I understand relativistic mass and the equations underpinning it. My question deals with how to calculate relativistic mass when an object is viewed from different frames of reference.
Consider a space probe launched from a planet orbiting Star A (we will call it Probe A). Probe A launches into space, away from its planet at 90% of the speed of light relative to Star A. The relativistic mass will be 5.3 times the rest mass.
Now consider an observer on a planet orbiting a distant Star B (we will call him Observer B). Star B is hurling through space at the exact same velocity (speed and direction) as Probe A, but tangential to the path of Probe A, so there is no danger of a collision between Star A and Star B. Observer B is not aware his star system is moving – to him, of course, his star is stationary. When Observer B views Probe A, he measures a velocity of zero, and therefore the relativistic mass of Probe A equals the rest mass when viewed by Observer B.
How can the same object (Probe A) have different relativistic masses based on the observer?