Give at least two advantages for the use of large reflecting mirrors in astronomical telescopes.

Solve the problem.

Comet Hale-Bopp, which was clearly seen in April of $1997$, orbits the sun in an elliptical orbit every $4200$ years. At perihelion, the closest point to the sun, the comet is approximately $1 \mathrm{AU}$ from the sun, as shown in the accompanying figure (Sky and Telescope, April $1997$, used with permission. Guy Ottewell, Astronomical Calendar, $1997$, on earlier page). At aphelion, the farthest point from the sun, the comet is $520 \mathrm{AU}$ from the sun. Find the equation of the ellipse. What is the eccentricity of the orbit?

Earth moves in a roughly circular orbit around the sun at a distance of approximately 150 000 000 km. To estimate longer distances in space, scientists measure in multiples of the Earth-sun radius, or astronomical units ( $1 \mathrm{AU}=149597870.691 \mathrm{~km})$. NASA defines $1 \mathrm{AU}$ as the radius of an unperturbed circular orbit of a massless theoretical body revolving about the sun in $\frac{2 \pi}{k}$ days, where $k$ is a constant exactly equal to $0.01720209895$.

One year on Mars represents one complete rotation. How long (in radians) is 1 Mars-year on Earth? How long is this in Earth-days?

In what two ways does an astronomical telescope differ from a terrestrial telescope?

For the following exercise, use Kepler's Law, which states that the square of the time, $T$, required for a planet to orbit the Sun varies directly with the cube of the mean distance, $a$, that the planet is from the Sun.
Using Earth's distance of 1 astronomical unit (A.U.), determine the time for Saturn to orbit the Sun if its mean distance is $9.54$ A.U.

For the following exercises, use Kepler’s Law, which states that the square of the time, T, required for a planet to orbit the Sun varies directly with the cube of the mean distance, a, that the planet is from the Sun. Using Earth’s distance of 1 astronomical unit (A.U.), determine the time for Saturn to orbit the Sun if its mean distance is 9.54 A.U.

How many grams of gold (Au) are there in 15.3 moles of Au?

In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun: $a_{1}=0.4, \quad\left\{a_{n}\right\}=\left\{0.4+0.3 \cdot 2^{n-2}\right\}, n \geq 2$ where n is the number of the planet from the sun. Determine the ninth and tenth terms of Bode’s sequence.

Dites ou sont les personnes selon leurs activités;

Québec – la piscine – au stade – la gare – au centre commerciale – au concert – au bureau – au café – la médiathèque

Tu vas à la féte de Saint-Jean

Answer the following question based on the techniques that are best suited to measuring various astronomical distances.
What range of astronomical distances can we currently measure using both Cepheids and distant standards (white dwarf supernovae)?

How many grams of gold (Au) are there in 15.3 moles of Au?

The sun emits roughly the same amount of energy as a black body with a temperature of $5700 \mathrm{~K}$. What equilibrium temperature $T$ will a perfectly black copper sphere reach if exposed to sunlight at a distance of one astronomical unit from the sun? The diameter of the sun forms a $0.50^{\circ}$ angle with the earth.

What are some of the advantages of using mirrors rather than lenses for astronomical telescopes?

Most galaxies, including our own Milky Way, have supermassive black holes at their centers. Recently, astronomers were able to track one star, named $\mathbf{S} 2$, as it orbited the black hole at the center of our galaxy. The star's actual orbit is elliptical, but we'll model it as a circular orbit. S2 has a period of 15 years and a radius of $1000 \mathrm{au}$, where $1 \mathrm{au}=1$ astronomical unit is the distance of the earth from the sun.

a. What is the speed of S2? Give your answer as a fraction of $c$, where $c=$ the speed of light $=3.0 \times 10^8 \mathrm{~m} / \mathrm{s}$. b. What is the mass of the black hole? Give your answer as a multiple of $M_{\mathrm{s}}$, where $M_{\mathrm{s}}=1$ solar mass $=2.0 \times 10^{30} \mathrm{~kg}$.