## QUESTION

Motion

1. Use the value for the acceleration due to gravity on the moon to complete this extension.

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Use the value for the acceleration due to gravity on the moon to complete this extension. Boost the LM to an altitude of ~300 m such that the y-Velocity will be zero at this point.

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Boost the LM to an altitude of ~300 m such that the y-Velocity will be zero at this point.

(You may have to pause the simulation to get the sequence down.) Have the LM tilted 90 0

to the left or to the right so that if you fired the engines the resulting velocity would be

along the x-axis.

2. Once at this altitude, and with the LM in the proper position, fire the engines for a short

burst so that the LM gains a velocity of ~0.5 m/s (make sure you write down the exact

velocity).

3. Predict where the LM will crash if you let it continue on its path to the surface of the moon.

Does your prediction match the readout for the LM’s range on the display panel? (Note,

you may have to maneuver your LM so that you have an initial x-position = 0m. Do this

before you set the LM in position at the 300 m altitude. If this is too difficult, just note

your initial x-position.) Find the % error between your prediction and the actual range

14 mins ago

## ANSWER

**Motion Analysis: Lunar Module Trajectory and Predictive Accuracy**

**Introduction**

In this analysis, we will examine the motion of a Lunar Module (LM) on the Moon’s surface. We will consider the effects of gravity and engine thrust to predict the LM’s trajectory and compare it with the actual range obtained from the display panel. This exercise aims to demonstrate the application of physics principles to real-world scenarios in space exploration.

**Boosting the LM to 300m altitude**

To achieve a zero y-velocity at an altitude of approximately 300 meters, we will employ the acceleration due to gravity on the Moon. According to lunar conditions, the acceleration due to gravity is approximately 1.6 m/s^2.

To begin, we will tilt the LM 90 degrees either to the left or right. This positioning ensures that firing the engines will result in a velocity along the x-axis, parallel to the lunar surface. The specific choice of left or right tilt will depend on the desired direction of movement.

**Firing the engines for a short burst**

Once the LM reaches the desired altitude, we will initiate a short burst from the engines to achieve a velocity of approximately 0.5 m/s. It is important to record the exact velocity achieved during this maneuver for subsequent analysis.

**Predicting the LM’s crash point**

To determine the crash point of the LM, we need to consider the combined effects of gravity and the initial velocity acquired in step 2. By extrapolating the LM’s trajectory from the point of the short burst to the lunar surface, we can estimate where it will crash.

To enhance the accuracy of our prediction, we will assume an initial x-position of 0 meters, aligning with the display panel’s reference frame. This step ensures that our calculations closely match the measurements provided by the LM’s onboard instruments.

After executing the trajectory prediction, we will compare our estimated crash point with the range displayed on the panel. If the prediction matches the readout, it indicates that our calculations accurately captured the influence of gravity and engine thrust on the LM’s trajectory.

**% Error Calculation**

To assess the accuracy of our prediction, we will calculate the percentage error between our estimated range and the actual range provided by the LM’s display panel. The formula for percentage error is:

% Error = [(Actual Range – Predicted Range) / Actual Range] * 100

By comparing these values, we can quantitatively evaluate the effectiveness of our predictive model.

**Conclusion**

In this analysis, we explored the motion of a Lunar Module on the Moon’s surface, considering the effects of gravity and engine thrust. By boosting the LM to an altitude of 300 meters and firing the engines for a short burst, we acquired the necessary parameters for predicting the crash point of the LM.

By comparing our prediction with the range displayed on the LM’s panel, we evaluated the accuracy of our model. The percentage error calculated between the predicted and actual ranges provides a quantitative measure of the predictive model’s effectiveness.

This exercise demonstrates the practical application of physics principles in the context of space exploration. Accurate trajectory predictions are crucial for mission planning and ensuring the safety and success of lunar landings.