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Summary of Current Information
 A. The Parent Star B. The Exoplanet

### III. Calculating the Surface Temperature of the Exoplanet

As a reasonable first approximation, the surface temperature of a planet can be related to how far the planet is from the parent star and how large and how hot the parent star is. To begin, the surface temperature and radius of each spectral type of star, as determined by astronomers, is presented below.

 SPECTRAL TYPE 5 B0 B5 A0 A5 F0 F5 G0 G5 K0 K5 M0 M5 Radius (sol. rad.) 17.8 7.59 3.98 2.63 1.78 1.35 1.20 1.05 0.93 0.85 0.74 0.63 0.32 Temperature (K) 35000 21000 13500 9700 8100 7200 6500 6000 5400 4700 4000 3300 2600
(Note: 1 AU = 215 solar radii.)

Locate the necessary information for this exoplanet and its star from the table above. Then enter the appropriate values in the form below. Remember that the formula is:

 Tp = (Rstar / 2 apl)1/2 Tstar
 ( K) = [( solar radii / 215 ) / (2 AU)]1/2 K (Press the calculate button to estimate the average surface temperature of the exoplanet.)

where

• Tp is the average surface temperature of the planet in Kelvin degrees
• Rstar is the radius of the parent star in AU
• a is the average distance the planet is from the star, i.e., the semi-major axis of the planet's orbit about the star, in AU.
• Tstar is the surface temperature of the parent star in Kelvin degrees
(Note: The 1/2 power represents the square root of the quantity in parentheses.)

Press the "Next Page" button to continue your analysis.

### Explanations

Notes on Temperature Scales

There are three primary temperature scales used throughout the world in science, commerce and everyday life.

1. Fahrenheit - used mainly in the United States for everyday temperatures. Water freezes at 00F and boils at 2120F.
2. Celsius - most widely used temperature scale around the globe. Water freezes at 00F and boils at 2120F.
3. Kelvin - used mainly in certain areas of physical science such as astronomy. It uses the same size of degrees as does the Celsius scale, but a Kelvin temperature has a value 273.15 degrees higher than the corresponding Celsius temperature. Rounding to a whole degree, water freezes at 273 K and boils at 373 K.
 Some Temperature Points gold melts Venus surface lead melts water boils Earth (average) water freezes Mars surface oxygen liquifies absolute zero 1336 K 730 K 600 K 373 K 290 K 273 K 180-270 K 90 K 0 K

Notes on Habitable Planets and Temperature

Several factors determine the surface temperature of a planet:

• The surface temperature and size of the parent star.
• The distance the exoplanet is from the parent star.
• The albedo of the exoplanet - the fraction of light reflected from the planet compared to that impinging on the planet.
• The emissivity of the exoplanet - a measure of how well a planet radiates thermal energy.

If one assumes that the exoplanet has a significant atmosphere (a necessity for a habitable planet) and is a perfect absorber and radiator (that is, albedo and emissivity effects are ignored), then the average temperature of the surface of the exoplanet, in Kelvin degrees, can be estimated by the formula used above.

For a planet to be habitable for life as we know it, its surface temperature must be restricted to a fairly narrow range. Since water is one primary necessity, the planet's temperature must be considerably less than the boiling point of water and generally higher than its freezing point. (We can survive at temperatures less than the freezing point of water for periods of time, but our food supply from plants depends upon temperatures well above the freezing point of water.

Thus the broadest temperature range for life is between 0oC (32oF) and 100oC (212oF). This translates to 273 K and 373 K. (These temperatures are for one atmosphere of pressure. If the pressure is less or more than this, then these temperatures will be somewhat lower or higher than those given here.)

Hints (Reminders)

• Use the appropriate buttons. Do not press the "Enter" key.
• Enter or change numbers only in the appropriate boxes.
• Complete all "calculations" in order from the top of the page to the bottom.