As we recall from a previous episode of TFP, adjusting an airplane's "max gross weight" v-speeds to account for less-than-gross weight is easy. We multiply the v-speed published for max gross weight by a number which is the square root of (current weight divided by max gross weight). This works for Vx, Vy, Va, Vg, Vs, and Vs0.
We also know that some v-speeds change as the airplane climbs to higher altitudes. I'm specifically interested in (indicated) Vy and Vx. As the airplane reaches its so-called "absolute ceiling," Vy and Vx converge (See the FAA's "Airplane Flying Handbook.") So we know that Vy must decrease and Vx must increase as the airplane climbs.
My question is: What are the formulae that correctly compute adjusted (indicated) Vy and Vx given Vy and Vx at sea level and current altitude?
And a corollary question: Does Vg change as the airplane climbs?
References to the sources would also be appreciated.
PS: For Vs and Vs0, for those who are interested. The Vs and Vs0 as "true airspeeds" increase with altitude, but indicated airspeeds for Vs and Vs0 do not change, because as the airplane climbs, the same indicated airspeed equates to the faster true airspeed.