Calculating Acceleration with Mass and Power

[PhoenixKnight]

Hello,

First, I'm not much of a physicist. My area of study is largely in environmental sciences and geology, but I've been trying to determine the appropriate equations to use to calculate the rate of acceleration for an object in a vacuum using its mass and the power available to drive it.

I was hoping that someone might be able to help me with this problem.

The mass of the object is 750,000,000 kilograms, and the power available is 200,000 gigawatts.

How does one calculate the acceleration using these values?

Thanks in advance,

~Phoenix Knight

 

[A.T.]

I depends how you drive it and how that nominal power is defined. If the power is the change in kinetic energy in the initial rest frame, then it cannot be a fixed value because the force would go to infinity at low speeds:

power = force * velocity
acceleration = force / mass = power / (mass * velocity)

But this is just at non relativistic speeds.

 

[PhoenixKnight]

Alright, so there is more information required to determine this?

Would these values help?

- The object has an initial velocity of 3070.00 m/s.
- The desired cruising velocity is 98.2% of c (294,396,193.76 m/s)
- The drive is exerting a constant force produced by 200,000 gigawatts of energy.

How does the velocity affect the acceleration?

Ultimately, I want to know how long it will take the object to accelerate from its initial velocity to its cruising speed.

Thanks!

 

[A.T.]

- The drive is exerting a constant force produced by 200,000 gigawatts of energy.

What kind of drive? What do the 200,000 gigawatt represent? You can calculate all kinds of energies in all kinds of reference frames.

If it is a rocket with constant thrust, but non-constant mass (due to fuel consumption) you have to use this:
http://en.wikipedia.org/wiki/Relativistic_rocket#Relativistic_rocket_equation

 

[PhoenixKnight]

For this scenario I have been assuming the drive to be a very advanced technology that consumes little to no mass.

Perhaps something that employs manipulation of gravity, negative mass or distortion of space-time to produce propulsion? However, I do not want the hypothetical technology to be any kind of alcubierre or related warp drive because I want to limit the object to sub-luminal velocities.

It is, however, proving quite difficult to find any real information on feasible drive technologies with a minimal requirement for reaction mass...

Any suggestions?

 

[A.T.]

For this scenario I have been assuming the drive to be a very advanced technology that consumes little to no mass.

The most efficient one:
http://en.wikipedia.org/wiki/Relativistic_rocket#Matter-antimatter_annihilation_rockets

 

[PhoenixKnight]

Matter-Antimatter is actually something I considered. The only questions I have about it are how much anti-matter would be needed to accelerate to cruising velocity and then decelerate back to a resting velocity? And how do you get that much anti-matter?

Thanks for your help, by the way. I'm finding your input very helpful!

 

[Lsos]

Even if your drive uses no reaction mass, the incredible amount of energy required for what you want will still add considerable mass to the spaceship...if you intend to carry the energy on board, of course.

Besides that, "how do you get that much antimatter?" is trivial compared to the MANY other questions you need to answer.