How would I calculate how close a ship can approach the sun?

In summary, a spherical ball of radius 1m radiates energy according to Stefan-Boltzmann law. The distance needed for incoming and radiated energy to be equal is calculated using the inverse square law.
  • #1
CricK0es
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Homework Statement


It's not a piece of homework, I'm doing a project and I've been wondering how I may be able to show it mathematically. I've covered the material before but it was a long long time ago...

Homework Equations

The Attempt at a Solution


[/B]
A-Thinking about modelling my "ship" as a spherical ball of radius, 1m.
B- Use Stefan-Boltzmann Law to determine how much energy is radiated, under the assumption it's a blackbody, at its maximum temperature.
C- Then assuming the radiated energy is equal to the incoming energy from the sun.
D- Calculating the distance required for these two values to be equal.

I feel like it's fairly hand wavey but it doesn't have to be particularly accurate, just a ball park figure. But for D, is it sufficient to use the inverse square law for intensity, or would I have to be more rigorous. As in, treating every point on the surface of the sun as a point source and integrating... Probably too complicated for what I'm looking for.

Anywho. Any help would be appreciated and thank you in advance.
 
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  • #2
I guess this will be basically a matter of shielding and what has to be shielded: life or just electronics? If it is life, then even leaving the van Allen belt couldn't be said safe. The preferred material for such a shielding is water, so I would look for absorption rates of water, and don't forget all kind of particles and radiation.
 
  • #3
fresh_42 said:
I guess this will be basically a matter of shielding and what has to be shielded: life or just electronics? If it is life, then even leaving the van Allen belt couldn't be said safe. The preferred material for such a shielding is water, so I would look for absorption rates of water, and don't forget all kind of particles and radiation.

I'm just considering the pure structure of the ship as opposed to having any lifeforms aboard and for the time being I'm focusing on IR and Visible wavelengths
 
  • #4
The Wikipedia article on the Stefan-Boltzmann Law has a section titled Effective Temperature of the Earth which you will find informative. :wink:
 
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  • #5
gneill said:
The Wikipedia article on the Stefan-Boltzmann Law has a section titled Effective Temperature of the Earth which you will find informative. :wink:
Ahhh that's absolutely perfect. Thank you ;)
 

1. How can I determine the safe distance for a ship to approach the sun?

To calculate the safe distance for a ship to approach the sun, you would need to use the equation of universal gravitation: F = G(m1m2)/r^2. G is the universal gravitational constant, m1 and m2 are the masses of the sun and the ship respectively, and r is the distance between the two. By setting F equal to the force required to overcome the gravitational pull of the sun, you can solve for r to determine the safe distance.

2. Is there a specific unit of measurement to use when calculating the distance a ship can approach the sun?

Yes, the standard unit of measurement for distance in scientific calculations is meters (m). However, for larger distances, astronomical units (AU) are often used. 1 AU is equal to the average distance between the Earth and the sun, which is about 149.6 million kilometers or 93 million miles.

3. Can I use the same calculation for any type of ship?

Yes, the equation for determining the safe distance to approach the sun applies to any object, regardless of its size or shape. However, the mass of the ship should be taken into consideration when calculating the force of gravity.

4. How accurate is this calculation for determining the safe distance to approach the sun?

The calculation is highly accurate, as it is based on the fundamental laws of physics. However, it is important to note that there may be other factors at play, such as solar wind and radiation, that could affect the safe distance for a ship to approach the sun.

5. Are there any other methods for determining the safe distance for a ship to approach the sun?

There are other methods, such as using computer simulations or advanced mathematical models, that can also be used to determine the safe distance for a ship to approach the sun. However, these methods may require more advanced knowledge and technology.

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