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{{Infobox scientist |
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The surface temperature of a planet can be calculated by equating the power received by the planet with the power emitted by a blackbody of temperature <var>T</var>. |
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| name = David Kipping |
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| fields = [[Astronomy]] |
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| workplaces = [[Columbia University]] |
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| alma_mater = [[University College London]] (Ph.D. 2011) <br> [[University of Cambridge]] (M.Sc 2007, M.A. 2006) |
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| doctoral_advisor = [[Giovanna Tinetti]] |
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| known_for = [[Exomoons]] <br> [[Exoplanets]] |
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| awards = [[Keith Runcorn Prize]] (2012) |
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'''David Kipping''' is an assistant professor of astronomy at [[Columbia University]]. His primary research interests include [[Exoplanets]], [[Exomoons]], and [[Astrostatistics]]. |
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Take the case of a planet at a distance <var>D</var> from a star of [[luminosity]] <var>L</var>. |
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== Research == |
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Here the area of the planet that absorbs the power from the star is <var>A<sub>abs</sub></var> which is some fraction of the total surface area <math>A_{\rm total} = 4 \pi r^2</math> where <var>r</var> is the radius of the planet. This area intercepts some of the power which is spread over the surface of a sphere of radius <var>D</var>. We also allow the planet to reflect some of the incoming radiation by incorporating a parameter <var>a</var> called the [[albedo]]. An albedo of 1 means that all the radiation is reflected, an albedo of 0 means all of it is absorbed. The expression for absorbed power is then: |
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<math>P_{\rm abs} = \frac {L A_{\rm abs} (1-a)}{4 \pi D^2}</math> |
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== References == |
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The next assumption we can make is that the entire planet is at the same temperature <var>T</var> and the power is radiated over an area <var>A<sub>rad</sub></var> which is again some fraction of the total area of the planet <math>A_{\rm total} = 4 \pi r^2</math> where <var>r</var> is the radius of the planet. There is also a factor <var>ε</var>, which is the [[Emissivity]] and represents atmospheric effects. ε ranges from 1 to 0 with 1 meaning the planet is a perfect blackbody and emits all the incident power. The [[Stefan–Boltzmann law]] gives an expression for the power radiated by the planet: |
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{{reflist}} |
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== External links == |
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<math>P_{\rm rad} = A_{\rm rad} \varepsilon \sigma T^4</math> |
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* [http://www.davidkipping.co.uk/ David Kipping Homepage] |
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Equating these two expressions and rearranging gives an expression for the surface temperature: |
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* {{Google Scholar id|UXY08zEAAAAJ}} |
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* [http://coolworlds.astro.columbia.edu/ Cool Worlds Lab] |
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{{DEFAULTSORT:Kipping, David}} |
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<math>T = \left (\frac{A_{\rm abs}}{A_{\rm rad}} \frac{L (1-a)}{4 \pi \sigma \varepsilon D^2} \right )^{\tfrac{1}{4}}</math> |
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[[Category:Living people]] |
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[[Category:Year of birth missing (living people)]] |
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Note the ratio of the two areas. Common assumptions for this ratio are 1/4 for a rapidly rotating body and 1/2 for a slowly rotating body. This ratio would be 1 for the [[subsolar point]], the point on the planet directly below the sun and gives the maximum temperature of the planet.<ref>Swihart, Thomas. "Quantitative Astronomy". Prentice Hall, 1992, Chapter 5, Section 1.</ref> |
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Lets look at the Earth. The Earth has an albedo of 0.367<ref>http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html</ref>. The emissivity is more variable and there are many [[climate models]] for it but a good average for Earth is 0.5. The Earth is a fairly fast rotator so the area ratio can be estimated as 1/4. The other variables are constant. This calculation gives us an effective tempurature of the Earth of 298K. Considering how complicated the system is, this is a good estimate. |
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Also note here that this equation does not take into account any effects from internal heating of the planet. |
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{{Reflist}} |
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Revision as of 20:26, 21 November 2019
David Kipping | |
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| Alma mater | University College London (Ph.D. 2011) University of Cambridge (M.Sc 2007, M.A. 2006) |
| Known for | Exomoons Exoplanets |
| Awards | Keith Runcorn Prize (2012) |
| Scientific career | |
| Fields | Astronomy |
| Institutions | Columbia University |
| Doctoral advisor | Giovanna Tinetti |
David Kipping is an assistant professor of astronomy at Columbia University. His primary research interests include Exoplanets, Exomoons, and Astrostatistics.
Research
References
External links
- David Kipping Homepage
- Jhmadden/sandbox publications indexed by Google Scholar
- Cool Worlds Lab