For this assignment we will focus on calculating the Sidereal Period of Mars. Let’s say that on January 1st, mars is seen to be in opposition. [in some random year]. Then 13 months later (on February 1st of the following year) Mars is observed to be in Conjunction.

The Sidereal Period of Mars.

Let’s say that on January 1st, mars is seen to be in opposition. [in some random year]. Then 13 months later (on February 1st of the following year) Mars is observed to be in Conjunction. What is the Sidereal Period of Mars that would be calculated from these observations? Include a figure in your solution to show how you reach this answer. Assume that Mars and Earth both have perfectly circular orbits. Note that these are fictitious dates and the Sidereal Period determined in this problem is not the real Period of Mars. (Six points) It has been determined that a comet has an orbit with an eccentricity of 0.980 and a semi-major axis of 20.0 A.U..

The Sidereal Period of Mars.

What would the object’s velocity be when it is at (a) perihelion and (b) aphelion? (Two points). A star’s spectrum is recorded (i.e. observed). The hydrogen “Balmer alpha” spectral line has a measured wavelength of 656.1 nanometers (nm). what is the radial velocity of this star If the “rest wavelength” of this spectral line is 656.3nm? Also, Think carefully about “significant figures” in this question. It’s a tricky question. As full marks requires the correct number of significant figures in the final answer please note that, this is the most difficult sig. fig. question as of yet (two points)

The Sidereal Period of Mars.

5. The molecules that are trapped in a planet’s atmosphere depend on their mass, the planet’s mass, the planet’s radius, and the planet’s temperature. The equation showing the temperature limit is given in Module 5c (the planet must be cooler than this to retain the gas over times on the scale of the lifetime of the Solar System). (a) On a log-log plot draw the lines showing the temperature limits for molecular hydrogen (H2) and carbon dioxide (CO2) as a function of M/R (where M is the mass in Earth masses [i.e. M = M/MEarth ] , R is the radius in Earth Radii). [Plot log(Temperature) on the y axis and log(M/R) on the x axis.]

The Sidereal Period of Mars.

Show your calculations for one of the molecules. (b) Then, for all of the planets (not including dwarf planets), make a table showing the data (M, R, M/R, log(M/R), surface temperature, and log (surface temperature) ). Add points on the plot in (a) for the surface temperature of all of the major planets. (You will need to look these up somewhere. You will find that this can be a bit confusing! For example some internet sites confuse average temperature with lowest temperature. Giant planets don’t have a surface but you can find something like this, perhaps called cloud layer temperature.)

The Sidereal Period of Mars.

Your final plot will have two lines (one for each of the molecules) and eight points (one for each planet). (c) Briefly discuss the results. Which planets are close to a limit and what might that mean for gas retention? (Six points) 6. Find the properties of a “Least-Energy Orbit” for a spacecraft moving from the Earth’s orbit to Mars’ orbit. “Show your calculations”. The spacecraft’s orbit has its perihelion at the Earth’s orbit and aphelion at Mars’ orbit (assume that both the Earth’s and Mars’ orbits are perfect circles! . (a) Show a sketch of the three orbits (Earth, Mars, and spacecraft). The Sidereal Period of Mars.

The Sidereal Period of Mars.

(b) How long does it take for an unpowered spacecraft to move from Earth’s orbit to Mars’ orbit? answer to be given in days. (c) How fast is the spacecraft need to be moving in its orbit at the beginning of its trip? (i.e. when it is at the Earth’s orbit, but again ignore the Earth itself)? where M is the mass of the Sun, r is the distance from the Sun (which varies continuously except in the special case of a circular orbit), and a is the semi-major axis of the orbit. Give your answer in meters/second. Hint: the masses of the Earth and Mars are not needed here! (Four points).https://youtu.be/cMPQX1b5r0s

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