Problem #1: You observe that a K star in a star cluster has a flux of 6.23 x 10-14 W/m2.
a) Assuming that this K star is a Main Sequence star and that Main Sequence K stars have a luminosity of 0.4 Lo, calculate the distance to the star cluster.
b) Further observations shows that this particular K star is actually a red giant star (i.e., it's not on the Main Sequence). Since the luminosity of K giants is more like 100 Lo, what is the true distance to this cluster?
Problem #2: A Hydrogen atom in an interstellar cloud makes a transition from its 54th excited state to its 43rd excited state, and in doing so, lowers it energy by 4.31 x 10-22 Joules and launches a photon.
a) What is the frequency of the photon emitted by this process (according to the atoms in the cloud)?
b) If you are in a spaceship traveling toward this cloud at as speed of 10% of the speed of light, what frequency light do you measure?
Problem #3: Assume for a moment that all of the hydrogen in the Sun is converted into helium via nuclear fusion (this doesn't really happen).
a) How much of the Sun's total mass would be converted into energy? Assume that the Sun is 80% hydrogen by mass. (Note: I am not asking how much hydrogen gets used up, but instead how the total mass of the Sun (i.e., hydrogen and helium) changes through the fusion process.)
b) How much energy would be produced?
c) How long would it take for the Sun to radiate this much energy at its current luminosity?