# Gravity of Earth combined with centripetal force

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1. Mar 3, 2015

### SpiderET

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.

2. Mar 3, 2015

How?

3. Mar 3, 2015

### SpiderET

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 [Broken] (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 [Broken] 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: May 7, 2017
4. Mar 3, 2015

5. Mar 3, 2015

### SpiderET

It is nice that at least somebody is reacting to my question, but I dont 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.