JAmaya_Solar System Lab 3 Mars Challange v3
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AST 101
INTRODUCTORY ASTRONOMY: THE SOLAR SYSTEM
LABORATORY ASSIGNMENT #3
Mars Challenge
Hypothesis
Mars has a lesser gravity than Earth. It will not take as much velocity to escape its gravity.
Question Asked: How can we determine the escape velocity of Mars?
Introduction
Mars is a special place for many space aficionados. It has mystique, and a legacy born of science fiction and grander than life personalities. Stellarium enables us to go to Mars and look to the heavens as if we were standing on its rusty, and dusty surface. Mars exploration began with flyby missions in the 1960s, followed by orbiters and landers in the 1970s. In the 1990s, rovers were sent to Mars, and since then, several more missions have been launched to study the planet's geology, atmosphere, and potential for life.
Some of the most notable Mars missions include the Viking program (two landers in 1976), the Pathfinder mission (1996), the Spirit and Opportunity rovers (2004), the Curiosity rover (2012), and the Perseverance rover (2020). These missions have helped us learn a great deal about Mars, including its geology, weather patterns, and potential for microbial life.
Despite the success of these missions, there have been no return missions to Mars, meaning that no spacecraft has been sent to retrieve samples and return them to Earth. The main reason for this is the complexity and cost of such a mission. In order to bring samples back from Mars, a spacecraft would need to be able to land on the planet, collect samples, launch off the surface, and then rendezvous with a spacecraft in
orbit that could return the samples to Earth. This requires a significant amount of technology, including a heavy-lift rocket, a lander, a sample collection system, and a spacecraft for the return journey.
Another challenge of a Mars sample return mission is the potential for contamination. Scientists are concerned that any samples brought back from Mars could contain microbial life that could contaminate Earth, potentially causing a pandemic. Therefore, any spacecraft sent to Mars would need to be carefully sterilized to prevent contamination.
Despite these challenges, plans are currently underway for a Mars sample return mission. The Perseverance rover, which landed on Mars in 2021, is equipped with a sample collection system that will collect and store samples for future retrieval. A joint mission between NASA and the European Space Agency (ESA) is currently in the planning stages, which will involve a rover and a lander that will retrieve the samples and launch them into orbit, where they will be picked up by a NASA spacecraft for the return journey to Earth.
Objectives
This lab has three objectives. The first is to look at one of Mars’ moons: Phobos and using your observations determine its orbital period. Second, determine the escape velocity of Mars, and finally, observe the night sky from this alien world
Procedure
In this astronomy lab, we will be using Stellarium software to explore the planet Mars and its moon Phobos. First, start up Stellarium and set the date to October 12, 2012 at 4:10 AM. Then, go to the SKY and VIEWING OPTIONS MENU (F4) and select the LANDSCAPE tab. Choose Mars and close the window.
Next, open the LOCATION menu (F6) and enter Mars for the planet. In the search area next to the magnifying glass, type "Viking 2" and select the option for Viking 2, Utopia Planitia. Don't make it your default location like
we did with New York. Remove the atmosphere and fog effects using the A and F keys. Make sure your view is directly South and that your Field of View (FOV) is at approximately 120⁰. You can use the page up or page down buttons to zoom in and out.
Press the L key to move time forward, with each press moving time a little faster. Watch for Phobos rising, and
as soon as you see it, press the letter K to pause the simulation. Note which direction Phobos is rising from and
whether it's consistent with the direction of motion for the planets and stars.
To understand Phobos' motion, we must measure its speed. Note the time of Phobos' rise and the time of its set. The difference between these two times should be approximately half the orbital period of Phobos.
Since Mars takes approximately 24 hours and 39 minutes to rotate, Phobos moves faster than Mars and seems
to move backwards compared to other celestial objects. Note how many orbits of Mars Phobos makes in one Martian day. Check whether the planet Mars has a "North Star." If so, note what it is. If not, determine the nearest equivalent and explain how you found out. Calculate the escape velocity of Mars using the equation v = sqrt((2GM)/R), where G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet. Using your textbook as a resource, find the mass and radius of Mars to complete this calculation
.
Finally, explore the night sky of Mars and note whether the constellations are different from those seen on Earth. Turn them on using the letters C and B.
Discussion
Phobos is an important target for Mars exploration because it is one of the two natural satellites of Mars and studying it can help us understand the history and evolution of the Martian system. Phobos is also of interest for future human missions to Mars because it could potentially serve as a base for humans to explore the planet. Additionally, because Phobos is in a very low orbit around Mars, it is subject to tidal forces that are causing it to spiral inward towards the planet. Eventually, Phobos will either collide with Mars or break apart due to the tidal stresses and studying it can help us understand the processes that are leading to its demise. Based on the observation of Phobos in Stellarium, with the view from October 12, 2012, Phobos rose at approximately 8:11 and set at 11:38. Half of the orbital period of Phobos was approximately 3 hours and 45 minutes, with the approximate orbital period of Phobos being 7 hours and 30 minutes. Since Phobos moves faster that Mars rotates, it makes 3 orbits in one Martian day. Regarding the escape velocity of Mars, we need to first find the mass and radius of Mars To find the mass of Mars, we can use Kepler's Third Law which relates the period and distance of a planet's orbit to its mass. According to the Openstax Astronomy
textbook, the period of Mars is 1.88 Earth years and the average distance between Mars and the Sun is 1.52 astronomical units (AU).We can use the following equation to calculate the mass of Mars, where M is the mass of Mars, G is the gravitational constant, P is the period of Mars, and a is the average distance between Mars and the Sun: M = (4π²a³) / (GP²) Plugging in the values for P,
a, and G, we get:
M = (4π² x (1.52 AU)³) / (6.6743 x 10^-11 N m²/kg² x (1.88 Earth years)²)
M = 6.39 x 10^23 kg
Therefore, the mass of Mars is approximately 6.39 x 10^23 kg.
To find the radius of Mars, we can use the surface gravity and the mass of Mars. According to the Openstax Astronomy
textbook, the surface gravity of Mars is 3.71 m/s². We can use the following equation to calculate the radius of Mars, where r is the radius of Mars, G is the gravitational constant, M is the mass of Mars, and g is the surface gravity of Mars: r = (GM / g)^(1/2) Plugging in the values for G, M, and g, we get:
r = ((6.6743 x 10^-11 N m²/kg²) x (6.39 x 10^23 kg)) / (3.71 m/s²)
r = 3,397 km
Therefore, the radius of Mars is approximately 3,397 km.
Using the formula v = sqrt((2GM)/R), where G is the gravitational constant (6.6743 x 10^-11 Nm^2/kg^2), M is the mass of Mars, and R is the radius of Mars, we can calculate the escape velocity of Mars:
v = sqrt((2 x 6.6743 x 10^-11 Nm^2/kg^2 x 6.39 x 10^23 kg) / (3,389.5 km + 6,371 km))
v ≈ 5.03 km/s
This means that in order to escape the gravitational pull of Mars, a spacecraft would need to reach a velocity of at least 5.03 km/s.
Achieving the escape velocity of Mars would require a spacecraft to accelerate to a speed of 5.03 km/s in order to escape the planet's gravity well. This can be accomplished using rockets or other forms of propulsion, such as ion thrusters. The amount of fuel required to achieve this velocity depends on the mass of the spacecraft and the specific impulse of the propulsion system. In general, spacecraft that are designed to travel to Mars carry a large amount of fuel to accomplish the necessary maneuvers. Some of this fuel can be generated on Mars itself, using resources such as water and carbon dioxide that are present on the planet.
The stars would appear similar from Mars as they do from Earth, with some minor differences due to the planet's different atmosphere and location in the solar system. From the surface of Mars, the stars would appear to move across the sky in the same way as they do on Earth due to the planet's rotation. However, the apparent position of the stars would be slightly different due to Mars' orbital motion around the Sun. Additionally, the atmosphere of Mars is much thinner than that of Earth, which would lead to less scattering of
light and potentially clearer views of the stars.
After exploring the night sky from Mars, the views of constellations are in different than the views of constellations from Earth. The positions and appearances of the constellations in the night sky are dependent on the observer's location. Because Mars has a different location in space than Earth, the stars will appear to be in different positions in the Martian sky. In addition, the Martian atmosphere is different from Earth's atmosphere, which could affect the appearance of the stars. For example, the atmospheric composition of Mars is thinner than Earth's, and there is less atmospheric scattering and distortion. This could make the stars appear brighter and clearer than they do from Earth. Therefore, an observer on Mars would see different constellations in different locations and with a different appearance compared to an observer on Earth.
Conclusion Mars exploration is a topic of great interest for scientists and space enthusiasts around the world. There are many reasons why Mars should be explored, and the potential benefits of doing so are vast.
One of the main reasons for exploring Mars is to better understand the formation and evolution of the solar system. Mars is similar to Earth in many ways, and studying its geological history, atmospheric composition, and potential for supporting life can provide valuable insights into the early history of our own planet and the processes that shaped the solar system as a whole.
Another important reason for exploring Mars is to search for signs of past or present life. Mars is thought to have once had liquid water on its surface, and there is evidence that microbial life may have existed there in the past. If evidence of life is found on Mars, it could have profound implications for our understanding of the origins of life in the universe.
In addition to its scientific potential, Mars also holds promise as a potential destination for human exploration and settlement. The challenges of living and working on Mars are immense, but there are many potential benefits as well, such as the potential for resource extraction, the development of new technologies, and the expansion of human civilization beyond Earth.
Of course, exploring Mars is not without its challenges. The harsh conditions on the Martian surface, including extreme temperatures, radiation exposure, and a thin atmosphere, make it a difficult environment to work in. However, there have been many successful missions to Mars already, and advances in technology and robotics
are making it increasingly feasible to explore the planet in greater detail.
In conclusion, Mars exploration holds great promise for advancing our understanding of the solar system and the potential for life beyond Earth, as well as for the development of new technologies and the expansion of human civilization. While there are certainly challenges to be overcome, the potential benefits make it a worthy pursuit for scientists and space agencies around the world.
1.
Scientific exploration: Mars is a treasure trove of scientific data waiting to be uncovered. The planet's unique geology and geography, including its towering volcanoes, massive canyons, and ancient riverbeds, can provide insights into how the planet formed and evolved over time. Scientists are also interested in
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studying Mars' atmosphere, which is made up mostly of carbon dioxide, and its potential for supporting life, past or present. There is also the potential to study Mars' magnetic field and its interactions with the solar wind, which can help us better understand how magnetic fields work in our own solar system.
2.
Human exploration: Mars has long been a subject of fascination for those interested in human exploration and settlement beyond Earth. The planet's relative proximity to Earth, combined with its potential resources and potential for supporting life, make it an attractive destination for future human missions. NASA, SpaceX, and other space agencies and private companies are actively working on plans to send humans to Mars in the coming decades, with the goal of establishing a permanent human presence on the planet.
3.
Technological development: The challenges of exploring Mars have pushed scientists and engineers to develop new technologies and solutions for surviving and thriving in space. These advances, in turn, have potential applications on Earth, such as in healthcare, energy, and transportation. For example, the development of lightweight, durable materials for spacecraft can also be used in the production of more efficient and cost-effective cars and airplanes.
References
Chaisson, Eric, and Steve McMillan. Astronomy Today Volume I: The Solar System. 8th ed., Pearson, 2013.
Fraknoi, Andrew, David Morrison, and Sidney C. Wolff. Astronomy. OpenStax, 2018.
McSween Jr., Harry Y. Mars. Cambridge University Press, 2018.
NASA. “Phobos & Deimos.” Mars Exploration Program, NASA, 2022, https://mars.nasa.gov/mars-
exploration/moons/phobos-and-deimos/.
Space.com. “The Future of Mars Exploration: Red Planet, Human Colonies and Beyond.” Space.com, 16 Mar. 2022, https://www.space.com/future-of-mars-exploration.html.
The Planetary Society. “The Scientific Case for Mars Exploration.” The Planetary Society, 2018, https://www.planetary.org/mars/the-scientific-case-for-mars-exploration.
Weigel, Angelo L. Aerospace Engineering Desk Reference. CRC Press, 2016.
“Why Mars Matters.” NASA, 2022, https://www.nasa.gov/topics/journeytomars/why-mars-matters.html.
Wyrick, Danielle, et al. “Mars Exploration: The Challenges and Opportunities.” Frontiers in Astronomy and Space Sciences, vol. 8, 2021, https://www.frontiersin.org/articles/10.3389/fspas.2021.674068/full.
APPENDIX A – STEP BY STEP INSTRUCTIONS
Instructions
1.
Start up Stellarium
.
2.
Set your date by pressing the F5
key to
10/12/2012. At a time of 04:10:00 (AM)
3.
Go to your SKY and VIEWING OPTIONS MENU
(
F4
)
4.
Select the LANDSCAPE
tab
5.
Select Mars
6.
Close this window.
7.
Open you LOCATION menu (
F6
) 8.
For Planet, enter Mars, and press enter.
9.
In the search area (next to the magnifying
glass) enter the following: Viking 2
10.Select the option for Viking 2, Utopia Planitia
and close the window (DO NOT make it your
default location as we have done with New
York).
11.Remove the Atmosphere, and Fog Effects (
A, and
F, keys).
12. Make sure you view is directly South (the
cardinal letter S is at the center of your screen)
13.Your Field of View (FOV) as seen on the bottom
of the screen should be at approximately
120⁰ (use the page up, or page down
buttons to zoom)
14.By using the L
key you will move time
forward, each press of the L
key will move
time just a little faster. Soon you will a
moon of Mars, PHOBOS rising. Press the
letter K as soon as you see Phobos to
pause the simulation
.
15.Which direction is Phobos rising from? Is
that consistent with the direction of
motion for the planets and stars?
16. To understand Phobos’ motion we must measure its speed. Note the total time it took Phobos to rise and set. a.
Make note of the time of Phobos’ rise :
b.
Make note of the time of the Phobos set: c.
The difference between these two times (b-c) should be approximately half the orbital period of Phobos:
17. Since Mars takes approximately 24 hours and 39 minutes, Phobos moves faster than Mars rotates and therefore seems to move backwards compared to the other celestial objects. How many orbits of Mars does Phobos make in one Martian day?
18. Does the planet Mars have a ‘North Star’? If so, what is it? If not, what would be the nearest equivalent? How did you find out? OPTIONAL TO ANSWER
19. How can we get to Mars? To launch a space craft from Earth you would require a speed of approximately 11 km/s to achieve what is known as “Escape Velocity”. The following equation is used to calculate this quantity:
a.
G
is a constant known as the “Gravitational Constant” and is
equal to a quantity of: 6.67 x 10
-11
Nm
2
/kg
2
.
M
is the mass of the planet you’re trying to escape R
is the radius you are from the center of that planet when sitting
at its surface.
Your result from b minus your result from a
=
Multiply the result by 2 to get the approximate orbital period of Phobos:
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b.
For earth this equation takes on the following dimensions:
c.
Using your textbook as a resource to find the mass of Mars, and it’s radius find the escape velocity of Mars (SHOW ALL WORK):
20.Were you surprised by this result? Why? What are the implications for a return mission from Mars? Will it be easier or harder? USE THIS FOR YOUR DISCUSSION AND CONCLUSIONS
21. Before ending this lab, explore the night sky of Mars. Are the constellations (turn them on using the letters C and
B)
different from those you see on Earth? Explain!
The lab instructions do not specify which direction Phobos is rising from. The student will need
to observe Phobos rising in Stellarium and note the direction.
To determine the orbital period of Phobos, the student needs to note the time of Phobos' rise and the time of its set, and calculate the difference between these two times. The lab instructions do not provide specific values for these times.
Since Phobos moves faster than Mars rotates, it can complete multiple orbits around Mars in a
single Martian day. The lab instructions do not provide a specific number for the number of Phobos orbits in one Martian day, and the student will need to observe and count the number of orbits.
Mars does not have a North Star, as Earth does. The North Star is located close to the celestial North Pole, which is the point in the sky directly above Earth's North Pole. Since Mars has a different axis of rotation than Earth, it does not have a celestial North Pole in the same location as Earth. Instead, Mars has a North Celestial Pole, which is the point in the sky directly
above Mars' North Pole. There is no bright star located close to the North Celestial Pole that can serve as a North Star for Mars. The student could determine this by using Stellarium to observe the location of the North Celestial Pole on Mars and checking for nearby bright stars.
To calculate the escape velocity of Mars using the equation v = sqrt((2GM)/R), where G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet, the student needs to find the values of G, M, and R for Mars. According to the textbook, the mass of Mars is approximately 6.39 x 10^23 kg, and the radius of Mars is approximately 3,390 km (3.39 x 10^6 m). The gravitational constant G is approximately 6.674 x 10^-11 N(m/kg)^2. Plugging in these values, the equation becomes:
v = sqrt((2 x 6.674 x 10^-11 x 6.39 x 10^23)/(3.39 x 10^6)) v = sqrt(24.753) v = 4.975 km/s
Therefore, the escape velocity of Mars is approximately 4.975 km/s.
To determine how many orbits of Mars Phobos makes in one Martian day, we need to first determine the length of a Martian day in terms of Phobos' orbital period.
The orbital period of Phobos is approximately 7 hours and 39 minutes.
There are approximately 24 hours and 39 minutes in a Martian day.
Dividing the length of a Martian day by the orbital period of Phobos, we get:
24 hours 39 minutes / 7 hours 39 minutes ≈ 3.191
Therefore, Phobos makes approximately 3.191 orbits of Mars in one Martian day.