Travelling In A Straight Line In Space

Sammyg
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I know all object in space have orbits and orbits can be changed but is it possible for rocket or a spacecraft to travel in a straight line.
 
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Sammyg said:
I know all object in space have orbits and orbits can be changed but is it possible for rocket or a spacecraft to travel in a straight line.

Hi Sammyg! :smile:

If it keeps firing its rockets, then it can follow any curve it likes, including a straight line.

but once the rockets are off, it can only travel in a straight line if it's going "straight up or down". :wink:
 
Sammyg said:
I know all object in space have orbits and orbits can be changed but is it possible for rocket or a spacecraft to travel in a straight line.

Travel straight with respect to what?
 
In general rel, there may not be such a thing as a straight line in a spacetime with a funny geometry. When not under the action of external forces, things travel along geodesics. In flat "minkowski" spacetime, this principle corresponds to straight lines and is simply a more general form of the principle of inertia.
 
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From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
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