Fact is that we have no means of measuring mass, only of comparing masses.

I disagree. We only need a way to determine what one unit of mass is. Currently it's defined by comparing it to a platinum bar that is kept . Now its determined by using the constants of nature. See:

https://en.wikipedia.org/wiki/KilogramThe kilogram is the only SI base unit with an SI prefix ("kilo", symbol "k") as part of its name. It is also the only SI unit that is still directly defined by an artifact rather than a fundamental physical property that can be reproduced in different laboratories. Three other base units in the SI system are defined relative to the kilogram, so its stability is important. ... The 118-year-old cylinder that is the international prototype for the metric mass, kept tightly under lock and key outside Paris, is mysteriously losing weight — if ever so slightly".

I suppose its because of this last comment that there is a proposition to change it to be defined in terms of the fundamental constants of nature. However we can certainly measure the mass of an object without having that bar or a copy of it where we take the measurements. For example; place a charged particle in a cyclotron and measure the speed v and the radius of the circle R in which the particle moves and you can determine the mass of the object from that and the magnitude of the magnetic field. See:

http://home.comcast.net/~peter.m.brown/sr/cyclotron.htmThe relationship is p = qBR = mv

However, just for fun, let's consider

m = m_{0}/√(1 - v^{2}/c^{2})

which may be familiar.

Certainly. Especially to me. [^] But what does this have to do with your argument below?

We know that distant bodies in the universe are retreating from us, and thus us from them, at an accelerating rate.

Are you referring to the accelerating expansion of the universe?

Now consider planet X with an orbiting moon, rushing away from us at a finite and increasing v.

Since you refer to "us" it means that you're referring to a particular frame of reference. However you haven't made it clear at this point what that frame of reference is. Would you mind stating it for us, please? Thank you.

If by "us" you mean that those observers who are standing on the planet then why is the moon rushing away from us at a finite and increasing v. That's not possible for a moon in orbit of a planet when the only force acting on the moon is the gravitational field of the planet. I.e. since the definition of

**moon** is

*a large round object like the moon that circles around a planet* then the total energy of the moon is less than zero (where the zero of the gravitational potential is taken to be at infinity) the motion of the moon must be in an ellipse with a circular orbit being a special case of an elliptical orbit. Why are you phrasing this motion as

*rushing away from us at a finite and increasing v* since when the moon is moving away its speed is decreasing in order for the total energy to be conserved, i.e. when moving away from the planet the gravitational field of the planet does a negative amount of work on the moon thus reducing the kinetic energy and therefore reducing its speed.

Since the mass of both planet and moon will be increasing, so will their mutual gravitational force. Describe the change in the moon's orbit.

Why is the mass of the planet increasing? From what frame of reference are you making these observations from?

Besides, that's a rather complicated problem in general relativity. I haven't worked with those kinds of problems in a few years. Do you really need me to do that or is this simply a rhetorical question?

Note that "from the viewpoint of a stationary observer on earth" is irrelevant: if you are standing on X, is the moon getting closer or further away?

That depends on the kind of orbit its in. Is it moving in an elliptical orbit or a circular orbit.