The small angle formula is an approximation of trigonometry. The basic concept is based upon something like this. (usually written as ) represents the linear diameter of the object being measured. This could be a single object, like the moon, or the separation between two stars in a binary system. (usually written as ) is the distance to the object, and is of course the angle. You can write as an equation representing the system. This works if and are measured in the same units, and if is measured in radians.Thank you so much! it helped me so much
But may I ask, what is the small angle formula?
The small angle formula is an approximation for very large values of (and hence very small values of ) where the formula is approximately .
To get a more useful form of this equation, note that 1 radian = 206265 arcseconds, and 1 parsec = 206265 AU. This means that the function is also valid if is is AU, is in parsecs, and is in arcseconds. These are the units you're most likely to see in problems.
It can be in any unit, so long as G (the gravitational constant) is expressed in the same units; the units should cancel out to end up as units of force.For Newton's Law of Gravitation in what unit is R? (star separation distance)
How do I convert? I can't find any reliable ways of doing it (and I'm not entirely sure how to derive the formula).for 2a you look at the peak in B and see that it is slightly above 2446560 JD. Convert a value of around 2446562 JD to the Gregorian calendar and you should get around may 11th, 1986, which is probably pretty close.On the same test: can anyone explain how to do 2.a and 2.c?
(that was a great test btw, I ended up scoring ~55 or so).