Gravity of Earth combined with centripetal force

In summary, the equator has weaker gravity because of the effects of Earth's rotation and the distance between the surface and the center of the Earth on the equator. A satellite that would orbit Earth in a perfect circle from pole to pole would still measure different gravity on different parts of its orbit because of the small variations in gravity that are caused by things like mountains and oceans.
  • #1
SpiderET
82
4
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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  • #2
SpiderET said:
satellite would be measuring gravity
How?
 
  • #3
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
 
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  • #5
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.
 
  • #7

1. What is the relationship between gravity and centripetal force?

The gravity of Earth combined with centripetal force creates the centripetal acceleration that keeps objects in orbit around the Earth. In other words, gravity provides the force that pulls objects towards the center of the Earth, while centripetal force provides the acceleration necessary to keep them in orbit.

2. How does the strength of gravity and centripetal force change with distance from the Earth?

The strength of gravity and centripetal force both decrease as distance from the Earth increases. This is because the force of gravity is inversely proportional to the square of the distance between two objects, while the centripetal acceleration is directly proportional to the distance. Therefore, as objects move farther away from the Earth, they experience a weaker gravitational pull and require less centripetal force to maintain their orbit.

3. How does the mass of the Earth affect the gravity and centripetal force?

The mass of the Earth is directly proportional to both the gravity and centripetal force it exerts on objects. This means that the larger the mass of the Earth, the stronger its gravitational pull and the more centripetal acceleration is required to keep objects in orbit.

4. Can the gravity of Earth and centripetal force be overcome?

Yes, the gravity of Earth and centripetal force can be overcome by an object's own inertia or by external forces, such as a rocket's thrust. This is how spacecrafts are able to escape the Earth's orbit and travel to other planets.

5. How do gravity and centripetal force affect the shape of Earth's orbit around the Sun?

Gravity and centripetal force work together to create an elliptical orbit for the Earth around the Sun. The force of gravity pulls the Earth towards the center of the Sun, while the centripetal force from its orbital motion keeps it from falling into the Sun. This results in a nearly circular orbit with a slight elliptical shape due to the varying distances between the Earth and the Sun throughout its orbit.

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