1. What solar temp is needed for the peak intensity of radiation to occue at .2 micrometers? Remembering that humans can see light only between .4 and .7 microns, would the sun look brighter or dimmer at this new temp?
2. How much variation in earth orbital distance from the sun is needed to alter the solar constant by 10%?
THANKS!!
gsd
1. To determine the solar temperature at which the peak intensity of radiation occurs at 0.2 micrometers, we can use Wein's Law. Wein's Law states that the wavelength at which the peak intensity occurs is inversely proportional to the temperature: λmax = b / T, where λmax is the wavelength of maximum intensity, b is a constant, and T is the temperature.
First, we need to convert the wavelength to meters since the units in Wein's Law are in meters. 0.2 micrometers is equal to 0.2 × 10^-6 meters.
Now we have the equation: λmax = b / T = 0.2 × 10^-6 m.
Solving for T, we have:
T = b / λmax.
Let's assume b is a constant value of 2.898 × 10^-3 m·K.
T = 2.898 × 10^-3 m·K / 0.2 × 10^-6 m = 2.898 × 10^4 K.
Therefore, the solar temperature needed for the peak intensity of radiation to occur at 0.2 micrometers is approximately 28,980 Kelvin.
Regarding whether the Sun would look brighter or dimmer at this new temperature, it depends on how the human eye perceives different wavelengths of light. Since humans can see light between 0.4 and 0.7 micrometers, we observe visible light primarily in the green to red region. If the peak intensity moves to 0.2 micrometers (UV region), the Sun will emit more ultraviolet radiation than visible light, which our eyes are not sensitive to. Consequently, the Sun would appear dimmer to us since we can't sense that high energy radiation as well.
2. The solar constant is a measure of the amount of solar radiation received at Earth's distance. To calculate the variation in Earth's orbital distance required to alter the solar constant by 10%, we can use the inverse square law.
The solar constant represents the average amount of solar irradiance received at the Earth's distance from the Sun, which is approximately 149.6 million kilometers. Let's assume the solar constant is 1361 Watts per square meter (W/m²).
The inverse square law states that the intensity of radiation decreases as the square of the distance from the source. So, to increase or decrease the solar constant by a certain percentage, we need to adjust the distance using the inverse square relationship.
Let's assume we want to alter the solar constant by increasing it by 10%. To calculate the required change in Earth's orbital distance, we'll use the formula:
(ΔD / D)^2 = 1 + (ΔC / C),
where ΔD is the change in Earth's orbital distance, D is the average distance from the Sun, ΔC is the change in the solar constant, and C is the original solar constant.
Rearranging the formula, we get:
ΔD = D × sqrt(1 + (ΔC / C)) - D.
Plugging in the values:
ΔD = 149.6 million km × sqrt(1 + (0.10)) - 149.6 million km.
Calculating this, we find:
ΔD ≈ 4.85 million kilometers.
Therefore, to alter the solar constant by 10%, Earth's orbital distance from the Sun would need to change by approximately 4.85 million kilometers.