From: Anders Sandberg (asa@nada.kth.se)
Date: Sun Jul 13 2003 - 05:44:13 MDT
On Sat, Jul 12, 2003 at 08:26:35PM -0400, ABlainey@aol.com wrote:
> In a message dated 12/07/2003 11:12:16 GMT Daylight Time, asa@nada.kth.se
> writes:
>
> > For a static field in such a "slow gravity" universe nothing would
> > change. But imagine sending out Voyager towards Jupiter. At first it
> > experiences the weak tug towards the place where Jupiter was a long time
> > ago, and is accelerated that way. As it approaches the region where
> > Jupiter is, the acceleration will change direction and move towards the
> > current position, and as Voyager continues beyond it will shift back
> > towards an old position.
> >
>
> I can see that. Wouldn't the gravitational force also be weaker than
> expected if the voyager past the planet on its sun orbital trailing
> end ? A kind of gravital doppler shift.
I made a matlab program (included at the end for those of you who like
to play with it), and it seems to say the opposite (assuming I coded
right, which is anybody's guess :-). The trailing side has a stronger
force compared to the non-moving case. It looks more like a sonic boom
than a doppler shift. If the planet is releasing gravity waves, they
will of course be doppler shifted.
> > Even worse, Jupiter is actually moving "supersonically" in this setting!
> > If Voyager is approaching from straight ahead of the planet it will not
> > experience any gravitational field since Jupiter is moving faster than
> > the information about where it is is spreading through the gravity
> > field. So on one side of Jupiter you would actually be weightless! On
> > the other side all the information is present and you get normal
> > gravity. And you get a discontinous bow shock where you go from no
> > gravity to a mix of several accelerations pointing towards many former
> > positions (likely just causing an inward accleration into the shock
> > cone).
> >
>
> I can't quite agree with this, although very nearly. I can see what you are
> saying and I am probably nit picking.
> My take would be that the gravitational force would be normal on the leading
> side of the planet and you would 'appear to be' weightless on the other side.
> The fact really is that you would not be weightless, rather that the planet
> itself would be moving away from you faster than it is attracting you. so you
> would still be constantly falling towards the planet surface, but getting
> further away.
I think you are mixing up frames here. I'm looking at a planet moving
relative to a grid of stationary observers who at the time t=0 reports
their observations. You are looking at the planet while moving with it.
Hmm, interesting. An observer on the planet surface would, if gravity
behaved like it does here, observe the same gravity all around the
surface regardless of where it was moving. An external observer would
not see the same.
My model is based on having gravity disturbances move relative to a
fixed spacetime *at a constant speed relative to this frame*. There
cannot be a fast or slow gravity wave in my model, all gravity waves
move at the speed g. Just like light in relativity and sound in still
air. If we allow gravity waves of different speeds then things get
*really* messy and interesting. I guess a fast moving planet would have
a field that moved fast to a receiver, while a slowly moving planet
would have a slowly expanding field. I think we need extra assumptions
here, and the whole thing starts to look like the theory of nonlinear
waves. Very interesting, but confusing.
Here is my little crude program:
s=1; % Grid resolution
[x,y]=meshgrid(-5:s:5,-5:s:5);
N=size(x,1);
v=1.4; % Velocity of mass
t=-100:0.1:0;
pos=[v*t' 0*v*t']; % Position of mass at different times
fx=zeros(N); % x-force
fy=zeros(N); % y-force
ti=zeros(N);
st=zeros(N); % Strength of field
for i=1:N
for j=1:N
s=1;
sss=[];
for tt=1:size(t,2)
dist=norm([x(i,j) y(i,j)]-pos(tt,:));
%sss=[sss dist+t(tt)];
ss=sign(dist+t(tt)); % Check if we have found edge of
lightcone
if (ss ~= s)
fx(i,j)=fx(i,j)+(pos(tt,1)-x(i,j))/(dist^3);
fy(i,j)=fy(i,j)+(pos(tt,2)-y(i,j))/(dist^3);
ti(i,j)=ti(i,j)+1;
end
s=ss;
end
%clf
%subplot(2,1,1)
%hold on
%plot(t,sss)
%plot(t,t*0,'r');
%subplot(2,1,2)
%imagesc(fx>0)
%drawnow
st(i,j)=sqrt(fx(i,j)^2+fy(i,j)^2);
end
end
clf
hold on
quiver(x,y,fx,fy)
contour(x,y,log(st))
-- ----------------------------------------------------------------------- Anders Sandberg Towards Ascension! asa@nada.kth.se http://www.nada.kth.se/~asa/ GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y
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