The simple answer is "no"
Mapping from a sphere (planet) to a rectangular map will create distortion, for the same reason you can;t take an orange peel and flatten it out into a rectangle. Projection can preserver one or more (but not all) of:
* Area
* Shape
* Direction
* Bearing
* Distance
* Scale
http://en.wikipedia.org/wiki/Map_projection
For example, the equirectangular is great around the equator, but pinches the poles when used in the fashion you created your map, as distance is not preserved. (And to have a scale bar on such a projection makes no sense at all). here is your map:
-Rob A>