Gravitational Time Dilation & Orbits of Objects

[Warfen]

For example if there were two objects orbiting each other and one was much heavier than the other, for instance a dwarf star and a neutron star. Would the lighter object have a greater gravitational pull than it's mass would say it should because it's pull was operating longer on the heavier object due to time dilation.

 

[Simon Bridge]

Welcome to PF;
Yes and no.
GR is needed to properly describe the kinds of system where an orbit passes close to a primary ... the more massive the primary, the farther away "close" is.
So the effect is felt in the Solar System - check out the subtleties of Mercury's orbit:
http://www.einstein-online.info/elementary/generalRT/planetAstray

However - objects do not pull on each other in general relativity. Gravity is a pseudoforce that comes from the geometry of space-time. If we want to know about the pseudoforce we need to pick a reference frame (i.e. you see centrifugal and coriolis forces in a rotating frame) ... in the frame where the gravity pseudoforce was apparent, every action has an equal and opposite reaction: so the lighter mass will have exactly the same attraction as the heavy one. So if you've been having trouble finding an answer to your question, this is probably why.

Try modifying it so you ask if some orbits in GR are tighter than the relative masses would indicate for Newton... i.e. Does Newton predict the same orbits for a heavier mass.

 

[A.T.]

Does Gravitational Time Dilation affect the orbits of things?

There would be no orbits at all without a gradient in gravitational time dilation. The gradient in gravitational time dilation, is directly related to the gravitational free fall acceleration. Additionally to that there is also spatial distortion, which causes orbits to precess.

See the diagrams here:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

 

[alw34]

Does Gravitational Time Dilation affect the orbits of things
yes. Time dilation, or time distortion IS a component of gravity. good start.

Would the lighter object have a greater gravitational pull than it's mass would say it should because it's pull was operating longer on the heavier object due to time dilation.

let me try 'no' as an answer, with caveats. Time dilation and spatial distortion, the curvature of spacetime in your example IS 'gravity', and is a bit different than Newton envisioned, that is, more precise. Hence the effects already described in prior posts: time dilation does affect orbits relative to Newton's predictions.

"longer" or "shorter' depends from where you make your observational measurements, that is, your frame of reference mentioned in post #2. Regarding, 'operating longer', keep in mind local time, say at each of the objects, ticks along steadily at an unchanging rate. Radioactive decay, for example, takes as long at one as the other. Yet if we compare clock times, say, with a distant observer, all three clocks tick at different rates.

PS: Your example reminds me of our global positioning system, a light satellite object orbiting around a 'much heaver' object, earth. There is a LOT going on, and if you want some details:

https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Relativity

 

[Warfen]

Thank you all for your answers. I guess I am still thinking in a Newton way but mixing in Relativity concepts which is the crux of my confusion.