I need to find a formula that will allow me to calculate the temperature at any distance from the sun

February 2nd, 2011 @10:50 am

Extrapolate the formula, using the surface temoerature, and instead of the earth distance, substitute the distance you want to caluclate the temperature at.

Measuring the Sun’s Temperature

One method, called Wien’s law, uses the wavelength of the peak emission, wavelengthpeak, in the Sun’s continuous spectrum. The temperature in Kelvin = 2.9 × 106 nanometers/wavelengthpeak.

Another method uses the flux of energy reaching the Earth and the inverse square law. Recall from the Stellar Properties chapter that the flux is the amount of energy passing through a unit area (e.g., 1 meter2) every second. From the Inverse Square Law of Light Brightness, you find that the solar flux at the Earth’s distance = the Sun’s surface flux × (Sun’s radius/Earth’s distance)2 = 1380 Watts/meter2. Since the Sun’s photosphere is approximately a thermal radiator, the flux of energy at its surface = sigma × (the Sun’s surface temperature)4, where sigma is the Stefan-Boltzmann constant. Rearranging the equation, the photosphere’s temperature = [(solar flux at Earth)/sigma) × (Earth distance/Sun's radius)2]1/4.

These two methods give a rough temperature for the Sun of about 5800 K. The upper layers of the photosphere are cooler and less dense than the deeper layters, so you see absorption lines in the solar spectrum. Which element absorption lines are present and their strength depends sensitively on the temperature. You can use the absorption line strengths as an accurate temperature probe to measure a temperature of about 5840 K.

Read the link, you’ll have to scroll down to come up to the stuff I have cut and paste above.

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Hope you find this useful.

February 2nd, 2011 @11:13 am

There are many variables that need specified. For example, is the temperature you want to measure a black body temperature? Or, is it the temperature earth might be at that distance? On a planet with an atmosphere the temperature is controlled not only by the amount of heat provided by the sun, but also the amount of heat reflected by clouds in the atmosphere and the amount retained by the insulating effect of the atmosphere.

February 2nd, 2011 @11:23 am

With a very lomg probe.

that’s a weird ?