1) The equation of hydrostatic equilibrium holds for none-gaseous bodies like the Earth and Moon (and other rocky planets). Estimate the central pressure of the Earth and Moon, and compare with that of the Sun.
2) Estimate the thermal energy per particle at the center of the Sun, and compare with the ionization energy of Hydrogen (13.6 eV). What do you conclude?
3) If all the Sun's internal pressure were to suddenly vanish, how long would the Sun take to collapse? (Hint: what timescale are we talking about?).
5) Estimate how long the Sun would last if powered by (a) thermal energy (b) chemical energy (c) nuclear energy. Which sources are viable, and why?
6) Several films and TV programs (e.g. the film "Sunshine") feature the premise that a star (e.g. the Sun) is dying for some reason, and needs to be "restarted" by delivering a nuclear bomb or two to its core. Let's examine the logistics of this.
The largest nuclear bombs produced have yields of a few megatons. A megaton is roughly equivalent to 4,000 TJ of energy (T = Tera, 10 to the power 12). The bomb releases all its energy over a time of roughly a minute. Therefore calculate the power of the bomb (energy released per second, in J/s), and compare with the Sun's luminosity. How many bombs would we need to deliver to the Sun to make an impact? To put it in perspective, convert the number you found into something more relatable - e.g. it is equivalent to every human on Earth having how many nuclear bombs?