A star 56 pc away has an apparent magnitude of 6.9. What is its absolute magnitude?

Expert Answers
lemjay eNotes educator| Certified Educator

To solve, apply the formula:


d is the distance of the star from the Earth in parsecs

m is the apparent magnitude of the star, and

M is the absolute magnitude.

Plugging-in the values of d and m to the formula, it yields an equation:

`56=10 * 10^((6.9-M)/5)`

Then, solve for M. To do so, divide both sides by 10.


Then, take the logarithm of both sides.


The right side simplifies to:


Then, multiply both sides by 5.


Subtract 6.9 from both sides.

`5log5.6 - 6.9=-M`

And, divide both sides by -1.

`-5log5.6 + 6.9=M`

`6.9- 5log5.6=M`


Rounding off to nearest tenths, it becomes:


Therefore, the absolute magnitude of the star is 3.2 .