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- W1014602710 abstract "A gravitational ellipse is the mathematical result of Newton's law of gravitation. [Ref.1] The equation describing such an ellipse, is obtained by differentiating space-by-time twice. Le Verrier [Ref.2] stated: 'rotating gravitational ellipses are observed in the solar system'. One could be asked, to adjust the existing gravitational equation in such a way, that a rotating gravitational ellipse is obtained. The additional rotation is an extra variable, so the equation will be a three times space-by-time differentiated equation. In order to obtain a three times space-by-time differentiated equation we need to differentiate space-by-time for the third time. Differentiating space-by-time twice gives the following result.[Ref.3] begin{equation} centerline{ $(ddot{X})^2 + (ddot{Y})^2 = (ddot{R} - R dot{a}^2 )^2 + (Rddot{a} + 2 dot{R} dot{a} )^2 $} end{equation} A third time differentiation of space-by-time gives the result: begin{equation} centerline{ $(dddot X )^2 + (dddot{Y})^2 = (dddot{R} - 3dot{R} dot{a}^2 - 3 R dot{a} ddot{a} )^2 + (Rdddot{a} + 3 dot{R} ddot{a} + 3 ddot{R} dot{a} - Rdot{a}^3 )^2 $} end{equation} We are now simply performing the necessary mathematical exercise to produce the new equation, which describes rotating gravitational ellipses. newline centerline{includegraphics{20150202_RotatingEllipse.png} }newline I assume that the reader accepts the mathematical differential equation, which defines a rotating gravitational motion as observed. But we now have two equations defining rotating gravitational ellipses as observed in nature: the EIH equations (Ref.4) and the above equation 2, which obeys the Euclidean space premises." @default.
- W1014602710 created "2016-06-24" @default.
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- W1014602710 date "2015-04-01" @default.
- W1014602710 modified "2023-10-16" @default.
- W1014602710 title "A rotating gravitational ellipse" @default.
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!["A gravitational ellipse is the mathematical result of Newton's law of gravitation. [Ref.1] The equation describing such an ellipse, is obtained by differentiating space-by-time twice. Le Verrier [Ref.2] stated: 'rotating gravitational ellipses are observed in the solar system'. One could be asked, to adjust the existing gravitational equation in such a way, that a rotating gravitational ellipse is obtained. The additional rotation is an extra variable, so the equation will be a three times space-by-time differentiated equation. In order to obtain a three times space-by-time differentiated equation we need to differentiate space-by-time for the third time. Differentiating space-by-time twice gives the following result.[Ref.3] begin{equation} centerline{ $(ddot{X})^2 + (ddot{Y})^2 = (ddot{R} - R dot{a}^2 )^2 + (Rddot{a} + 2 dot{R} dot{a} )^2 $} end{equation} A third time differentiation of space-by-time gives the result: begin{equation} centerline{ $(dddot X )^2 + (dddot{Y})^2 = (dddot{R} - 3dot{R} dot{a}^2 - 3 R dot{a} ddot{a} )^2 + (Rdddot{a} + 3 dot{R} ddot{a} + 3 ddot{R} dot{a} - Rdot{a}^3 )^2 $} end{equation} We are now simply performing the necessary mathematical exercise to produce the new equation, which describes rotating gravitational ellipses. newline centerline{includegraphics{20150202_RotatingEllipse.png} }newline I assume that the reader accepts the mathematical differential equation, which defines a rotating gravitational motion as observed. But we now have two equations defining rotating gravitational ellipses as observed in nature: the EIH equations (Ref.4) and the above equation 2, which obeys the Euclidean space premises."](?object=%22A%20gravitational%20ellipse%20is%20the%20mathematical%20result%20of%20Newton's%20law%20of%20gravitation.%20%5BRef.1%5D%20The%20equation%20describing%20such%20an%20ellipse%2C%20is%20obtained%20by%20differentiating%20space-by-time%20twice.%20Le%20Verrier%20%5BRef.2%5D%20stated%3A%20'rotating%20gravitational%20ellipses%20are%20observed%20in%20the%20solar%20system'.%20One%20could%20be%20asked%2C%20to%20adjust%20the%20existing%20gravitational%20equation%20in%20such%20a%20way%2C%20that%20a%20rotating%20gravitational%20ellipse%20is%20obtained.%20The%20additional%20rotation%20is%20an%20extra%20variable%2C%20so%20the%20equation%20will%20be%20a%20three%20times%20space-by-time%20differentiated%20equation.%20In%20order%20to%20obtain%20a%20three%20times%20space-by-time%20differentiated%20equation%20we%20need%20to%20differentiate%20space-by-time%20for%20the%20third%20time.%20Differentiating%20space-by-time%20twice%20gives%20the%20following%20result.%5BRef.3%5D%20begin%7Bequation%7D%20centerline%7B%20%24(ddot%7BX%7D)%5E2%20%2B%20(ddot%7BY%7D)%5E2%20%3D%20(ddot%7BR%7D%20-%20R%20dot%7Ba%7D%5E2%20)%5E2%20%2B%20(Rddot%7Ba%7D%20%2B%202%20dot%7BR%7D%20dot%7Ba%7D%20)%5E2%20%24%7D%20end%7Bequation%7D%20A%20third%20time%20differentiation%20of%20space-by-time%20gives%20the%20result%3A%20begin%7Bequation%7D%20centerline%7B%20%24(dddot%20X%20)%5E2%20%2B%20(dddot%7BY%7D)%5E2%20%3D%20(dddot%7BR%7D%20-%203dot%7BR%7D%20dot%7Ba%7D%5E2%20-%203%20R%20dot%7Ba%7D%20ddot%7Ba%7D%20)%5E2%20%2B%20(Rdddot%7Ba%7D%20%2B%203%20dot%7BR%7D%20ddot%7Ba%7D%20%2B%203%20ddot%7BR%7D%20dot%7Ba%7D%20-%20Rdot%7Ba%7D%5E3%20)%5E2%20%24%7D%20end%7Bequation%7D%20We%20are%20now%20simply%20performing%20the%20necessary%20mathematical%20exercise%20to%20produce%20the%20new%20equation%2C%20which%20describes%20rotating%20gravitational%20ellipses.%20newline%20centerline%7Bincludegraphics%7B20150202_RotatingEllipse.png%7D%20%7Dnewline%20I%20assume%20that%20the%20reader%20accepts%20the%20mathematical%20differential%20equation%2C%20which%20defines%20a%20rotating%20gravitational%20motion%20as%20observed.%20But%20we%20now%20have%20two%20equations%20defining%20rotating%20gravitational%20ellipses%20as%20observed%20in%20nature%3A%20the%20EIH%20equations%20(Ref.4)%20and%20the%20above%20equation%202%2C%20which%20obeys%20the%20Euclidean%20space%20premises.%22){kind=link}