# 天体物理学代写|ASTRONOMY 1 ASTRO1001 University of Glasgow AssignmentONLINE TUTOR

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## Instructions:

Astronomy is the scientific study of celestial objects and phenomena beyond the Earth’s atmosphere, including planets, stars, galaxies, and other celestial bodies. It is a fascinating field that has captured the attention and imagination of people for thousands of years.

There are several subfields within astronomy, including solar system physics, positional astronomy, and dynamical astronomy.

Solar system physics is the study of the physical properties of the planets, moons, asteroids, and comets in our solar system. This includes their composition, structure, atmospheres, and orbits. Solar system physics also investigates the formation and evolution of the solar system, as well as the interactions between the various bodies.

Positional astronomy is concerned with measuring the positions, distances, and motions of celestial objects. This involves the use of telescopes, cameras, and other instruments to gather data on the positions of stars, galaxies, and other objects. Positional astronomy also includes the study of celestial coordinate systems, which are used to locate objects in the sky.

Dynamical astronomy is the study of the motions of celestial objects, including their orbits and gravitational interactions. This field includes the study of celestial mechanics, which deals with the mathematical description of the motions of objects in space. Dynamical astronomy also investigates the formation and evolution of galaxies, and the interactions between galaxies and other celestial bodies.

In conclusion, astronomy is a vast and complex field that encompasses many different areas of study. Solar system physics, positional astronomy, and dynamical astronomy are just a few of the many subfields within this fascinating discipline. The study of astronomy has helped us to understand the universe around us and has inspired us to ask even more questions about the nature of the cosmos.

a. A globular cluster has $10^6$ stars each of apparent magnitude +8 . What is the combined apparent magnitude of the entire cluster?

$\begin{gathered}+8=-2.5 \log \left(F / F_0\right) \ F=6.3 \times 10^{-4} F_0 \ F_{\text {cluster }}=10^6 \times 6.3 \times 10^{-4} F_0=630 F_0 \ m_{\text {cluster }}=-2.5 \log (630)=-7\end{gathered}$

b. Find the distance modulus to the Andromeda galaxy (M31). Take the distance to Andromeda to be $750 \mathrm{kpc}$.

$\mathrm{DM}=5 \log \left(\frac{d}{10 \mathrm{pc}}\right)=5 \log (75,000)=24.4$

c. An eclipsing binary consists of two stars of different radii and effective temperatures. Star 1 has radius $R_1$ and $T_1$, and Star 2 has $R_2=0.5 R_1$ and $T_2=2 T_1$. Find the change in bolometric magnitude of the binary, $\Delta m_{\text {bol }}$, when the smaller star is behind the larger star. (Consider only bolometric magnitudes so you don’t have to worry about color differences.)

$$\begin{gathered} \mathcal{F}{1 \& 2}=4 \pi \sigma\left(T_1^4 R_1^2+T_2^4 R_2^2\right) \ \mathcal{F}{\text {eclipse }}=4 \pi \sigma T_1^4 R_1^2 \ \Delta m=-2.5 \log \left(\frac{\mathcal{F}{1 \& 2}}{\mathcal{F}{\text {eclipse }}}\right) \ \Delta m=-2.5 \log \left(1+\frac{T_2^4 R_2^2}{T_1^4 R_1^2}\right) \ \Delta m=-2.5 \log \left(1+\frac{16}{4}\right)=-1.75 \end{gathered}$$
So, the binary is 1.75 magnitudes brighter out of eclipse than when star 2 is behind star 1 .