Radiation from the Sunkeeps us all alive, but with the thinning of the ozone layer, it is important to limitexposure. The intensity of radiation is inverselyproportional to the square of the distance thatthe Sun’s rays travel.The formula
I=k/d^2 models the relationshipbetween intensity, I , inwatts per square metre (W/m^2), and distance, d , in astronomical units (AU). The intensity of radiation from the Sun is 9140 W/m^2 on Mercury, which is 0.387 AU away.
If the intensity on Earth is x, then
since Id^2 = k is constant,
9140*.387^2 = 1x
As for rate of change, who says it's changing?
Determine the intensity of radiation andits rate of change on Earth, which is 1 AUfrom the Sun.
The answer says the ROC is -2737.8
To find the constant of proportionality, k, in the formula "I = k/d^2," we can use the given intensity and distance values for Mercury.
1. Start by rearranging the formula to solve for k:
I = k/d^2
k = I * d^2
2. Substitute the given values into the equation:
k = 9140 W/m^2 * (0.387 AU)^2
3. Calculate the value of k:
k ≈ 1346.8897 W/m^2 * AU^2
Therefore, the constant of proportionality, k, is approximately 1346.8897 W/m^2 * AU^2.
This value can be used to determine the intensity of radiation at different distances from the Sun using the formula I = k/d^2, where I is the intensity in watts per square meter (W/m^2) and d is the distance in astronomical units (AU).