how do people calculate the size and temperature if planets and stars.
In: Mathematics
People have mentioned how it works for stars, but for planets it’s much harder (assuming its exoplanets).
Most detections of exoplanets involve the planet crossing their host star in our line of sight, like of like how our moon eclipses our sun. We can measure the dip in brightness of the host star, calculate the size the planet must be to cause that dip.
We can also measure the duration of the dip in brightness, which gives us a measurement of the period of the orbit, which also tells us how far the planet is away from the star. From that, we can calculate how much energy it receives from the star and how hot it could be, but the actual temperature depends on the chemical composition of the planet and the atmosphere.
Paralax is used to measure distance, and it’s created by two different points of view. For example, if you close one eye at a time and look at an object without moving your head, you notice that the object has different views. The farther the object is the smaller the paralax effect is. Scientist take a photo from two different points of view, usually opposites sides of earth’s orbit and the distance be calculated with simple trigonometry. Scientists can compare emission spectrums from the object and find its composition, if the light emitted by the object appears to be shifted to the high energy side of the light spectrum, it’s blue shifted and moving closer to us, if it’s shifted to the low energy side, it’s red shifted and moving away from us. The hotter an object is, the brighter it is and by comparing the star to a theoritical perfect emitter of light, aka a blackbody, we know its temperature. The moon can be used to measure the star’s diameter. Scientists know how fast the moon moves through it’s orbit. They measure how long it takes for the star to be covered by the moon and with the distance calculated earlier, a measurement can be made.
Temperature for stars is fairly easy, stars emit a blackbody spectrum which is temperature dependent. If you measure the distribution of colours emitted by the star then you can determine its temperature. Hotter stars are more blue, cooler stars more red.
Size you can again work out by the light emitted. If you know how bright a star appears and you know it’s distance then you can work out how much light it is emitting in total. This depends only on its temperature and surface area, since we know the temperature this gives us the surface area. We know the relation between the size of a sphere and it’s surface area.
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