hey what does the unit sr stand for as used here http://www.n3kl.org/sun/images/noaa_proton_G8_3d.gif?
This unit is the "steradian," and it reasures what is called "solid angle." Solid angle is a concept that most people do not get introduced to until they take physics or university mathematics. The definition of steradian works by analogy with the definition of the ordinary radian.
radian: Start with a circle of radius R, and select an arc of the circle. Now measure the length of that arc (S) and divide by the radius of the circle (R ) to get the radian measure of the angle, theta = S/R.
steradian: Start with a sphere of radius R and select a patch of area on the sphere. Now measure the area of that patch (A) and divide it by R^2 to get the steradian measure of the solid angle, omega = A/R^2.
Things to notice here:
The radian is defined as a ratio of lengths, and the steradian as a ratio of areas, so both are dimensionless and are independent of size. If you scale up the picture, bot R and S (and R^2 and A) will grow proportionately, so the ratios remain constant.
The radian is defined without mentioning two lines forming an angle. This is because you can always draw two lines from the center of the circle to the ends of your arc, and the angle between these lines is theta. Similarly, for the steradian you could draw lines from the boundary of your area patch to the center of the sphere, forming a cone (not necessarily a cone with smooth sides, of course, its cross section would be the same shape as the patch of area). You could say that the solid angle formed at the point of the cone is omega, but this is harder to picture than with the ordinary angle between two lines.
For the radian, the measure of an entire circle is of course (2piR)/R = 2pi, which is the origin of the fact that 2pi radians = 360 degrees. In the case of steradians, the measure of th entire sphere is (4piR^2)/R^2 = 4pi, so there are 4pi steradians in a complete sphere.
Radians are an appropriate way of measuring visual distance independent of actual distance. For instance, the angle between the line of sight to two stars determines the distance between their images on your retina, and has little to do with how far the stars are away from each other. This produces your visual sense of separation. Similarly, steradians are an appropriate way of measuring visual size independent of distance. The steradian measure of the cone of light entering your eye from an object determines how much area the image will take up on your retina, and and has little to do with the actual size of the object. A nearby toy house and a distant real house could "appear the same size" in the sense that they occupy the same number of steradians of solid angle.
Hope that helps!
--Stuart Anderson
radian: Start with a circle of radius R, and select an arc of the circle. Now measure the length of that arc (S) and divide by the radius of the circle (R ) to get the radian measure of the angle, theta = S/R.
steradian: Start with a sphere of radius R and select a patch of area on the sphere. Now measure the area of that patch (A) and divide it by R^2 to get the steradian measure of the solid angle, omega = A/R^2.
Things to notice here:
The radian is defined as a ratio of lengths, and the steradian as a ratio of areas, so both are dimensionless and are independent of size. If you scale up the picture, bot R and S (and R^2 and A) will grow proportionately, so the ratios remain constant.
The radian is defined without mentioning two lines forming an angle. This is because you can always draw two lines from the center of the circle to the ends of your arc, and the angle between these lines is theta. Similarly, for the steradian you could draw lines from the boundary of your area patch to the center of the sphere, forming a cone (not necessarily a cone with smooth sides, of course, its cross section would be the same shape as the patch of area). You could say that the solid angle formed at the point of the cone is omega, but this is harder to picture than with the ordinary angle between two lines.
For the radian, the measure of an entire circle is of course (2piR)/R = 2pi, which is the origin of the fact that 2pi radians = 360 degrees. In the case of steradians, the measure of th entire sphere is (4piR^2)/R^2 = 4pi, so there are 4pi steradians in a complete sphere.
Radians are an appropriate way of measuring visual distance independent of actual distance. For instance, the angle between the line of sight to two stars determines the distance between their images on your retina, and has little to do with how far the stars are away from each other. This produces your visual sense of separation. Similarly, steradians are an appropriate way of measuring visual size independent of distance. The steradian measure of the cone of light entering your eye from an object determines how much area the image will take up on your retina, and and has little to do with the actual size of the object. A nearby toy house and a distant real house could "appear the same size" in the sense that they occupy the same number of steradians of solid angle.
Hope that helps!
--Stuart Anderson
champion !
thankyou for educational response
thankyou for educational response