General Science 2310

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STELLAR PROPERTIES

RADIUS

Reading from text : not covered

The prevailing model we have of stars suggests that all stars are spherical in shape, The one piece of information necessary to specify the spatial dimensions of a star is the radius of the sphere.
If you know the distance to a star, you can measure its radius directly by measuring the angle from one edge to the other the angular diameter. We can measure the radius of the Sun directly. The angle that the Sun subtends as viewed from Earth is about 0.5 degrees of arc or 1,800 arc seconds. Of all the stars listed in table 14.2 of the text, only the radii of Betelgeuse and Alderbaran have angular diameters more than a few milli arc seconds, all the others are much too small to be measured directly.
Lunar Occultation is a technique in which the angular diameter of a star is measured by timing an event in which the light from the star is eclipsed by the Moon. The clock starts as the light begins to diminish and stops when the light has been totally blocked
This is only possible because the moon has almost no atmosphere and its angular speed is very well known. It takes the Moon about 27.3 days to complete one sidereal revolution, So the Moon moves through about 0.5 arc seconds every second, so to move through an angular diameter of one milli arc second it takes the Moon about 2 milliseconds which is easily within the capacity of modern timing equipment.
Only stars within 5 degrees of the ecliptic can be measured by Lunar Occultation. A star that is part of an eclipsing binary system can also have its diameter measured by timing methods. A binary star is a member of a system of two stars that revolve around their center of mass. An eclipsing binary is a binary star whose plane of orbit is exactly on the line of sight from Earth. In the case of an eclipsing binary you know that when the stars appear maximally separated they are moving either directly away from us or directly towards us, so that a careful analysis of the Doppler shifted spectrum will yield their true speeds. Knowing the true speeds, the timing of an eclipse will give the diameters of both stars, The duration of totality will allow you to measure the difference in diameters, and the duration of partial eclipse will give you the diameter of the smaller star.
More commonly the diameters of stars are calculated from their luminosity and their temperature. Given the temperature, you can use the theory of blackbody radiation to calculate the total power per unit surface area ( recall this is proportional to T⁴), so you can infer the surface area of the star by dividing the luminosity ( total power output) by the total power per unit surface area. Then assume the star is spherical, it is a simple matter to calculate the radius once you know the surface area.

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