Make a list of each main phase of the Moon, describing roughly when the Moon rises and sets for each phase. During which phase can you see the Moon in the middle of the morning? In the middle of the afternoon?

What are advantages and disadvantages of apparent solar time? How is the situation improved by introducing mean solar time and standard time?

The table lists the distances (in megaparsecs where 1 megaparsec $\approx 3.1 \times 10^{19} \mathrm{km}$) and velocities (in kilometers per second) of four galaxies moving rapidly away from Earth. Source: Astronomical Methods and Calculations, and Fundamental Astronomy.

$$\text{Galaxy}\quad \text{Distance} \quad \text{Velocity} \\ \begin{array}{ccc} \text{Virga} &{15} & {1600} \\ \hline \text{Ursa Minor} & {200} & {15,000} \\ \hline \text{Corona Borealis}& {290} & {24,000} \\ \hline \text{Bootes} & {520} & {40,000}\\ \hline \end{array}$$

$a.$ Plot the data points letting $x$ represent distance and $y$ represent velocity. Do the points lie in an approximately linear pattern? $b.$ Write a linear equation $y=m x$ to model this data, using the ordered pair $520, 40,000$. $c.$ The galaxy Hydra has a velocity of $60,000$ km per sec. Use your equation to approximate how far away it is from Earth. $d.$ The value of $m$ in the equation is called the Hubble constant. The Hubble constant can be used to estimate the age of the universe $A$ (in years) using the formula $A=\frac{9.5 \times 10^{11}}{m}$ Approximate $A$ using your value of $m$.

Compare and contrast linkage analysis and genome-wide association studies. How are they similar? How are they different?

Find $\mathcal{L}\{f(t)\}$ for the function $f$ defined below.

$$f(t)=\left\{\begin{array}{ll}{4,} & {0 \leq t<3} \\ {0,} & {3 \leq t<6} \\ {f(t+6)=f(t),} & {\text { for all } t \geq 0}\end{array}\right.$$

Explain three lines of evidence that indicate that the seasons in North America are not caused by the changing Earth-Sun distance as a result of Earth’s elliptical orbit around the Sun.

Why is Tycho Brahe often called “the greatest naked-eye astronomer” of all time?

If the major axis of an ellipse is 16 cm, what is the semimajor axis? If the eccentricity is 0.8, would this ellipse be best described as mostly circular or very elongated?

In 1996, astronomers discovered an icy object beyond Pluto that was given the designation 1996 TL 66. It has a semimajor axis of 84 AU. What is its orbital period according to Kepler’s third law?

Does a solar eclipse occur during the (new Moon, first-quarter, or full-Moon) phase of the Moon ?

Let $f(x)=3x^4+4x^3$. Sketch the graph of the function using the approach presented in this section.

Does a solar eclipse occur during the new-Moon, first-quarter, or full-Moon phase of the Moon?

What is the average distance from the Sun (in astronomical units) of an asteroid with an orbital period of 8 years?

Why is it difficult to construct a practical calendar based on the Moon’s cycle of phases?