# At what point, if any, would a spaceshp burn up in space?

1. Feb 12, 2009

### Darrin

Hi, I hope I'm posting in the right forum.

So I've been working on a game design and was toying with the idea of using acceleration and maximum speed. There are game design problems with not just putting a maximum speed on a ship like players never being able to catch each other.

However I was thinking that there might be some interesting limits. One limit for example is the amount of acceleration a human body can withstand sustained. 3Gs is probably no problem but 10gs starts to get dangerous fast.

My question is this. It was my understanding that space is not empty. Space is filled with molecules of matter, be it very hydrogen or space dust. My guess is the closer to planets and various other stellar objects the more junk there is. At what point does the speed of a space ship start building up dangerous friction when moving through these particles? Is it 1/10th of c, higher or lower?

The second part of the question concerns thing about things like solar winds and the Casimir effect. Would these effect the metal hull of spaceship more as it increased in speed?

Anything else you can think of? Any help would be appreciated.

2. Feb 12, 2009

### pallidin

In a true sense, what you're asking is "rocket science"

How NASA deals with impact potentials at speeds of, say, 100,000mph is a critical factor with respect to survivability, and I have no answer.

What I do know is that you can ask NASA. They have a public Q&A and FAQ available on the internet.

3. Feb 12, 2009

### Mapes

Hi Darrin, welcome to PF. You might be interested in the details of the http://en.wikipedia.org/wiki/Bussard_ramjet" [Broken], which is intended to travel fast enough that the density of interstellar gas becomes significant.

Last edited by a moderator: May 4, 2017
4. Feb 13, 2009

### Nabeshin

This is a really ballpark calculation, so if any of you take issue with my assumptions, realize that they are just that: assumptions.

If there is a spaceship traveling through the interstellar medium, how much heat would it acquire per second?

If we assume the ISM is at rest relative to the moving ship, moving at say, .1c, then we can use conservation of momentum to see:
$$m_{s}v_{s}=(m_{s}+m_{p})v_{f}$$ Where $$m_{p}$$ is the mass of the particles in the ISM.

Let's take an average mass of material in the ISM to be 2amu (it's mostly hydrogen, after all), and the mass of the ship to be 6 million kg (the massof the saturn V rocket).

$$v_{f}=\frac{m_{s}v_{s}}{m_{s}+m_{p}}$$

Now, there is a loss of energy in this collision, and we will assume it is all converted into heat.

$$\frac{1}{2}m_{s}v_{s}^{2}-\frac{1}{2}(m_{s}+m_{p})v_{f}^{2}=\Delta E$$

Substituting in for vf from the equation above and simplifying yields:
$$\frac{1}{2}v_{s}^{2}(m_{s}-\frac{m_{s}^{2}}{m_{s}+m_{p}})=\Delta E$$

For the values stated, this corresponds to 1.35x10^-27J/particle in the collision with the ISM. Now, the density of the ISM in the Milky Way is approximately 1 million particles per meter cubed, and let's assume our ship has a cross-sectional area of 10m^2 for simplicity's sake. That means the ship passes through a volume of (.1c*1s*10m^2)=3*10^8m^3 every second, which corresponds to a collision with about 3*10^14 particles per second.

Multiplying by the energy per particle yields 40,500J/s converted to heat via the collisions. I don't know, but to take an average material, Iron, say, we have a specific heat capacity of 500J/kg*K. Also I will assume only 10% of the mass of the ship is in direct contact, and as heat convection is not perfect, only 10% is actually heated by the collision.

So, we have:

$$\frac{40500J}{s}*\frac{kg*K}{500J}*\frac{1}{3*10^5kg}=.00027K/s$$

Now, this value seems relatively low to me (and I haven't taken any SR effects into account, but they should be minimal at .1c).

In general, it looks something like this:
$$\frac{\Delta K}{s}=A*v_{s}*\rho *\Delta E *\frac{1}{SH} *\frac{1}{m_{c}}$$
Where $$\rho$$ is the density, SH is the specific heat of the material, and Mc is the mass in contact (some proportion of the total mass).

If we substitute in delta E, the final form is:

$$\frac{\Delta K}{s}=\frac{1}{2}v_{s}^{3}*(m_{s}-\frac{m_{s}^{2}}{m_{s}+m_{p}})*A*\rho*\frac{1}{SH}*\frac{1}{m_{c}}$$

Last edited: Feb 13, 2009
5. Feb 13, 2009

### jmatejka

I think Kinetic energy danger(from dust) comes before thermal danger(In a dirty space environment). A space shuttle window was once damaged by a paint chip. Shuttle velocity was 18,000 mph (+/-). I dont know what the paint chips velocity was at the time of impact.

6. Feb 13, 2009

### Darrin

Very nice. Thanks for the thoughtful responses.

So far the factors that seem to effect a ship so far.

Particle Damage
Acceleration Limitation on the human body
Force required to accelerate something heavy
Fuel mass
Fuel gathering
Engine effiency
Friction (very minor)
Solar Winds (minor)

Thanks again!

7. Feb 13, 2009

### Nabeshin

This is certainly true. Even at the relatively modest speeds of a space shuttle, any macroscopic particles have a catastrophic effect during a collision. The kinetic energy of individual particles of the ISM is, however, quite negligible (10^-10J).

To expand upon my previous post with regards to thermal heating due to particle collisions, it is obvious that given an infinite amount of time, the temperature of the ship will become infinite. Obviously this is not the case. As the temperature of the hull of the ship increases, it radiates more energy away. If we assume that the hull radiates as a black body, it's radiation at a given temperature is given by the stefan-boltzman law as:

$$J=\sigma T^{4}$$ Where J is the total energy radiated per unit area.

The function of heat increase derived in the above post is essentially independent of temperature (the only time-dependent factor is the specific heat of the given material; if anyone has a temperature variation model for this or a sense of how large the variation is, that would be helpful), so it can be regarded as constant with respect to temperature. I'll call this function C.

If we take the energy radiated away from the body, multiply by the cross-sectional area of the radiating portion (for simplicity's sake, we'll assume this is the same as the cross-sectional area used before), and multiply by the specific heat capacity of the material, we obtain an expression for temperature change per second:

$$\Delta K=\sigma T^{4}*A*SH$$

Combining the functions C and the radiating function provides the following differential equation:
$$\frac{dT}{dt}=C-\sigma T^{4}*A*SH$$

Not sure if this is solvable (probably not) for T as an explicit function of time, but this should represent a rough approximation of the temperature as a function of time.

8. Feb 16, 2009

### Nabeshin

Update:

For the specific choice of parameters described earlier, the maximum temperature achieved by the hull of the spacecraft is about 515K (this value is reached within about a month of continuous travel). Therefore I conclude that heat from molecular collisions is not a threat to any interstellar spacecraft.

9. Feb 16, 2009

### DaveC426913

Things that pose no practical limit on spaceship travel: friction, solar wind

Things that will pose a practical limit: blue-shifted hard radiation. As the craft approaches relativistic speeds, the normal radiation permeating space will climb up the EM band: Radio > visible > UV > X-Ray > Cosmic. This will become lethal if not mitigated.