Hello,

Please see attached photo for reference.

I am trying to place a section of a 'ring' behind a circular/spherical object (see black arrow and box in attached image). I have made the simple ring by removing the fill, and keeping the stroke, of the ellipse tool. Whenever I try to remove a section of the ring (say for example by using Path > Division) InkScape will introduce new lines which curve alongside the circle (red arrow). 

How would I be able to cut the ring such that the region indicated by the black arrow and box is placed behind the circle without creating those secondary lines?

Thank you so much. :)

You have send the ring to the back.

Decide the cut point. I like it to be on the vertical midpoint of the ring.

Draw the cutting path, if it is made of multiple paths use Path>Combine

Then bring that cutting path to the front ( it's always the path highest in the paint order that cuts ) 

Object>Raise to Top

Then Select the cutting path, then shift click the object to be cut.

Path>Cut Path. 

I have attached a file with the 3 stages.

You can always cut the ring at the exact point it touches the circle.

That would involve making a copy of the circle, bringing it to the top and doing the same procedure. 

However I like the first method, as it allows for resizing of the circle without having to repeat the operation

I presume your rings were made with the ellipse tool. Select them and [Path > Object to Path].

Now go to the node tool [n] and select the nodes at left and right. In the tool controls bar, click on [Break path at selected nodes] to create separate sub-paths.

[Path > Break Apart] or [shift+ctrl+k] converts sub-paths to individual shapes.

Now use the select tool [s] and select the planet and the foreground ring segments and in the tool controls bar [Raise to Top].

Yet another method. Keep the ellipse intact and instead, split the planet into two semicircles. I like this because it's easier to adjust the orbiting rings.