Question: How do scientists measure the temperature of the earth's core, the sun's surface and the temperature of other planets?

Susan Cartwright answered on 14 Jun 2015:

The Sun’s surface temperature is measured directly from the radiation it emits. There are several ways to do this. First, the Sun is a hot dense object, and like other hot dense objects it emits light with a spectrum – that is, a distribution of intensity against wavelength – described by the Planck function, which depends on temperature. In principle, you fit the Sun’s spectrum to the Planck function and read off the temperature. In practice, the Sun’s spectrum is not an exact Planck function, so what you do is work out the temperature that corresponds to the same total amount of energy emitted. This is called the effective temperature, and is what you find tabulated in books on the properties of stars. For the Sun it is 5780 K.

Another method is to use the dark absorption lines that we see in the spectrum of the Sun. These are caused by electrons in atoms absorbing photons of exactly the right wavelength to supply the energy they need to get them to a higher quantum energy level – a quantum leap, in the original scientific sense. Different atoms, and even different ionisation states of the same atom, produce different lines. By comparing the strengths of different lines, and our understnading from laboratory measurements and quantum mechanics of the temperature dependence of these lines, we can derive an “ionisation temperature” (comparing lines from different ionisation states of the same element) or an “excitation temperature” (comparing lines from different energy levels in the same ionisation state of the same atom). The numbers you get from this depend on the atom involved and the lines you use – the reason for this is that the lines are formed in the layers immediately above the visible surface of the Sun, and their temperatures aren’t all the same. All these different numbers are “real” temperatures, and they all help us to understand the structure of the solar atmosphere, but the effective temperature is the single most representative number.

Planetary temperatures are found in the same sort of way, aided in many cases by direct measurements from space probes. Note that different measurements can give very different – though still “real” – results: the temperature of the Venus cloud tops, which are all we can see in a telescope, is very different from the temperature of the planet’s surface.

The temperature of the Earth’s core is different: we can’t measure it directly. Instead, we determine the structure of the Earth’s interior by studying earthquakes, and then try to model its temperature by a combination of computer modelling and laboratory experiments. The earthquake data tell us that the Earth’s inner core is solid, and theoretical modelling tells us that it is mostly an alloy of nickel and iron, with some impurities such as gold (in the Earth’s early molten state, the heavy stuff sank into the core). Laboratory measurements of the melting point of nickel-iron alloys at the pressure encountered at this depth (about 3.5 million times atmospheric pressure!) suggest that the temperature of the Earth’s core is – coincidentally – about the same as the surface temperature of the Sun.