Drawing a comet

you could try using the drop shadow effect on different shapes to make up the head and body.  Play around with the interactive transparency tool.  Or perhaps take this into PhotoPaint and work with some layering and effects there to achieve your goal.  here's my sample.

Pretty nice, thanks Jeff. Good idea using several objects with various transparancies. Eventually the glow at the comet's head can then be created with a circle or ellipse with radial fountain fill with transparency too.

Regarding the stars which are a bit bigger than just a point: You might want to make a glow around it. The same with a Sun. Today I was working in Illustrator, although I actually hate it, and I am not very good with it. The problem was I couldn't import a certain file into CorelDRAW, so I had to do a Little Work in Illustrator. The was however one thing I found pretty nice in IL and it was the gradient fill. You can apply transparency (even different ones) to every point on the gradient slider. It made it quite simple to produce a star with glow, as shown below:

Now I tried the same in CorelDRAW. It is not so simple, I find and I have trouble getting it to look realistic. I made a White Circle on the blue background, then Applied the transparency Tool and placed several points on the Fountain Transparency line. I cannot seem to make the White fade out continously into the blue. When using the Edge Pad option in the context Toolbar it helps, but I don't find it working very well. Maybe I have overlooked something? I use CorelDRAW X5, by the way. 

Erik 

Like Ariel says, try a Mesh fill.

There's a feature that was new in X5; Transparency in meshes.
This means you can create the stars from a circle with a mesh of only four fields (2 x 2), where the center is an opaque white and all the nodes along the circle's edge are transparent.
In combination with the, also new, "Smooth mesh color" (button in Property Bar) the effect will be similar to what you showed from Illustrator.