doubly depressed cubic

[AntonioLao]

If division of vectors is defined and applied to their norms then Newton’s universal law of gravitation becomes a doubly depressed cubic. Recall that the general cubic is x+ax+bx+c=0. For depressed cubic, ax=0, while for doubly depressed, c=0 also, the reduced form becomes x+bx=0 where b is a positive or nagative numerical constant.

Before Einstein formulated his classical nonlinear tensor field equations of general relativity, the point-particle or point-mass Newton’s scalar equation is F=-GMm/r. The negative sign signifies attractive conservative central forces. However, modern vector notations is F=-GMmu/r where G is the constant of gravitation, M is the big mass, m is the small mass, u is the unit vector, r is the distance between the 2 masses. The unit vector is simply the ratio of a finite vector r with its norm |r| or u=r/|r|. Rearranged, r+GMm(r/|r|F)=0. If the scalar r has unit of length then r has unit of volume in 3-space. It is implied that for sun-planet or earth-NASA systems, M>>m. Finally, in real domain, the absolute value of (r/|r|F) is simply r/F or in the complex domain as modulus. The r is the independent variable and F could be the free parameter of unit forces equivalent to the cosmological constant (L) of general relativity. The general form is r+br=0 where b=GMm/F. Its exact solutions are r=0, and r=±√-b for positive b while for negative b, the solutions are r=0 and r=±√b. These imply pure real and pure imaginary solutions. Nonetheless, the one and only real solution is r=0, which is really the one and only big bang singularity. The others can only imply that physical reality is totally irrational complex or truly imaginary, becoming triply depressing for anyone to ponder, without going under, remaining somber forever.

[Profpat]

"The others can only imply that physical reality is totally irrational complex or truly imaginary, becoming triply depressing for anyone to ponder, without going under, remaining somber forever."

Ok Antonio just when I thought I knew it all....now I'm depressed.

[mkirkpatrick]

"The others can only imply that physical reality is totally irrational complex or truly imaginary, becoming triply depressing for anyone to ponder, without going under, remaining somber forever."

Ok Antonio just when I thought I knew it all....now I'm depressed.

I am feeling low in mood too,prehaps because it is 43c too hot to think!




regards michael.

[Profpat]

[quote=mkirkpatrick;58176]I am feeling low in mood too,prehaps because it is 43c too hot to think!

Ouch I looked at my conversion chart and that is 109 degrees. It seems like during the summer Phoenix and Baghdad are the 2 hottest cities in the world between 107 and 115 most of the time. But your city is pretty close.

Anytime it's hotter outside than your internal body temperature. be careful of heat stroke.

Best,

Pat

[austintorn@aol.com]

Cool off, guys, right here:

[mkirkpatrick]

[quote=Profpat;58179]

I am feeling low in mood too,prehaps because it is 43c too hot to think!

Ouch I looked at my conversion chart and that is 109 degrees. It seems like during the summer Phoenix and Baghdad are the 2 hottest cities in the world between 107 and 115 most of the time. But your city is pretty close.

Anytime it's hotter outside than your internal body temperature. be careful of heat stroke.

Best,

Pat

Thanks Pat,am getting up at 6am,having swim,doing any chores,then resting in the
afternoon until it cools down.

regards michael.

[AntonioLao]

Have someone invented freon fibre clothings?

[Profpat]

Isn't freon bad for the environment?

[AntonioLao]

temporarily it is the lesser of 2 evils.

[Profpat]

temporarily it is the lesser of 2 evils.

Michael will just have to be careful that he recycles properly.