Paper link: http://www.uphysicsc.com/2017-GM-A-670.pdf

Thanks in advance.

  • 4
    Welcome to TeX.SE! It seems a simple article documentclass to me.
    – CarLaTeX
    Oct 18 '18 at 7:42

I agree with @CarLaTeX! In my opinion the source code is like that (I haven't written the bibliography references…):

\usepackage{graphicx} % to include pictures
\usepackage{siunitx} % to typeset units
\usepackage[margin=3cm]{geometry} % approximately

\title{Problem A: Solar Sailing to Mars}
\author{Team 670}
        Solar sails became reality lately, being far more affordable then most of modern methods
        of propulsion in space. They obviously have some limitations, as they can work effectively
        only in close proximity of the Sun and can not propel spacecrafts towards the Sun. Using such
        solar sails for missions to the Mars has been discussed previously by many groups and seem to
        have a lot of potential, especially if time is not the most limiting factor. Our limiting factor
        was a mass of an entire ship fixed at \SI{2000}{\kilogram}. In our work we suggest a heuristic approach to
        optimize an angle of incidence during flight, while keeping this angle fixed for fixed periods
        of time. With numerical simulations we found optimal routes for different ratio (q) of sail to
        ship mass. With such an optimization we concluded, that most promising is to have q ratio
        equal to \num{0.46}, what gives \SI{1080}{\kilogram} of payload. Such a spaceship would reach Mars in about
        532 days.

    A solar sail is a modern concept of cosmic travel, where a spacecraft is propelled by light pressure
    from photons emitted from the Sun. It offers obvious advantages of fuel conservation and possible
    weight reduction. Using solar sail can become the future of cosmic exploration, but it also demands
    a new approach to planning a mission.
    Indeed, the concept significantly differs from conventional methods, where for most part the vessel
    travels along an elliptical path with gravity being the only acting force, and the orbit is changed
    by short boosts at perihelion / aphelion. Light pressure constantly affects the sail, which makes
    equations of motion more complicated and trajectories impossible to derive analytically.
    Therefore we evaluated trajectories numerically with variable parameters of sail size and orientation
    angle with respect to position vector (which can be modified throughout the flight by rotating the
    sail at low energetic cost). Our goal is to optimize $\eta=\frac{m}{T}$, where
    $m$ is the mass of a spacecraft, and $T$
    the time of a mission.
    In our case we consider a mission to Mars, where we start at the moment of planet’s closest
    approach to Earth. Similar problem has been presented previously by [5], but with less constraints
    than in our case. We decided to use a different with semi-heuristic algorithm attached in Appendix

    \section{Mathematical model of solar sail}
    We model a solar sail as a flat surface tilted at an angle
    between line connecting the center of
    the Sun and normal vector to sail surface. The net force acting on a sail is proportional to an
    effective cross section of a solar sail and scales with a $\cos(\theta)$. We assume that sun is a uniform
    black sphere at a temperature equal to \SI{5778}{\K} [4]. Therefore, solar radiation impulse on a sail can
    be estimated based on total radiation emitted by black body according to equation:

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