Please answer these questions and show work.

1. The mass of the Sun is about 2x1030 kg. The Sun was about 71% hydrogen when it first formed. About 11% of the total amount of the Sun's hydrogen is available for fusion within the Sun's core. [3 points]

(a) What is the total mass of hydrogen available for fusion, in kg?

(b) The Sun fuses about 600 billion kg of hydrogen each second. Calculate how long the Sun's initial supply of hydrogen can last. Give your answer in both seconds and years. Hint: use the result you calculated in part (a).

(c) We know that our Solar System is about 4.5 billion years old. Using your calculation above, how much longer do we have until the Sun runs out of hydrogen?

2. You discover a spectral type G2 star orbiting an unseen companion with a semimajor axis of 7 million km, and an orbital period of 2.2 Earth days. [2 points]

(a) What is the mass of the unseen companion? Give your answer in both kg and Solar masses. You will need to use Newton's version of Kepler's 3rd Law, the gravitational constant, G = 6.67 x 10-11 m3 kg-1 s-2, and the mass of a G2 star (which is the same as the mass of the Sun), 2.0 x 1030 kg. In this case, remember to use the TOTAL mass of the stars, not just the mass of one star in your calcuation.

(b) Is the unseen companion a white dwarf, a neutron star, or a black hole? What evidence is there in favour of your choice?