Google says Earth's radius is 6371km.

One NASA web site sasy it is 6371.00 km.
https://mobile.arc.nasa.gov/public/iexplore/missions/pages/solarsystem/earthfacts.html

WGS84 has it are 6378.1370 at equator and 6356.7523 to the north pole.

Wikipedia:
https://en.wikipedia.org/wiki/World_Geodetic_System#1984_version

It has a photo that depicts WGS84 with the non-round Earth, as well as a
theoretical route Earth. They get the 6371 by a weighted average of both
with equatorial diameter representing 66% of it and the polar one 33%.

Anyone have an explanation on why equatorial is given twice the weight
as polar? Is that due to shape of Earth, or because it is felt
calculations are more likely for latitudes below roughly 45 (aka USA) ?

And from a NASA or any space business purposes, it it correct to state
that the ellipsoid nature of planet causes precession, and that since
precession makes for real changes in orbit each day, that they need to
factor this in? Or would they use a round Earth model and apply a
precession "constant" ?

I think Marjory Taylor Green should be elected President of USA, she'd
have no problem declaring the Earth to be flat. Think about how much
simpler all distance calculations would be :-) (ok, Orbit become quite
complex around an object shaped like a coin since circular orbits would
in act be highly elliptical, but NASA has scientists who can do the math
, right?

(All this because I am trying to match what Garmin's software calculates
as distance from some 2000 track points and I get to about 318.5km
instead of 319 :-)

Just this Wednesday, JF Mezei explained that ...
> Google says Earth's radius is 6371km.
>
> One NASA web site sasy it is 6371.00 km.
> https://mobile.arc.nasa.gov/public/iexplore/missions/pages/solarsystem/earthfacts.html
>
> WGS84 has it are 6378.1370 at equator and 6356.7523 to the north pole.
>
> Wikipedia:
> https://en.wikipedia.org/wiki/World_Geodetic_System#1984_version
>
> It has a photo that depicts WGS84 with the non-round Earth, as well as a
> theoretical route Earth. They get the 6371 by a weighted average of both
> with equatorial diameter representing 66% of it and the polar one 33%.
>
> Anyone have an explanation on why equatorial is given twice the weight
> as polar? Is that due to shape of Earth, or because it is felt
> calculations are more likely for latitudes below roughly 45 (aka USA) ?

Take a profile of the earth (that is, a 2D projection), and trace the
edge starting at the equator and moving towards the pole. (This is the
same as following a line longitude from the equator to the pole.)
Where does the "radial" distance change most rapidly? Where does it
change more slowly? I think the average distance would be the integral
of dr/d(THETA) from 0 to 90, divided by the path integral from equator
to pole, but I'm definitely feeling rusty here.

> And from a NASA or any space business purposes, it it correct to state
> that the ellipsoid nature of planet causes precession, and that since
> precession makes for real changes in orbit each day, that they need to
> factor this in? Or would they use a round Earth model and apply a
> precession "constant" ?

Isn't orbital precession mostly due to orbital period not being an even
divisor of the earth's rotational period? Geosync orbits don't seem to
precess.

> I think Marjory Taylor Green should be elected President of USA, she'd
> have no problem declaring the Earth to be flat. Think about how much
> simpler all distance calculations would be :-) (ok, Orbit become quite
> complex around an object shaped like a coin since circular orbits would
> in act be highly elliptical, but NASA has scientists who can do the math
> , right?

Just like Canada does.

> (All this because I am trying to match what Garmin's software calculates
> as distance from some 2000 track points and I get to about 318.5km
> instead of 319 :-)

Add up the tolerances of 1999 legs.

/dps

--
But happiness cannot be pursued; it must ensue. One must have a reason
to 'be happy.'"
Viktor Frankl

On Jun/16/2021 at 16:28, JF Mezei wrote :
> Google says Earth's radius is 6371km.
>
> One NASA web site sasy it is 6371.00 km.
> https://mobile.arc.nasa.gov/public/iexplore/missions/pages/solarsystem/earthfacts.html
>
> WGS84 has it are 6378.1370 at equator and 6356.7523 to the north pole.
>
> Wikipedia:
> https://en.wikipedia.org/wiki/World_Geodetic_System#1984_version
>
> It has a photo that depicts WGS84 with the non-round Earth, as well as a
> theoretical route Earth. They get the 6371 by a weighted average of both
> with equatorial diameter representing 66% of it and the polar one 33%.
>
> Anyone have an explanation on why equatorial is given twice the weight
> as polar? Is that due to shape of Earth, or because it is felt
> calculations are more likely for latitudes below roughly 45 (aka USA) ?

Earth's radius is approximately given by the formula R=... in
https://rechneronline.de/earth-radius/

If you integrate that formula over the surface of the Earth you will get
your 2/3 equatorial radius + 1/3 polar radius. It is normal that the
weight of the equatorial radius is bigger than that of the polar radius.
The pole is a point, the equator is a circumference; the area of Earth
within a km of a pole is a little over 6 km^2, the area of Earth that is
within a km of the equator is about 80,000 km^2.

Alain Fournier