Simulating gravitational attraction between bodies
Just a note on your commenting:

Should you be breaking XML comments up across lines like that?

/// &lt;summary&gt;
/// Class used for calculating
/// how an object orbits another
/// object.
/// &lt;/summary&gt;


I feel that should be three lines:

/// &lt;summary&gt;
/// Class used for calculating how an object orbits another object.
/// &lt;/summary&gt;


Likewise, I feel that the following comment:

/// &lt;summary&gt;
/// FixedUpdate is run once per frame.
/// FixedUpdate is used so that calculations
/// don't need to be multiplied by Time.deltaTime.
/// &lt;/summary&gt;


Could be rewritten as:

/// &lt;summary&gt;
/// FixedUpdate is run once per frame.
/// &lt;/summary&gt;
/// &lt;remarks&gt;
/// FixedUpdate is used so that calculations don't need to be multiplied by Time.deltaTime.
/// &lt;/remarks&gt;


Personally, I think breaking comments along multiple lines like that makes it harder to read. You're eyes have to jump to unnatural places.

Likewise, the &lt;remarks&gt; bit is nice because those comments aren't shown in Intellisense, but they can still be placed in the generated XML documentation files.

The only other bit I would mention, is the use of this. You should either use it consistently, or try to limit it. Sometimes (especially in larger cases) it helps to clear things up. But if you use it for some of the properties and not others, it can have a negative impact.

I'm referring to the following:

Vector3 CalculateGravitationalForce()
{
    this.parentPosition = this.parentObject.transform.position;
    Vector3 force = this.parentPosition - transform.position;
    float distance = force.magnitude;
    float strength = (this.gravityConstant * this.parentMass * this.objectMass) / (distance * distance);
    force.Normalize();
    force = force * strength;
    return force;
}


Where does transform.position come from? The fact that you use this on all the other properties/fields of the class but not that one throws confusion into the mix. It's not a local variable, that much is true. But where exactly does it come from, is a little harder to notice right out of the box.

Again, these are all suggestions. Whether or not you like/use them is up to you, but this is how I would write it out.