Exploring General Relativity: Altitudes Where Oblate Earth Approximation Applies

[Gear300]

TL;DR Summary

Questions on GR and oblate Earth.

This is actually two questions. They are

1. In which courses or field work is general relativity taught as method and not philosophy?
2. At which altitudes does the oblate Earth approximation matter? At stealth bomber altitudes? Somewhere between Earth and Moon (in perhaps inertial gyroscope calculations?) ?? (Someone once told me that people should have ground for correcting others that the Earth is not a sphere, so as to not sound annoying.)

 

[Hornbein]

Summary: Questions on GR and oblate Earth.

This is actually two questions. They are

1. In which courses or field work is general relativity taught as method and not philosophy?
2. At which altitudes does the oblate Earth approximation matter? At stealth bomber altitudes? Somewhere between Earth and Moon (in perhaps inertial gyroscope calculations?) ?? (Someone once told me that people should have ground for correcting others that the Earth is not a sphere, so as to not sound annoying.)

General relativity is generally taught as method. I don't know that it has ever been considered a philosophy.

2. I'm not sure but I think it matters for satellites orbiting the Earth.

 

[FactChecker]

There are government models, GRS80 and WGS84, of the shape of the Earth that are standard and often used. I do not know which users really require it or if they are just using them out of an abundance of caution. I know that airplane inertial reference systems use them. Even NOAA, who maintains the models, says this: "Please note that the GRS80 and WGS84 are considered to be the same. Actually, there is a very small difference in the flattening which results in the semi-minor axis, b, being different by 0.0001 meters. There is no known application for which this difference is significant." But that is regarding the difference between the two models. I am sure that many applications would not work well if a spherical Earth was assumed.

 

[Gear300]

Very well. Thanks for the answers.

Gear300

 

[collinsmark]

The Earth's precession is a function of the Earth's oblateness. In simple terms, right now Polaris is the Earth's "North Star," but it wasn't always that way, nor will it always be that way in the future. The Earth's celestial poles gradually rotate in a circle with respect to the stars every 26,000 years or so. This axial "precession" wouldn't happen if the Earth was completely spherical. Scientists have known about Earth's precession to some degree or another for thousands of years, believe it or not. (General relatively [GR] isn't so critical here. You can model it with Newtonian mechanics quite well. But the oblateness is still a key factor when modeling.)

The effects of Earth's oblateness is probably most pronounced in anything dealing with low-Earth-orbit (LEO) satellites. And this is also one application where general relativity (GR) is also critical. For example, GPS, GLONASS, or other global positioning satellite systems absolutely must account for both.

A while ago, I wrote a computer program to track satellites based on their orbital elements (not dissimilar to what heavens-above.com implements). The program does not take GR into account and models orbits as Kepplerian. I still had to model ground locations (i.e., observing locations) based on Earth being a oblate spheroid, not a sphere. Had I modeled Earth as a sphere, it would have caused significant pointing errors. To elaborate, there are several different types of latitude: geocentric latitude and geodetic latitude, being most used. It's often important to distinguish between the two (or any other type). (See more: https://en.wikipedia.org/wiki/Latitude#Auxiliary_latitudes.)

Geodetic latitude $( \phi)$ and geocetric latitude $(\theta)$.

If I'm not mistaken, most maps use geodetic latitude which takes into account the Earth being an ellipsoid. So that's another application where the Earth's oblateness is considered: maps.

 

[Baluncore]

The Earth's equatorial radius is 6378137 m ; The flattening is about 1 in 298.25722 ;
So the pole is about = 21384.685 m below where it would be if the Earth was a sphere with the same equator. That is just over 70,000 feet.

Jet aircraft usually fly at about 30,000 feet, but aircraft must control altitude by air pressure, so they automatically follow the flattened Earth's surface towards the poles.

Early aircraft used magnetic compasses to find the destination region, then used a localiser radio beacon to find the airport. The oblate Earth did not therefore interfere significantly with navigation.

Since GPS became accepted for navigation, those localiser radio beacons have been decommissioned. The WGS84 geoid used by GPS takes into account the flattening, so aircraft no longer need magnetic compasses or precision altimeter QNH corrections on route.

The vertical variation of GPS, and between the WGS84 geoid and sea level can be up to 100 metres, so some form of precision beyond GPS is required for blind landings. Part of that destination accuracy comes from glideslope indicators and the QNH altimeter correction.