Talk:Variable-mass system

NASA's website is wrong
Citation 4 on this page links to NASA Glenn's derivation of the rocket equation. Several years ago I emailed them to point out the two errors they made in their derivation, which unfortunately they haven't bothered to correct. The errors cancel each other out and give the correct result despite violating the laws of physics. The first error is that they begin by applying Newton's Second Law to a system of varying mass without accounting for it as indicated at the top of the Wiki article with the vrel term, apparently incorrectly thinking the u dm term is supposed to account for varying mass.

Expanding the left side of the equation:

M du + u dM = Veq d mp

Immediately after that they make a second error which cancels out the first when they simply handwave away resulting erroneous term:

Assume we are moving with the rocket, then the value of u is zero:

M du = Veq d mp

There are two possible meanings of "moving with the rocket", both of which lead to contradictions. It could mean they are deriving the equation in a noninertial reference frame fixed to the rocket and accelerating with the rocket. The problem is that Newton's Second Law assumes an inertial reference frame, otherwise you have to add fictitious forces. But putting that aside for a second, accelerating with the rocket means the M du term is also zero, leaving a trivial equation and short-circuiting the derivation.

The other possible meaning is that they have chosen an inertial reference frame that happens instantaneously to have the same velocity as the rocket even though the rocket is accelerating. This is problematic because it implies that the equations of motion of a rocket belong only to one preferred reference frame, which is false since Newtonian mechanics are equivalent in any inertial frame. But putting that aside for the moment, it also means the velocity u is in general nonzero, so it doesn't drop out, and the exhaust velocity Veq is no longer a constant, since its value is assumed to be fixed relative to the rocket while the rocket changes velocity relative to the "preferred" reference frame.

Someone please tell me either I'm crazy, or NASA is making an embarrassing mistake on their website and miseducating their visitors. MarcusMaximus (talk) 07:19, 22 February 2016 (UTC)

Effect of rain / sunshine
Let's take a load of hay on truck bed and think what is the required force to move it if it rains and the load gets heavier and what is the effect of drying in sunshine on the force. Do the same equations apply?Linkato1 (talk) 19:06, 29 October 2017 (UTC)


 * Yes, the truck gets heavier or lighter by a factor of dm/dt and the force is proportional to that times the velocity of the truck at an instant. Malnu (talk) 16:04, 23 February 2024 (UTC)