This doesn't provide the distance info but will provide 'rubbery lines' between satellites and central body and has been done in the 3D window. The distance information can be calculated separately and overlaid via the video editor later.
Rubbery lines - (Rendered with OpenGL)
Add the central sphere, then one satellite.
Add a Nurbs Path and rotate it to align roughly between the satellite and sphere and so it's Edit arrows are pointing to the sphere.
Bevel it with a new plane (scaled down to suit) so it forms a rectangular pipeline. (see Bevel below)
Give it a material slot and saturated colour to avoid shading. Remove specular.
Set it's origin point to the satellite end.
Select the satellite, then use shift-S to set the 3D cursor to the satellite's origin point. (Cursor to Selected)
Select the line and use SH-S again to set it's origin point to the satellite's OP. (Selected to cursor)
The line will be now be rotating from the satellite's origin point.
Give the line/path a constraint --> Track to --> the Sphere. (look at sphere)
Goto Edit mode and select it's sphere-end control point. Press CTL-H and select "Hook to New Object".
Back in Object mode, pull the new empty (hook) down to the center (or surface) of the sphere.
Parent the Hook-Empty to the sphere. ("Keep Transform")
When the sphere moves, the line should maintain a connection between the two objects.
Add a new satellite. Duplicate the line and move it down to near the new satellite.
Select the satellite and press SH-S --> Cursor to selected.
Select the new line, press SH-S again --> Selected to cursor.
The rest of the line's properties are inherited so that's all that's needed.
Repeat the procedure for each new satellite.
If the satellites need to roam about also, simply parent each line to it's respective satellite. ("Keep Transformation") (Child=line)
This is just an ordinary plane scaled down to suit the resultant cross section size of the path.
Add it, size it, then convert it to a curve with ALT-C.
Got to the path, select the plane in the "Bevel Object" slot.
The plane can be rescaled anytime to adjust the cross sectional size.