Astrophysics: nuclear reactions orbital period spectral class equivalence principl

[creepypasta13]

Homework Statement

1. Suppose you are told that a star has been observed with a UBV color index of B-V=1.6 and that interstellar reddening is negligible. In addition, its apparent visual magnitude is 9.8. Detailed spectroscopy also reveals that the star has all the characteristics of a main sequence star (luminosity class V).
A) what is the spectral class of the star?
B) What is the bolometric correction?
C) What is the effective temperature?

2. An article in the Feb 2000 issue of SciAm on the equivalence principle suggests a problem. Gravitational binding energies are negative, but by mc^2 arguments, so should the mass associated with this energy be negative. Thus ,for example, the total mass of the sun should be less than the sum of its material parts when that negative mass is taken into account. Assuming the sun to be a constant density sphere, or anything else that is reasonable, by that fraction is the sun's mass decreased when gravitational binding energies are included?

The Attempt at a Solution

1. The textbook didn't cover this (it explicitly mentioned that you have to refer to another book to solve this). I looked up that other book, and couldn't find a table anywhere with B-V=1.6 IIRC. But it had a value close, about 1.57 I think, and mentioned that a star with 1.57 is red (cool). I then saw that red (cool) stars are Spectral Class M5 (from Table 3-3 in 'Galactic Astronomy' by Mihalas and Binney. Is this the right Spectral class?

2. I set the 'negative' mass equal to E_bind/c^2 = (3/5)*(G*M_sun^2)/(R_sun*c^2), as E_bind = (3/5)*(GM^2/R). Is that right? Then I set the 'new' mass = M_sun + M_negative

 

[NateD]

, and the 'original' mass = M_sun. Then I solved for the fraction by dividing new mass by original mass, which was quite simple. Is this the right approach?