:
You sure about that?
Yeah sorry it was supposed to be 5m. I converted it wrong but yea
 
J.Sterling47 said:
We got the radius to be close at about 6500km, but without taking into account the changing of the mass below.
If you are concerned about that, the first thing is to get an upper bound on how much difference that will make. Estimate the mass per floor of the building. Be generous. Likewise, maximise the effect by assuming all that extra mass is only one floor below (for simplicity). How much difference will that make to your answer?
 

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