Gravity of Earth combined with centripetal force

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Discussion Overview

The discussion revolves around the effects of Earth's gravity and centripetal force on satellites, particularly focusing on whether a satellite in a polar orbit would measure consistent gravitational force throughout its path. Participants explore the implications of Earth's rotation and shape on gravitational measurements, as well as referencing past experiments like Gravity Probe B and GRACE.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that gravity is weaker at the equator due to the combination of centripetal force from Earth's rotation and the equatorial bulge.
  • Another participant questions how a satellite would measure gravity, prompting a discussion on measurement techniques.
  • A participant describes the GRACE satellite's method of measuring gravity anomalies through precise distance measurements and GPS data.
  • There is a reference to Gravity Probe B, with a participant noting its orbit is not circular and expressing uncertainty about its data accessibility.
  • One participant expresses a desire for more sophisticated answers and acknowledges limitations in their own knowledge regarding GRACE and Gravity Probe B.
  • Links to external resources are shared to provide additional context and information on the discussed experiments.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the effects of centripetal force on gravitational measurements for satellites. There are multiple viewpoints on the relevance and applicability of past experiments like GRACE and Gravity Probe B, with some participants expressing uncertainty about their findings.

Contextual Notes

Participants acknowledge that Earth's shape and rotation introduce complexities in gravitational measurements, but the discussion remains open-ended regarding the specific impacts on satellites in polar orbits.

SpiderET
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Gravity is weaker on equator. What I know, this effect is due to combination of two factors:
1. Earth is rotating with surface speed 450 m/s on equator and this is causing centripetal force which is decreasing gravity.
2. Earth is flattered on poles, so that means that there is longer distance between surface and center of Earth on equator.

So my question is if there were a satellite which would be orbiting Earth in perfect circle (with the same distance from Earth center) from pole to pole and if this satellite would be measuring gravity of Earth, would it measure the same gravity on whole orbit?
I know, that Earth is not perfect object and there are small differences in gravity depeding on example of mountains and oceans, but apart from these small influences, would be gravity the same?
Or does this equator centripetal force have some effect on orbiting satellites?

Was there any real life experiment, which measured something similar? For example I know that Gravity probe B was orbiting from pole to pole, but what I know it has somehow automatically compensated measured gravity depending on longitude.
 
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SpiderET said:
satellite would be measuring gravity
How?
 
A.T. said:
How?

For example like GRACE:
By measuring the constantly changing distance between the two satellites and combining that data with precise positioning measurements from https://www.physicsforums.com/wiki/Global_Positioning_System (GPS) instruments, scientists can construct a detailed map of Earth's gravity anomalies.
The two satellites (nicknamed "Tom" and "Jerry") constantly maintain a two-way microwave-ranging link between them. Fine distance measurements are made by comparing frequency shifts of the link. As a cross-check, the vehicles measure their own movements using accelerometers. All of this information is then downloaded to ground stations. To establish baseline positions and fulfill housekeeping functions, the satellites also use star cameras, magnetometers, and GPS receivers. The GRACE vehicles also have https://www.physicsforums.com/wiki/Corner_reflector to enable laser ranging from ground stations, bridging the range between spacecraft positions and Doppler ranges.

http://en.wikipedia.org/wiki/Gravity_Recovery_and_Climate_Experiment
 
Last edited by a moderator:
A.T. said:
I guess you have answered your own question then.

It is nice that at least somebody is reacting to my question, but I don't deny that I would await some more sophisticated answer.
GRACE is similar, but not perfect and I have not the sufficient knowledge or access to GRACE data to answer the questions I have written in this thread.
GRACE has not circular orbit:
http://www.csr.utexas.edu/grace/gallery/animations/orbit/

Also Gravity probe B is similar, but not the same and I also have not the sufficient knowledge or access to its data.

I was hoping that somebody here will know more about this topic than me.
 

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