## 物理代写|天体物理学和天文学代写Astrophysics and Astronomy代考|ASTY221

statistics-lab™ 为您的留学生涯保驾护航 在代写天体物理学和天文学Astrophysics and Astronomy方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写天体物理学和天文学Astrophysics and Astronomy代写方面经验极为丰富，各种代写天体物理学和天文学Astrophysics and Astronomy相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|天体物理学和天文学代写Astrophysics and Astronomy代考|Declination of the Sun

While the declination of stars is constant, the position of the Sun changes in the equatorial system over the period of a year. This is a consequence of the inclination of Earth’s rotation axis with respect to the direction perpendicular to the ecliptic, which is equal to $\epsilon_0=23.44^{\circ}$. The angle $\epsilon_0$ is called obliquity of the ecliptic. The annual variation of the declination of the Sun is approximately given by 3
$$\delta_{\odot}=-\arcsin \left[\sin \epsilon_0 \cos \left(\frac{360^{\circ}}{365.24}(N+10)\right)\right]$$

where $N$ is the difference in days starting from 1st January. So the first day of the year corresponds to $N=0$, and the last to $N=364$ (unless it is a leap year). The fraction $360^{\circ} / 365.24$ equals the change in the angular position of Earth per day, assuming a circular orbit. This is just the angular velocity $\omega$ of Earth’s orbital motion around the Sun in units of degrees per day. ${ }^4$

The Sun has zero declination at the equinoxes (intersection points of celestial equator and ecliptic) and reaches $\pm \epsilon_0$ at the solstices, where the rotation axis of the Earth is inclined towards or away from the Sun. The exact dates vary somewhat from year to year. In 2020, for instance, equinoxes were on 20th March and 22nd September and solstices on 20th June and 21st December (we neglect the exact times in the following). In Exercise $2.2$ you are asked to determine the corresponding values of $N$. For example, the 20th of June is the 172nd day of the year 2020. Counting from zero, we thus expect the maximum of the declination $\delta_{\odot}=\epsilon_0$ (first solstice) for $N=171$. Let us see if this is consistent with the approximation (2.1). The following Python code computes the declination $\delta_{\odot}$ based on this formula for a given value of $N$ :

The result
$$\text { declination }=23.43 \text { deq }$$
is close to the expected value of $23.44^{\circ}$. To implement Eq. (2.1), we use the sine, cosine, and arcsine functions from the math library. The arguments of these functions must be specified in radians. While the angular velocity is simply given by $2 \pi / 365.24 \mathrm{rad} / \mathrm{d}$ (see line 4 ), $\epsilon_0$ is converted into radians with the help of math.radians () in line 5. Both values are assigned to variables, which allows us to reuse them in subsequent parts of the program. Since the inverse function math. asin () returns an angle in radians, we need to convert delta into degrees when printing the result in line 9 (‘ $\mathrm{deg}$ ‘ is short for degrees).

## 物理代写|天体物理学和天文学代写Astrophysics and Astronomy代考|Diurnal Arc

From the viewpoint of an observer on Earth, the apparent motion of an object on the celestial sphere follows an arc above the horizon, which is called diurnal arc (see Fig. 2.3). The time-dependent horizontal position of the object is measured by its hour angle $h$. An hour angle of $24^{\text {h }}$ corresponds to a full circle of $360^{\circ}$ parallel to the celestial equator (an example is the complete red circle in Fig. 2.3). For this reason, $h$ is can be equivalently expressed in degrees or radians. However, as we will see below, an hour angle of $1^{\mathrm{h}}$ is not equivalent to a time difference of one solar hour. By definition the hour angle is zero when the object reaches the highest altitude above the horizon (see also Exercise $2.4$ and Sect. 2.1.3). The hour angle corresponding to the setting time, when the object just vanishes beneath the horizon, is given by ${ }^6$

$$\cos h_{\text {set }}=-\tan \delta \tan \phi,$$
where $\delta$ is the declination of the object (see Sect. 2.1) and $\phi$ the latitude of the observer’s position on Earth. As a consequence, the variable $T=2 h_{\text {set }}$ measures the so-called sidereal time for which the object is in principle visible on the sky (stars are of course outshined by the Sun during daytime). It is also known as length of the diurnal are.

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。