In the last few weeks we learned a little about what it takes to land on the surface of the Moon. We learned about the maneuvers required to execute a safe landing and used a simulator to practice soft, hard and ‘impact’ (or crash) landings with landing speeds in the hundreds of meters per second (mps). We know that many of you are having fun practicing with the simulator. We thank all of you for taking the time to send us emails telling us what you learned and how well you are doing as lunar lander commanders and pilots. Next week we will share some of your “lessons learned”, top scores and impact speeds.

We know that many of you have become “OUTSTANDING” lunar lander commanders and pilots. Your scores tell us that you have performed many tight landings between boulders and precision landings like the Apollo 12 team of Conrad and Bean. Some of you have told us that you are trying to maximize the landing speed of your ‘impact’ missions. If you would like to improve your impact speed you can do a few experiments as an “impact analysis”. Here are a few suggested cases to run. It is important that you do all the burns in a continuous firing to achieve the best results. We recommend that you record the key parameters in a table. Remember that you can “Pause” the simulation at any point to make sure that you have the time to write down the key parameters. Please write back to let us know how you did (especially if you did even better!). Please also let us know your age so that we can publish your great results in our next blog post. We will also share with you our highest impact velocity and how we accomplished it. We hope that you continue to learn and have fun. We would love to hear what you learned from these experiments.

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Case 1: What happens when you use all the fuel to maximize the altitude of the craft then allow it to “free fall” under the influence of the moon’s gravity? What is the maximum altitude and vertical velocity achieved by the craft at the end of the continuous burn? Remember that you can “Pause” the simulation at any point to make sure that you have the time to write down the key parameters in your table. Make sure to monitor the craft’s altitude and vertical velocity (v_y). What happens to the vertical velocity as the altitude increases? What is the maximum altitude the LM achieves prior to beginning the “free fall” (hint: note the vertical velocity or v_y)? What is the vertical velocity (v_y) at this point? Make sure to record the maximum altitude in the table. What happens to the vertical velocity as the craft “free falls”? What was the landing speed or impact velocity? Was it higher than 250 mps? Can you “hypothesis” why?

Here is the “Sequence of Events” (or SOE) to execute the Case 1 maneuver: (only a single main engine burn depleting all the fuel – Maneuver 1)

1. Press “Reset” and immediately press the “Pause” button in the simulation. Record the “Initial Key Parameter” in the table – fuel (kg), altitude (m) and vertical velocity (v_y), horizontal velocity (v_x) both in (mps).

2. Maneuver 1 – Main Engine Continuous Burn: Press “Unpause” and immediately fire the main engine continuously until the fuel remaining = 0 kg. Try to “Pause” the simulation immediately after running out of fuel. Record the “Post Maneuver 1” key parameters - fuel (kg), altitude (m) and vertical velocity (v_y), horizontal velocity (v_x) both in (mps).

3. Monitor the craft’s altitude and vertical velocity (v_y). What happens to the vertical velocity as the altitude increases? Make sure to record the “Maximum Altitude” key parameters in the table – “Pause” the simulation if you need to. What is the vertical velocity (v_y) at this point? What happens to the vertical velocity as the craft “free falls”?

4. What is the landing speed or impact velocity? Record this “Impact Speed” in the table. Was it higher than 250 mps? Can you guess or “hypothesis” why?

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Case 2: What if we reserve ¼ of the fuel in the tank (~ 200 kg) to “assist” or add to the effect of gravity? This will require us to fire the main engine twice. The first maneuver to increase the altitude (like in Case 1) and the second firing to use the rest of the fuel to “assist” or add to the acceleration due to gravity. What direction does the craft’s acceleration and velocity vector need to be pointed to increase the impact velocity?

Remember you can turn on the “vector” option to watch the acceleration and velocity vectors as you fire the main engine (or thruster). If we want to increase our impact velocity then what direction does the main engine need to be pointing? Another way to think about this is to ask what direction the lunar lander’s axis needs to pointing (this is also called the LM’s “attitude”)? The dashboard provides you with the LM’s pointing vector at the very top. The pointing or attitude vector is aligned with the main engine and therefore represents the direction that the force is applied when the thruster is fired. This force vector accelerates the craft in that direction when the main thruster is firing. You can fire the main engine in different directions by changing the “attitude” of the craft using the “left” (<--) and “right” (-->) arrow keys. These keys fire the Reaction Control or attitude thrusters to “tilt” the craft in the direction of the arrows. If we tilt the attitude and fire the main engine - what happens to the acceleration and velocity vectors (remember the size represents the instantaneous magnitude of the vectors)? What happens when you stop firing the main engine? Can you guess or “hypothesis” why?

So, if we want to “assist” the acceleration due to gravity with our second main engine firing then we will have to align the acceleration vector (or craft attitude) with the direction of the gravitational force – this is in the same direction of the LM “free fall” in Case 1 or toward the surface of the moon. This means that we will have change our crafts attitude by 180 degrees to align the thrust in the proper direction to “add” to the acceleration due to gravity. We can do this by using either “arrow” key to “reorient” the craft and make the attitude vector point toward the moon. We will need to do this BEFORE we fire the main engine again to use up all the fuel. Therefore, Case 2 will require three maneuvers; two main engine burns and one 180 degree reorientation maneuver between the main burns. So, here is the “Sequence of Events” (or SOE) to execute the Case 2 maneuvers:

1. Press “Reset” and immediately press the “Pause” button in the simulation. Record the “Initial Key Parameter” in the table – fuel (kg), altitude (m) and vertical velocity (v_y), horizontal velocity (v_x) both in (mps).

2. Maneuver 1 – Main Engine Continuous Burn: Press “Unpause” and immediately fire the main engine continuously until the fuel remaining = 0 kg. Try to “Pause” the simulation immediately after running out of fuel. Record the “Post Maneuver 1” key parameters - fuel (kg), altitude (m) and vertical velocity (v_y), horizontal velocity (v_x) both in (mps).

3. Monitor the craft’s altitude and vertical velocity (v_y). What happens to the vertical velocity as the altitude increases? Make sure to record the “Maximum Altitude” key parameters in the table – “Pause” the simulation if you need to. What is the vertical velocity (v_y) at this point? What happens to the vertical velocity as the craft “free falls”?

4. Maneuver 2 – Reorientation: use one of the arrow keys [either “left” (<--) OR “right” (-->)] to reorient the attitude vector of the craft to point toward the lunar surface. This will align the thrust of the next main engine burn with the acceleration of the moon’s gravity to increase the impact velocity.

5. Maneuver 3 – Main Engine Continuous Burn #2: First you will need to “Pause” the simulation just before you fire the main engine again to record the “Pre-Maneuver 3” key parameters in the table. Then “Unpause” the simulation and immediately fire the main engine continuously until the fuel remaining = 0 kg. Make sure that you deplete the tank before you impact the surface of the moon. Do you think it makes a difference when you chose to do this maneuver during the “free fall”? You might want to run a few cases to find out. Can you guess or “hypothesis” why?

6. What is the landing speed or impact velocity? Record this impact velocity in the table. Was it higher than 250 mps? Was it greater than Case 1? Can you guess or “hypothesis” why?

These experiments demonstrate the Scientific Method (see the “We Love Rockets!” blog post). Do you like to do scientific experiments? Would you like to be a scientist?

We promised to provide you the answers to last week’s questions - so, here are the questions and answers:

Question: Why did the Apollo 12 lunar landing need to be so precise?

Answer: In November 1969, Conrad and Bean accomplished the second manned landing on the Moon and surprised themselves, proving Apollo could land precisely on a pre-selected patch of ground, this one just 150 meters, easily within "walking distance" from Surveyor 3. The American unmanned lander was situated just where mission planners believed it to be, inside the small crater where its 65 hour mission on the surface had ended two years earlier.

The Lunar Reconnaissance Rover (LRO) Narrow Angle Camera's (LROC NAC) captured this outstanding close-up of Apollo 12's perch on the northwestern rim of "Surveyor Crater" in the Sea of Storms (left). The Surveyor 3 spacecraft (right), Lunar Module descent stage, and Apollo Lunar Surface Experiment Package (ALSEP) along with astronaut tracks are all visible in this image of the Apollo 12 landing site. Credit: NASA/GSFC/Arizona State University

Here are a few pictures of the way the astronauts found Surveyor 3 on the surface of the Moon:

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Questions: What happens when you tilt the craft and fire the main engine? What happens when you apply the thrust with a horizontal velocity component (v_x)? Remember to turn on the “Vector” option. Note the difference between the velocity and acceleration vectors as you change the craft’s tilt angle to provide a horizontal velocity component. How does the simulation calculate these vectors?

Answer: Although most of the operations are self-explanatory, however, a brief description of acceleration is warranted. Acceleration is broken down into vertical and horizontal components, where the vertical component is normal to the Moon's surface. The instantaneous vertical and horizontal accelerations of a moving body in reference to this surface are Av=Vh2/r and Ah=–VhVv/r. To this we add the accelerations resulting from gravity and thrust. Gravity, of course, acts vertically downward. The vertical and horizontal components of thrust are a function of the pitch (or tilt) angle.

To calculate the velocity change over a period of time, the accelerations at the start of the period and the end of the period are averaged. Likewise, altitude is calculated using the average vertical velocity. Due to the interdependency of all the variables, this averaging technique requires the problem be solved by iteration.

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Next week we will share some of your “lessons learned”, top scores and impact speeds. Please write back to let us at magic@kelvin.net to let us know how you did (especially if you did even better!). Please also let us know your age so that we can publish your great results in our next blog post. We will also share with you our highest impact velocity and how we accomplished it. We hope that you continue to learn and have fun. We would love to hear what you learned from these experiments.

Keep Having Fun Learning!

Mystical Moon

"All one can really leave one's children is what's inside their heads. Education, in other words, and not earthly possessions, is the ultimate legacy, the only thing that cannot be taken away." -Dr. Wernher von Braun