Star A has an abs magnitude of 3. Star B has an abs magnitude 5. which statement is correct?

Question

If the radius of star A is smaller than the radius of star B then the temperature of star A is higher than the temperature of star B.

Star A is bluer than star B.

The radius of star A is larger than the radius of star B.

The apparent magnitude of star A is smaller than the apparent magnitude of star B.

Star A is closer to Earth than star B.

Answer 1

You can take it from me that the only self-consistent, stand-alone statement here that is CORRECT is STATEMENT 1:

"If the radius of star A is smaller than the radius of star B then the temperature of star A is higher than the temperature of star B."

The REASON for this is TWOFOLD,

First : that star A is INTRINSICALLY MORE LUMINOUS than star B. We can assert that because "absolute magnitude" is an INTRINSIC measure of luminosity. The absolute magnitude scale is essentially like a "ranking scale" (from more to less luminous) in which stars with a SMALLER absolute magnitude measure are more luminous ("brighter" in technically inaccurate popular language) than stars of HIGHER absolute magnitude measure. (Think "stars of 3rd brightest class" versus "stars of 5th brightest class" --- the 3rd brightest class is clearly brighter than the 5th brightest class.)

Second: the luminosity of a star, L, is proportional to its area (4 pi R^2) times the fourth power of its effective surface temperature, T^4. (For ease of writing I'm not using some lengthy subscript for that particular temperature --- I'm just calling it T.) I'll also just call the constant of proportionality in the whole equation C, incorporating the 4 pi into it. Then:

L = C R^2 T^4.

Then, for two different stars A and B, the ratios of their luminosities, radii and surface temperatures are connected by:

LA / LB= (RA / RB)^2 (TA / TB)^4, or equivalently (and better for our present purposes):

(LA / LB) (RB / RA)^2 = (TA / TB)^4.

O.K., now to draw our conclusion. We know LA > LB, or LA / LB > 1 (that was our first given). In addition, we've just been told that RA is SMALLER than RB, which means that RB is BIGGER than RA, or, in other words, RB / RA is also > 1.

So BOTH expressions multiplied together on the LHS are > 1, therefore the RHS is > 1, and thus TA / TB > 1.

And there we have it: the temperature of star A is higher than the temperature of star B.

NONE of the other statements, treated as stand-alone statements, are necessarily true because you don't have enough information to make them. Let's consider them, in turn, numbering them in further order:


2. "Star A is bluer than star B." You can't tell. You only know their absolute luminosities, and this time, NO information about their independent temperatures or radii. Without at least ONE of those bits of information, you can't go further.

3. "The radius of star A is larger than the radius of star B." Again, you can't tell, since you weren't given radius information directly, nor temperature information to help you infer the relative sizes of the radii.

4. "The apparent magnitude of star A is smaller than the apparent magnitude of star B." You can't say, since apparent magnitude differences depend on TWO things --- upon their absolute magnitudes AND upon their relative distances. Again, you've no information on the latter, so you can't say.

5. "Star A is closer to Earth than star B." Again, you simply can't tell --- you weren't given their apparent magnitudes, this time. Without those as well as their absolute magnitudes, you're sunk in trying to determine their relative distances!

This whole problem was clearly intended to make sure you understood how all these variables might or might not be connected, and which PAIRS of variables you need to have, in order to draw valid conclusions about the relative sizes of a third set of stellar properties.

Live long and prosper.

Answer 2

You can tell a star's total brightness by its absolute magnitude. The lower the number, the brighter it is. You can't tell total size that way, however, unless you assume they're main sequence stars. To calculate distance: d = √(A^2 M^(v-a)) d = distance A = 32.62 for light years or 10 for parsecs M = 2.512 v = apparent magnitude a = absolute magnitude

Answer 3

Tough Astronomy homework question that.

Try looking up what absolute magnitude means.
That should eliminate 2 for you right away.

Then check out the notes from the class you missed/fell asleep in which talked about giants. That'll eliminate another.

Meanwhile you may or may not care to reflect that the real object of taking a class is to learn something, not to scab the answers from somewhere. No-one is going to be there to give you the answers at job interviews.