Temperature of Asteroid When Sun Emits @ 6000K 350M Km Away

OUNT OF ENERGY ABSORBED = AMOUNT OF ENERGY EMITTED\phi = \sigma T^4 = \epsilon \sigma T_s^4T_s = \sqrt[4]{\frac{\phi}{\epsilon \sigma}}In summary, the temperature of the asteroid, assuming it is a black body, can be calculated using the Stefan's law and the equation for energy balance between absorption and emission, and is found to be T_s = \sqrt[4]{\frac{\phi}{\epsilon \sigma}}.
  • #1
babtridge
16
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If the sun at temperature 6000K emits onto an asteroid 350million km away, what is the temperature of the asteroid assuming it is a black body?

Any suggestions how to go about this please? :confused: :confused:
 
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  • #2
babtridge said:
If the sun at temperature 6000K emits onto an asteroid 350million km away, what is the temperature of the asteroid assuming it is a black body?

How much energy does the asteroid receive from the sun per unit time? How hot must it be to radiate this energy away at the same rate?

HINT: You'll need the equations for flux and the luminosity of a blackbody.
 
  • #3
babtridge said:
If the sun at temperature 6000K emits onto an asteroid 350million km away, what is the temperature of the asteroid assuming it is a black body?
Determine the radiation flux incident on the asteroid using the Stefan's law:

[tex]P = \sigma T^4[/tex] where P is the total power.

[tex]\phi = P/A = \frac{\sigma}{4\pi d^2}T^4[/tex]

The asteroid will absorb this radiation and raise its temperature until it is emitting at the same rate as it is absorbing, at which point its temperature wlll remain constant. The question asks you to find that temperature. It is a little tricky.

AM
 

Related to Temperature of Asteroid When Sun Emits @ 6000K 350M Km Away

1. What is the temperature of an asteroid when the sun emits at 6000K and the asteroid is 350 million kilometers away?

The temperature of an asteroid when the sun emits at 6000K and the asteroid is 350 million kilometers away is approximately 20K (-253.15°C or -423.67°F). This is because the asteroid is receiving a very small amount of energy from the sun, which is significantly reduced due to the inverse square law.

2. How does the distance from the sun affect the temperature of an asteroid?

The temperature of an asteroid decreases as it gets further away from the sun. This is because the energy from the sun spreads out over a larger area, resulting in less energy reaching the asteroid. This relationship is described by the inverse square law.

3. What is the significance of the sun's emission at 6000K in relation to the asteroid's temperature?

The sun's emission at 6000K is important because it is the average temperature of the sun's surface. This is the temperature at which the sun emits the most energy, which then travels through space and ultimately affects the temperature of objects, such as asteroids, that are in its path.

4. Is the temperature of an asteroid affected by factors other than the sun's emission and distance?

Yes, the temperature of an asteroid can also be affected by its composition, size, and rotation. Different materials have different abilities to absorb and retain heat, and a larger asteroid will have a greater surface area for the sun's energy to act upon. The rotation of the asteroid can also affect its temperature by exposing different areas to the sun's energy at different times.

5. How can scientists measure the temperature of an asteroid when it is 350 million kilometers away from the sun?

Scientists can measure the temperature of an asteroid using infrared spectroscopy, which detects the thermal radiation emitted by the asteroid. This allows them to determine the temperature of the asteroid's surface, even from a great distance. Other methods, such as thermal imaging, can also be used to estimate the temperature of an asteroid.

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