Astronomy

QUESTION 1

In discussion, you derived the formula for the peak radial velocity introduced on a star from an orbiting exoplanet. Here is one version of this relationship:

‘Where v is in meters/second (m/s), M_P is in Earth masses, M_S is in Solar masses and P is in Earth years.’

First, calculate the peak radial velocity introduced by a 1 Earth mass planet on a 1 solar mass star with a period of 1 year, assuming an edge-on orbit. Answer in m/s, but do not include the units in your answer.

QUESTION 2

Now, calculate the peak radial velocity introduced on a Sun-like star by a planet identical to Jupiter, again assuming an edge-on orbit. You will need to look up the mass of Jupiter and covert it to earth masses, and look up the orbital period of Jupiter. Answer in m/s without the units.

QUESTION 3

Based on the equation in Question 1, which of the following scenarios would result in the largest peak radial velocity? Assume all are in an edge-on orbit.

		A. “Massive star, massive planet, large orbital period.”
		B. “Massive star, small planet, short orbital period.”
		D. “Massive star, small planet, short orbital period.”
		E. “Small star, small planet, short orbital period.”
		F. “Small star, massive planet, short orbital period.”

QUESTION 4

Now let’s consider the effect of eccentricity on the peak radial velocity, which was assumed to be zero in the equation in Question 3. Draw a highly eccentric orbit of a planet, and consider the resulting motion of the star. Where in the planet’s orbit would the velocity of the star be the largest?

		A. “The velocity would have the same speed throughout the orbit.”
		B. “The velocity would be largest when the planet is furthest from the star (“apastron”, similar to “aphelion” for planets orbiting the sun).”
		C. “The velocity would be largest when the planet is closest to the star (“periastron”, similar to “aphelion” for planets orbiting the sun).”
		D. “The velocity of the star would be zero if the orbit is eccentric.”

QUESTION 5

Exoplanets.orgis a website that catalogs all of the known extrasolar planets found to date. For this assignment, we are going to use this website. Go to exoplanets.org and select “plots”. Make a plot of exoplanet orbital period (x-axis) versus exoplanet minimum mass (M x sini, y-axis), which will select for planets found using the radial velocity method. Click “advanced” and make the y-axis of the plot a log scale.

What is the planet with the smallest minimum mass?

		A. alpha Cen B b
		B. HD 180314 b
		C. Kepler-78 b
		D. YZ Cet b

QUESTION 6

Go back to the plots. Now make a plot of planet orbital period on the x-axis and planet radius on the y-axis. Find the exoplanetwith the smallest size. Which solar system planet is that planet most similar to?

		A. Mercury
		B. Venus
		C. Earth
		D. Mars

QUESTION 7

You will notice that the distribution of planets is different for radius vs. orbital period than for Msini vs orbital period. Think about why that might be. What two big groups do you see in the plot of radius versus orbital period? Check two answers.

		A. Large radius planets with large orbital periods
		B. Small radius planets with large orbital periods
		C. Large radius planets with short orbital periods
		D. Small radius planets with short orbital periods

QUESTION 8

Why would the distribution of planets for periods vs. Msinilook so different from the distribution of planets for period vs. radius? You can answer this question by experimentation with the website.

		A. They are the same planets in both plots, we are just plotting different quantities.
		B. They are different planets in the two plots: Some planets have a radius measurement but no mass measurement, and some planets have an Msini measurement with no radius measurement.