Gravitation not instantaneous = non elliptic orbits? When I studied physics some time ago my teacher explained that if we consider the gravitational atraction not instantaneous, such as the General Relativity says, the planets would be attracted towards the position were other planets were before and not the current one, getting spiral orbits instead of ellipses.
What was the solution to this problem? Because we do observe elliptic orbits.
I guess when we use speed "c" we can't continue using newton laws and we need the realtivity.
Many articles, even in the Wikipedia, say that the speed of the gravitons must be much higher than "c".
Is it a complet nonsense or some academics believe it?
regards
 A: Stable closed orbits are not possible according to general relativity. The orbits which we observe are not exactly elliptical according to GR but only approximately so. This approximation holds quite well for weak gravitational fields and lower velocities ($v<<c$). as per the predictions of GR the orbiting object loses energy in the form of gravitational waves and this loss of energy causes it to (slowly) spiral inwards. Though gravitational waves have not yet been directly detected till date, the effect on binary pulsars has been observed and is in agreement with the predictions of GR.
A: Celestial orbits are sure spiraled.The proof starts by refusing the area law of Kepler. In fact when the work equation is considered with its vectorial components, we write, with vectors, 
$$W=W_{radial}+W_{perpendicular}.$$
Then, $L_p$ being the distance, 
$$W_p=L_p\cdot F_p,$$
then the differential of $W_p$ is 
$$dW_p=dL_p\cdot F_p+L_p\cdot dF_p$$
where $F_p\cdot dt=m\,dV_p$ (Newton's law). When $F_p$ is replaced, we have 
$$dW_p=dL_p\cdot(m\, dV_p/dt)+L_p\cdot d(m\,dV_p/dt).$$
We know from physics $dW_p=0$,and for this we have to write
$(dV_p/dt)=0$, which means when integrating $V_p=Constant$. So, Kepler area law $(\frac12r\,V_p=Ct)$ is wrong.
On other hand, when the energy conservation equation is written we get, from the solution of a differential form, a new celestial orbit movement equation, $$r=-4t^2+4tT-\frac{2}{3}T^2$$
($t$=real time, $T$=life-time of the body)
This equation do not indicate an ellipse,but a parabola on Cartesian or a spiraled finite orbit on Polar. Newton has discovered this spirals, but commented wrongly, saying the orbits could not be spirals as it is going on "ad infinitum". He was induced by his period law.But period law do not exist in astronomy. And the orbits are on "ad finitum". See Newton's PRINCIPIA (page 296 by Andre Motte). In astronomy a new time law is valid for whole sun system: $r*V_p^2=Constant$. 
You must control this law with the known data of the celestial bodies. For Earth ($r=149597890$ km;$V_p=29,78607371$ km/sec) and the Constant=$1,32725E+11$.
Same constant for Mars,or Halley,or Pluto ,or for comet ISON. Try the evaluation, you will believe that orbits are not elliptical, no area law, no aphelion, no perihelion, no period. All celestial bodies are born from the inside of the sun(when $t=0$, $r<0$). Celestial bodies have a birth date,a living time and a death time. For Earth the actual time is approx 4600000000 years and the life time is 9263192008 years. By years we mean cycles around the sun, years are not 365 days for each cycling.Then what do you think about lightyear distance? Is that a correct definition?
