Monta Vista Invitational — Astronomy

Which process dominates the energy production in the core of a massive star nearing the end of its main-sequence life?

What is the primary driver of pulsations in a Cepheid variable star?

In the H-R diagram, which evolutionary track is characterized by a rapid transition from the main sequence to the red giant branch due to helium flash?

Which spectral line transition is most critical for studying the ionization state in H II regions?

What triggers the collapse of a white dwarf in a Type Ia supernova?

Which of these best describes the chemical composition shift in a star’s envelope during the asymptotic giant branch phase?

Which of these is a feature of blackbody radiation?

Which observational feature distinguishes Mira variables from other red giants?

What is the likely progenitor of a millisecond pulsar in a binary system?

The ____ is a stellar pulsation driver caused by opacity changes due to ionization in the star’s atmosphere.

The initial evolutionary path of a low-mass protostar on the H-R diagram, moving vertically at constant temperature.

The maximum mass a neutron star can have before collapsing into a black hole. (The term for it, not a numerical answer)

Name a key isotope produced in Type Ia supernovae before any decay has occurred.

Late-stage evolved stars with helium burning shells and hydrogen shells, rich in s-process elements.

Electromagnetic radiation emitted when charged particles are decelerated by other particles’ electric fields.

____ luminosity is the maximum luminosity a star can achieve when radiation pressure balances gravity.

At a frequency of ____ MHz in the water hole, the emission for neutral H can be found.

Let’s look at a hypothetical star and planet system. Let’s start with the star. Assume that we know the star has R = 0.1R ☉ and λpeak = 700 nm. What is the temperature of the star in Kelvin?

What is the luminosity of the star in W?

Using this, obtain luminosity in terms of solar units and get mass in solar units.

If you were observing this system 420.67 pc away, what would the apparent magnitude of the star be?

Ignore the above distance now. Let's say we saw an observed wavelength of 666.28 nm of the Hydrogen alpha line (which has a standard wavelength of 656.28 nm). What is the redshift of the star? Is it moving towards or away from us?

What is the velocity of the star with respect to you in km/s?

What is the distance to the star now if we use Hubble's Law in Mpc?

Let's look at the planet now. When we look at a transit, we see that the flux reduces by 1% during transit. What's the radius of the planet in m?

When we see a transit, the planet doesn't cause an even change in the star's flux as it travels across the observed surface. What phenomenon can explain this?

Can the planet sustain liquid water?

Let's look at all of Kepler's Laws and go deeper into them. What are Kepler's Three Laws?

We can use the First Law to do some calculations with the areas of all ellipses. What's the general form for the total area of an ellipse?

What would the distances for the periapsis and apoapsis be in terms of the semi-major axis and eccentricity?

What does this equation say about angular momentum, knowing about the nature of ellipses and circles?

So, how would the area of an ellipse approximately change with time based on angular momentum and mass, if the law stated earlier applies? Use the following diagram and assume that Δs is a really small distance travelled by the object with some velocity over Δt and can be approximated as a line. Hint: Find what ΔA is equal to as an approximated triangle and then divide by Δt and substitute the equation with L and m.

Now, looking at Kepler's Third Law, what force acts on an orbiting body? What net force can this force also be equated to as it orbits in an ellipse/circle? Write their equations too.

Knowing that there is only one force and one net force, the two can be equated with each other. When solving for T² (period of the orbit squared), what is the equation you get? (this should look familiar)

What does circular velocity equal to in a circular orbit? What about angular velocity?

Write the semi-latus rectum, knowing that it is equal to b²/a and is the distance to the star when perpendicular to the semi-major axis of an orbit, in terms of a and e.

What is the equation of ellipse using polar coordinates based on the semi-latus rectum? (distance follows r = l/(1+e cos(theta))

Knowing the value obtained for the change in area over change in time, we can plug in the area of the ellipse over the whole period of the orbit. We can then solve for T² and simplify all of the variables and get rid of b and e until we get Kepler's Third Law (woah). Show the derivation of this using this value.