[Geezer (OP)]

I forgot to mention that Newton defined force as F = dp/dt, not F = ma. The former is in the beginnning of the Principia and the later is Euler's expression for the force/mass/acceleration relastionship. The expression F = dp/dt is relativistically correct, where generally F = ma is not.

What's the difference?

[Pmb]

I forgot to mention that Newton defined force as F = dp/dt, not F = ma. The former is in the beginnning of the Principia and the later is Euler's expression for the force/mass/acceleration relastionship. The expression F = dp/dt is relativistically correct, where generally F = ma is not.

What's the difference?

They don't always have the same value, e.g. for v << c the mass of a rocket which is accclerating from its engines being turned on, and when the velocity is relativistic. Its best to define F = dp/dt and when v << c and m = constant.

[Geezer (OP)]

I forgot to mention that Newton defined force as F = dp/dt, not F = ma. The former is in the beginnning of the Principia and the later is Euler's expression for the force/mass/acceleration relastionship. The expression F = dp/dt is relativistically correct, where generally F = ma is not.

What's the difference?

They don't always have the same value, e.g. for v << c the mass of a rocket which is accclerating from its engines being turned on, and when the velocity is relativistic. Its best to define F = dp/dt and when v << c and m = constant.

Can rockets achieve relativistic velocities?

[Pmb]

Can rockets achieve relativistic velocities?

Theoreticaly, yes. But that would be to impractical to build.

[imatfaal]

Can rockets achieve relativistic velocities?

Theoreticaly, yes. But that would be to impractical to build.

Theoretically - Not really.

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It is clear from the above (MR is mass ratio of Mass_full over Mass_empty) that to accelerate a 1000kg rocket with a exhaust velocity of 10000 m/s (ie double what is currently achievable to make maths simpler) to a tenth of the speed of light you would need the mass of the full rocket to be 1000e^3000kg  - That is the mass of many many universes. Even taking the velocity of exhausted gases up to 10^6 m/s would require a rocket that outweighs an asteroid (10^17kg) - and that's at maximal efficiency and with make-beleive technology

Realistically - it is doubtful that even .05c is on the cards, even with the exotic tech envisaged for the future such as ion drive and fusion drive

[PmbPhy]

You are forgetting that the acceleration due to gravity is not constant and varies as you approach the body and the equations are only true for one instant the moment the body falls a little towards the gravitating mass the acceleration and therefore the force increases.

There is most definitely a force of gravity, even in GR. And the argument about how g changes with position on earth has no bearing.

The qualifier "onstant' is better referred to as "homogenous" or something. To many people "constant' refers to something that does not change in time,

OP - You're referring to what are called inertial forces. For more on that see:
http://www.newenglandphysics.org/physics_world/gr/inertial_force.htm

[Professor Mega-Mind]

To read more discourse on how the "force" of gravity alters space-time , and affects the flow of time ;
...............Reference Note .
Connect to "Does gravity attract masses ... or curve space ?" .
www.thenakedscientists.com/forum/index.php?topic=67385.new;topicseen#new
.................Also...
How does the expansion of space work ? 
www.thenakedscientists.com/forum/index.php?topic=79683.0new;topicseen#new
P.M.

[PmbPhy]

It seems to me that there is no "force of gravity",

There is a force of gravity just as there is a Coriolis force. See
http://www.newenglandphysics.org/physics_world/gr/grav_force.htm

[Paul25]

It's a warpage of space, but I rather think of it as an aberration

[Professor Mega-Mind]

Everything is an aberration...
But, what is the fundamental
 motivator ?  A round ball may be placed on a slanted surface , but what motivates it to roll downhill ?  There must be an ultimate motive force present , even through all space . Space-time is indeed , quite warped , but that , in and of itself , is not the cause of gravity , it is simply something that profoundly affects how gravity does what it does .
P.  .🤨

[alancalverd]

Can rockets achieve relativistic velocities?

Obviously. From the point of view of an observer in a galaxy receding at 0.9c,  I am moving at a relativistic velocity right now. He could measure my red shift to prove it.

[Bored chemist]

Don't expect Geezer to rush to respond to this nearly ten year old thread..