Exploring the Oblate Sphereoid of Earth: A Farm Boy's Perspective

[Robust]

Being essentially a farm boy I till, plant and cross-breed in strict accordance with that angle of incidence as coincident with the diurnal arc of the sun. Determined from this and considering the dimensions of Earth to include the uppermost limit of its atmosphere, I find it to be the shape of an oblate sphereoid with the diameter of its E/W dimension to be greater than that of the N/S dimension by a figure of 1.001129 ad infinitum. I would like to know how that figure might compare with the academic findings - if you will, please.

 

[Ravenlock]

I get 1.0033

 

[Integral]

Being essentially a farm boy I till, plant and cross-breed in strict accordance with that angle of incidence as coincident with the diurnal arc of the sun. Determined from this and considering the dimensions of Earth to include the uppermost limit of its atmosphere, I find it to be the shape of an oblate sphereoid with the diameter of its E/W dimension to be greater than that of the N/S dimension by a figure of 1.001129 ad infinitum. I would like to know how that figure might compare with the academic findings - if you will, please.

No physical measurement claims an infinite number of digits as you seem to. If you were to post a reasonable guess at your errors, which limit the number of meaningful digits you might find that your result is pretty meaningless.

 

[Robust]

No physical measurement claims an infinite number of digits as you seem to. If you were to post a reasonable guess at your errors, which limit the number of meaningful digits you might find that your result is pretty meaningless.

Hardly meaninless, Integral, when observing what is derived (on the stalk).. But what I'm asking is how does this figure of oblateness compare with what is assumed to be a measure of Earth's oblateness?

 

[Robust]

I get 1.0033

Interesting, Ravenlock! How do yiou derive that figure?

 

[Integral]

Hardly meaninless, Integral, when observing what is derived (on the stalk).. But what I'm asking is how does this figure of oblateness compare with what is assumed to be a measure of Earth's oblateness?

Without knowledge of your errors your number has no signifance.

 

[Integral]

According to my CRC Handbook of Chemistry and Physics (53rd Edition)
the Earth's oblateness is given as .003393 +/- 0.000097

a = equatorial radius = 6378.533 +/- .437 km
c = polar radius= 6356.912 +/-.437 km

$$\epsilon = \frac {a -c} a$$

I am not sure how this relates to your number as I have no idea what your number is.

 

[Robust]

According to my CRC Handbook of Chemistry and Physics (53rd Edition)
the Earth's oblateness is given as .003393 +/- 0.000097

a = equatorial radius = 6378.533 +/- .437 km
c = polar radius= 6356.912 +/-.437 km

$$\epsilon = \frac {a -c} a$$

I am not sure how this relates to your number as I have no idea what your number is.

Integral, interesting that your number gives the oblateness as .0033 and that given by Ravenlock as 1.0033. In the meantime I have to stay with my figure of 1.00112915039 until given the time and headspace to figure it further. Thanks much.

 

[Ravenlock]

Robust, both Integral and my numbers are correct we just obtained the answers differently. Like Integral said, without knowing what your number means, how can we give you numbers for comparison?

I assumed from reading your original post, that you calculated the equatorial radius to be 1.001129 times larger than the polar radius. So I went by that assumption and I came up with the number 1.0033. Is that what you were looking for?

 

[Robust]

Robust, both Integral and my numbers are correct we just obtained the answers differently. Like Integral said, without knowing what your number means, how can we give you numbers for comparison?

I assumed from reading your original post, that you calculated the equatorial radius to be 1.001129 times larger than the polar radius. So I went by that assumption and I came up with the number 1.0033. Is that what you were looking for?

Thanks`Ravenlock. My number is strictly speculative on my part. I wish to know what the determined vaiiation is between the polar and equatorial dimensions.

 

[Integral]

I gave you the numbers for equatorial and polar radius and my source above. I also provided you with the formal definition of oblateness. What more do you want?

 

[pervect]

There's one more useful to say. Because the atmospheric density changes with altitude, there are some important optical effects. Light does not travel in a straight line because it is refracted by changes in density in the atmosphere. This effect is important enough that it has to be accounted for in surveying.

http://mintaka.sdsu.edu/GF/explain/atmos_refr/bending.html does some calculations for horizontal ray bending, which is the worst case. (Vertical rays go straight up and don't bend at all).

I have to agree that it's very unclear what the poster is calculating, but it seems to me to be extremely likely that he is not taking into account atmospheric refraction.

 

[Robust]

There's one more useful to say. Because the atmospheric density changes with altitude, there are some important optical effects. Light does not travel in a straight line because it is refracted by changes in density in the atmosphere. This effect is important enough that it has to be accounted for in surveying.

http://mintaka.sdsu.edu/GF/explain/atmos_refr/bending.html does some calculations for horizontal ray bending, which is the worst case. (Vertical rays go straight up and don't bend at all).

I have to agree that it's very unclear what the poster is calculating, but it seems to me to be extremely likely that he is not taking into account atmospheric refraction.

Excellent, Pervect...exactly the kind of info I'm looking for. Don't know what I'll do with it yet, but the concept of atmospheric refraction makes a whole new ballgame for me. As the poet advises, I do start with the sun.

 

[tony873004]

For what it's worth, here's all of Earth's specs as given by JPL NASA. And it agrees with Ingegrel's numbers. If JPL/Nasa don't have it right, our space missions would fail miserably.

PHYSICAL PROPERTIES:
Mean radius, km = 6371.01+-0.02 Mass, 10^24 kg = 5.9736
Equ. radius, km = 6378.136 Mass layers:
Polar axis, km = 6356.752 Atmos = 5.1 x 10^18 kg
Flattening = 1/298.257 oceans = 1.4 x 10^21 kg
Density, gm cm^-3 = 5.515 crust = 2.6 x 10^22 kg
J2 (GEM T2, 1990) = 0.0010826265 mantle = 4.043 x 10^24 kg
gp, m s^-2 (polar) = 9.8321863685 outer core = 1.835 x 10^24 kg
ge, m s^-2 (equatorial) = 9.7803267715 inner core = 9.675 x 10^22 kg
go, m s^-2 = 9.82022 Fluid core rad = 3480 km
GM, km^3 s^-2 = 398600.440 Inner core rad = 1215 km
Mean rot. rate, rad s^-1 = 7.292115*10^-5 Surface Area:
Sidereal period, hr = 23.93419 land = 1.48 x 10^8 km
Mean solar day, days = 1.002738 sea = 3.62 x 10^8 km
Moment of inertia = 0.3308 Love no., k2 = 0.299
Mean Temperature, K = 270 Atm. pressure = 1.0 bar
Solar constant, W/m^2 = 1367.6 Vis. mag. V(1,0) = -3.86
Volume, 10^10 km^3 = 108.321 Geometric albedo = 0.367

DYNAMICAL CHARACTERISTICS:
Obliquity to orbit, deg = 23.45 Sidereal period = 1.0000174 yrs
Orbit velocity, km s^-1 = 29.7859 Sidereal period = 365.25636 days
Mean daily motion, n = 0.9856474 deg/d Escape velocity = 11.186 km s^-2
Hill's sphere radius = 234.9 Magnetic moment = 0.61 gauss Rp^3

 

[Robust]

Tony, good on you!...precisely what I was hoping for