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Calculating a star's radius is a somewhat lengthy process. You have to put together many tools that you have developed in various SkyServer projects. Even the largest star is so far away that it appears as a single point from the surface of the Earth - its radius cannot be measured directly. Fortunately, understanding a star's luminosity provides you with the tools necessary to calculate its radius from easily measured quantities.
A star's luminosity, or total power given off, is related to two of its properties: its temperature and surface area. If two stars have the same surface area, the hotter one will give off more radiation. If two stars have the same temperature, the one with more surface area will give off more radiation. The surface area of a star is directly related to the square of its radius (assuming a spherical star).
The luminosity of a star is given by the equation
L = 4pR2s T4,
Where L is the luminosity in Watts, R is the radius in meters, s is the Stefan-Boltzmann constant
(5.67 x 10-8 Wm-2K-4), and T is the star's surface temperature in Kelvin.
The temperature of a star is related to its b-v magnitude.
for b-v value go to link
The calculation is actually somewhat easier if we try to find the ratio of another star's radius to that of our Sun. Let Ls be the luminosity of the Sun, L be the luminosity of another star, Ts be the temperature of the Sun, T be the temperature of the other star, Rs be the radius of the Sun, and R be the radius of the other star.
We can then write the ratio of their luminosities as
L/Ls = (4pR2sT4)/(4pRs2sTs4) = (R/Rs)2(T/Ts)4
Solving for the ratio R/Rs yields
R/Rs = (Ts/T)2(L/Ls)1/2
The temperatures can be found approximately from the table above by looking at the B-V values. To find the ratio L/Ls, we can use the absolute magnitudes of the stars. The magnitude scale is a logarithmic scale. For every decrease in brightness of 1 magnitude, the star is 2.51 times as bright. Therefore, L/Ls can be found from the equation
L/Ls = 2.51Dm,
where Dm = ms - m
Let's look at the star Sirius. It has visual magnitude of -1.44, B-V of .009, and a parallax of 379.21 milli arc seconds. Finding its distance from its parallax yields
d = 1/p = 1/.37921 = 2.63 parsecs.
Its absolute magnitude is
M = m - 5 log d + 5 = -1.44 - 5 log (2.63) + 5 = 1.46
We know the temperature of the Sun is 5800K. From the chart, the temperature of Sirius is about 9500K. Our Sun has an absolute magnitude of 4.83. The difference in magnitude is 3.37. Putting everything together yields
R/Rs = (5800/9500)2(2.5123.37)1/2 = 1.76
Sirius has a radius approximately 1.76 times that of our Sun!
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How does he find the measure of a radius if he knows the measure of the diameter?
The radius of a circle is half the diameter.
How did they measure the diameter or radius of earth?
with a big tape measure
How do you find radius of can?
measure it÷ it by 2.
How do you find out the length of a radius?
Measure the diametre of the circle and divide by two to give the radius.
How do you find the measure of an arc knowing only the chord of arc and radius?
you have a triangle formed by the radius on 2 and the chord on the other. the angle in that triangle that is opposite the chord, find its measure in radians take that measure (in radians) and multiply it by the radius to get the arc length
How does he find the measure of a radius if he knows the measure of the diameter?
The radius of a circle is half the diameter.
How do you measure the radius?
measure from the middle out to one side
Do stars that are very hot and very dim have a small mass or a small radius?
stars that are dim probably have both a small mass and a larger radius.
How did they measure the diameter or radius of earth?
with a big tape measure
What unit would you use to measure the distances from stars?
To measure the distance of stars you have to measure by light years.
What is the measure of the radius of M?
7.4
How do find the radius of a circle?
measure it
How do you find radius of can?
measure it÷ it by 2.
How do you get the radius of a cylinder?
If you have a physical cylinder to measure, measure the "width" of the circle that is the cross section of the cylinder. That is the diameter, Half the diameter is the radius.
What is used to measure spherical radius?
You can measure the diameter, then divide that by 2.
How can you use radius in a sentence?
The teacher explained how to measure the area of a circle using radius.
How do you find out the length of a radius?
Measure the diametre of the circle and divide by two to give the radius.
