1 pc = 206265 AU, so multiply this with 16,000 (since a kpc = 1000 pc) to get the distance in AU. Solution: Before you can do anything, you need to convert the distance (16 kpc) into AU. If the outermost part of a galaxy is 16 kpc from the center and it takes 350 million years for that part of the galaxy to orbit around once, how much mass is contained within that galaxy? They are just too small! But that's the way it works.ġ. The only complication with this formula is that the units for "a" and "P" are rather inconvenient for measuring distances within a galaxy. P = the period of their orbits given in years.a = the average distance they are apart, given in A.M galaxy = mass of the galaxy contained within the limit given by "a", values are in terms of the Sun's mass.This formula is really only useful for estimating the mass of a galaxy that has organized motion, like our Milky Way. Kepler's Third Law for Galaxy Masses - Just like the previous version of Kepler's third law, but here the value for "k" is defined as the mass within a certain distance from the center of the galaxy ("a" in the formula). Again, put in the numbers and start calculating How bright will the supernova be in the night sky (or what is its apparent magnitude)? These supernova usually reach an absolute magnitude of around -17 when they are their brightest. The astronomical unit (symbol: au, 1 2 3 4 or AU or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to 150 million kilometres (93 million miles) or 8.3 light-minutes. A type II supernova just went off in the Andromeda galaxy. To "un-log" (d), take 10 to the power of 4.88Ģ. Put the numbers you're given into the formula Solution: you are looking for d in this case. For a star with its pulsation period it should have an absolute magnitude of -4.2. A Cepheid has an apparent magnitude of +15.2. To get values for d, you'll need to use the "un-log" function, which is 10 x, or "10 to the power of a number".Īlso be careful about the signs in this formula (+/-) and make sure you remember to treat them properly.ġ. Multiplication always is before addition or subtraction. When using this formula, you have to remember the order of multiplying things and adding/subtracting things. Many calculators also have what's called a Natural Log, usually abbreviated Ln - don't use this. Magnitude - Distance Formula - used to give the relationship between the apparent magnitude, the absolute magnitude and the distance of objects. Solution: First you'll have to convert the parallax value from milli-arcseconds to arc-seconds, by dividing the number by 1000. A star is observed to have a parallax shift of.
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