# Lab 4 – Atmospheres

The atmosphere’s of the planets and moons vary greatly. To understand why we have to know that every body has a certain speed called the escape velocity at which a particle can escape its gravitational pull and that the speeds of molecules in a gas depend on the gas’s temperature and molecular weight (mass). The escape velocity from a body is given by

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where M is the mass of the body, R is its radius and G is Newton’s constant of Universal gravity.
In comparison the speeds of particles in a gas are given by the Maxwell-Boltzmann distribution. In this case the root mean square velocity is given by

where T is the gas’s temperature, m is the particles molecular weight and k_B is a constant called the Boltzman constant.

Basically, if the speeds of the gas particles are even one tenth of the escape speed then the gas will slowly escape the planet or moon. If the speed of the gas particles are much less than the escape velocity the gas will be kept as an atmosphere.

#### Laboratory Tools

In this lab we will make use of the Gas Retention Simulator designed by the University of Nebraska-Lincoln.  This simulator shows how gas escapes from a region depending on its temperature and the escape velocity.  The box in the upper left corner,  Chamber,  is a chamber holds the gas. In the upper right panel the Distribution Plot shows the distribution of velocities for the selected gas and temperature. The box in the lower left, Chamber Properties, allow you to set the chamber properties, that is the temperature of the gas and the escape speed.  The panel in the lower right, Gases, allows you to choose up to 3 gasses to put in the chamber. Note you see nothing in the upper two panels if no gas is selected. To start the simulation click the start simulation button in the lower right side.  Note you must stop the simulation to make changes.

We will also use the Gas Retention Plot from the University of Nebraska-Lincoln Astronomy Department.   Here the upper left panel is the Gas Retention Plot.  The upper right panel, Gasses allows you to select which gasses your want on the Gas Retention Plot.  The middle right panel, Plot Options, allows you to choose which planets and moons you want displayed on the plot. The bottom panel, Custom Object Properties, allows you to control a red dot on the plot, by varying the temperature and a planets size and density.

#### Assignment

Let’s start with the Gas Retention Simulation and the case of Earth.  Set the temperature at 280 and allow escape from the chamber. Set the escape speed at 1,120 m/s, one tenth the escape speed from Earth. Now choose as the gasses, oxygen, nitrogen and helium and start the simulation. Which gasses stay in Earth’s atmosphere and which escape?

Now let’s change to Earth’s moon, same temperature of 280 but set the escape speed to 238 m/s.  Explore other gasses, can any gas remain on the Moon as an atmosphere?

Now let’s change to a situation like on Mars. Set the temperature to 220K and the escape speed to 500 m/s.  Set the gasses to oxygen, carbon-dioxide and water.  What happens and what does this tell us about the atmosphere on Mars?

Finally let’s look at the giant planets. Use the minimum temperature of the simulator 100K and the maximum escape speed 1900 m/s and set the gasses to helium and hydrogen.   This is actually less than one tenth the escape speed from Uranus, but the simulator only goes this high. Why do the giant planets have hydrogen and helium in their atmospheres, but terrestrial planets and moon don’t?

Now let’s turn to the Gas Retention Plot.  In the Plot Options panel click on all the planets and moons. Now in gasses click on hydrogen and helium.  Notice the difference between the giant planets and everybody else.  You can drag the red dot over to Earth’s location. Now move it up so that helium would stay bound to Earth. What would Earth’s radius have to be in that case?

Now click off hydrogen and helium and click on water. What planet can almost hold undo water? Click off water and click on carbon dioxide.  What temperature would Mercury have to be to keep carbon dioxide in its atmosphere?  Wh temperature would Earth’s Moon need to have?

#### Questions

1. Why is it easier for a planet to have carbon-dioxide than water vapor in its atmosphere?
2. How cold would the Earth have to be to keep hydrogen it its atmosphere?
3. If you found a new planet and determined it had no atmosphere what are the two possible explanations for why that would be the case?

# Lab 5 – Images of Saturn

In many areas of science the analysis of images is an important laboratory technique. In astronomy this takes a major role as telescopes are the main way we learn about astronomical phenomena. The analysis of images has become much easier in recent years because of the advent of digital images. Because images can be stored in the computer, measuring, analyzing and altering them have all become relatively simple.In this lab we will use a software package for analyzing digital images to study some pictures of Saturn and some of Saturn’s moons. All images used in this lab have been taken with the Cassini spacecraft, a NASA mission that was in orbit around Saturn from 2004 to 2017.  Thus these are the highest resolution close ups ever taken of the Saturnian system.

One of the most important issues in studying an image is determining the physical size of objects in the image. This is not easy because what the camera captures is the angular size of an object modified by the magnification of a telescope. When displayed on a screen the image can also be zoomed so that the apparent size of the image has little relation to its actual size. One can calculate the physical size of an image if you know the distance of the object, the magnification of the telescope and any zoom applied in displaying the image. Usually it is easier to just scale the image if you know the size of one thing in the image.  In this lab we will scale all images by knowing the diameters of Saturn and her moons.

 Name diameter Saturn 120,536km Titan 5150km Thythis 1060km Enceladus 499km

#### Laboratory Tools

In order to analyze images of Saturn we will use ImageJ which can be downloaded to your computer or run in the browser if you are using Chrome or Firefox. I recommend you run it in the browser, you can easily download Chrome or Firefox if you don’t have either one. To run it in your browser just click on Run in Chrome or Firefox.

You will also need the images of Saturn and Saturn’s moon which you can download here.

The ImageJ tool will appear like the top of a window having a menubar and menu selections. The top row will have File, Edit, Image, Process, Analyze, Plugins, Process, Help. Below that are a set of menu buttons many of which are drawing tools.  Below that will appear some text depending on what you are doing. To load an image use  File->Open…. Once an image is loaded it is important to set the scale before making any measurements.

Set the Scale – To set the scale first choose the straight tool, its the 5th box down. Then make a line across the diameter of the object. You will see the pixel values and the length in pixels under the boxes. Then choose Analyze->Set Scale and a new window will pop up. In that window the first row, Distance in pixels, should be the same number that was in under the boxes earlier.   In the second row, Known distance, enter the known diameter of the object.  In the fourth row, Unit of length, enter km. Then hit Ok. Now when you measure something it will be correctly scaled in kilometers.

Measure a Length – The straight tool can be used to measure a length if you can place the cursor and end it at the correct location.   If the intensity changes by a large amount the plot profile command can be much more accurate.

Line Profile – To get a line profile first use the straight tool to draw a line, and then choose Analyze-Plot Profile. A plot of intensity vrs distance will appear. You can use the line profile to measure a length where the intensity of the pixels change dramatically.  Placing the cursor on the plot will tell you the value of X which since you set the scale is now in kilometers.

Adjust Brightness/Contrast –  The contrast can be adjusted from Image->Adjust->Brightness/Contrast. This will bring up a new window that shows a histogram of the intensity values in the image.  From the histogram you can see that not all of the range is being used. To enhance the contrast click on set which will open another window with the minimum and maximum displayed value. Change one of these values to give a smaller range that covers the histogram of values you see. You can keep adjusting.

#### Assignment

1. jpg — Measure the width of the shadow Saturn’s rings cast on the planet using the line profile.
2. green saturn.jpg — Measure the height of the shadow from Saturn’s rings in this image. Measure the width of the rings, the distance from the inside of the rings to the outside.
3. jpg — Note this image has no scale.  Use line profile to determine the number of gaps in the rings.
4. titan ring.jpg — This is an image of Titan behind Saturn’s rings. Set the scale with the diameter of Titan. Measure the thickness of Saturn’s rings from this image.
5. titan lake.jpg — This is an image of Titan mostly in shadow but with one lake brightly reflecting light. Measure the diameter of the lake.
6. jpg — This is an image of Tythis which has not been calibrated. That is why it has the clear artifact on the right side. Measure the diameters of the two very large craters on Tythis.
7. jpg — This is an image of Enceladus, mostly in shadow. The geysers can been seen on the top of the moon. Measure the height of the geysers. Now change the brightness using the Adjust Brightness/Contrast as described above.  Remeasure the height of the geysers now that you can see them better.

#### Questions

1. Why might the shadow made by Saturn’s rings be larger than the thickness of the rings themselves?
2. If you know the lengths of two objects in the image, one smaller and one larger, which is better to use to determine the scale and why?
3. Compare the height of Enceladus’s geyser to its diameter. What would be the height of an equivalent ratio geyser on Earth?

# Lab 6 – Lunar Phases

The only object that emits a substantial amount of visible light in the Solar System is the Sun. Everything else we only see because it is lit up by the Sun.  Thus every object has a day side and a night side. A side that it lit up by the Sun, and a side that is not.  When we view objects in the Solar System how much is lit up will depend on the relative position of the viewer,  the object and the Sun. If the object moves over time then it will go through phases as a different fraction of its surface is visible to the viewer.

The phases of Earth’s Moon are the most common example of this, though nothing about it is unique to either Earth or her Moon.  The same phenomena occurs on all planets that have moons.

#### Laboratory Tools

In this lab we will be using the Lunar Phase Simulator developed by the University of Nebraska – Lincoln.  This simulator shows the phases of Earth’s Moon as it orbits the Earth. The main box shows the Earth and Moon from a top down view. Arrows indicate the direction of sunlight.  The box below Animation and Time Controls, allows you to start the animation and control its rate.  You can also advance time in units of days, hours or minutes, though not much happens in minute. Next to this box is Diagram Option. Check the box for show angle and show time tick marks. The upper right box Moon Phase, shows how the moon is illuminated given its location and the name of that phase. The pull down menu can also advance the moon to that phase. The box below, Horizon Diagram, shows the view of the celestial sphere.

#### Assignment

In this lab, for each of the phases of the moon listed below determine from the simulator the angle the moon makes with the sun, the percent of the moon illuminated and the time of day it will be for an observer when the moon is directly overhead. Please make sure to create a table in the program you use to create your report.

 Phase Angle with Sun Percent of Moon Illuminated Time that Moon is Overhead New Moon Waning Crescent First Quarter Waning Gibbous Full Moon Waxing Gibbous Third Quarter Waxing Crescent

#### Questions

1. The phases of the moon are described as waxing or waning and crescent or gibbous. What do these terms mean?
2. What phase must the moon be in for a solar eclipse to occur? How about a lunar eclipse?
3. For an observer on the moon if the moon is in the new phase what phase would they see the Earth being in?

# Lab 7 – The Seasons

The seasons are probably the most noticeable thing that occurs as the Earth revolves around the Sun. The seasons are caused by the tilt of Earth’s axis with respect to the Sun. That means as the Earth rotates around the Sun, the latitude where the Sun is directly overhead changes during the year.

#### Laboratory Tools

We will be using the Seasons and Ecliptic Simulator from the University of Nebraska-Lincoln. The main panel shows the Earth and Sun in either an orbit view or the celestial sphere.  The upper right panel shows either the angle the Sun’s rays make with the Earth (view from side) or where the Sun is overhead on the Earth (view from Sun).  You need to click the box for show subsolar point to see point where the Sun is overhead. In this panel  there is also a stick figure with which you can change the latitude of the observer.  The bottom right panel shows either the angle the Sun’s rays make with the Earth’s surface at the observer’s location (sunlight angle) or how spread out the Sun’s energy is on the Earth’s surface (sunbeam spread). The panel at the bottom shows the day of the year and allows you to start and stop the animation. You can also drag the redline to the day of your choice.

Also we will be using the Daylight Hours Explorer from University of Nebraska-Lincoln.  Note that there are instructions for how to download this that you should ignore, it will run perfectly fine in your browser.   The explorer shows the amount of day and night for each day of the year for a latitude specified in the Settings box.   There is also a Globe box that shows the Earth as a globe.

#### Assignment

Using the Seasons and Ecliptic Simulator start by placing your observer on the equator. Let the simulation run for a year. Observe the way the Sun’s rays change over the year.  Describe what the observer sees over the year. What will be the hottest and coldest days of the years (based only on sunlight) for this observer?

Now move the observer to the North Pole. Again observe the Sun’s rays and also the sunbeam spread. Describe the motion of the Sun in the sky for this observer.  How long is the observer in total darkness?  What angle above the horizon is the Sun on summer solstice?

Now move the observer to New York City, latitude 41 degrees.  Describe how the motion of the Sun changes for this observer. Now switch to the Daylight Hours Explorer. How much daylight is there on the longest day in New York City? How about the shortest?  What latitude to you have to reach to see 24 hours of daylight?

#### Questions

1. Why is it always colder at the poles then on the equator even though one can have 6 months of 24 hours of daylight?
2. If you live on the equinox is it more correct to say you have four seasons or two?
3. What would the seasons be like if the Earth’s tilt was 90° instead of 23.5°?

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