Edit columns#

Planetary Descent#

Todays mission is to examine the vegetation of a newly discovered class M planet. Because your ship is not equipped with teleportation, your researchers will have to take a shuttle to the surface. Your job is to bring them down safely.

Currently, your ship (and the shuttle) is orbiting in an altitude of 500km.
Once the shuttle leaves orbit, the planets gravity accelerates the shuttle constantly by $9.81 frac{m}{s^2}$.
At an arbitrary moment, the shuttle can activate its thrusters. The thrusters thrust with an acceleration of $10.0-100.0frac{m}{s^2}$.
You cannot deactivate the thrusters or change their strength (this produces a lot of cleanup work and is reserved for emergencies).
To reach your destination on the surface, you want to reach the surface within 1500 seconds.

When should you activate the thrusters and how strong should they be? Let's simulate the landing to find out!

Create a DataFrame with a single Column#

Simulate the ships' altitude over time with a resolution of one second. Start by creating the time as a column:

import pandas as pd
import numpy as np

seconds = np.arange(1500, dtype=np.int32)
df = pd.DataFrame({'seconds': seconds})

The dictionary format in the parentheses allows you to define a DataFrame with multiple columns as well.

Add Columns#

Because the gravity does not change, we create a new column and fill it up with one value:

df['gravity'] = 9.81

For the thrust, we create a new column, settting all values to zero:

df['thrust'] = 0.0

An alternative is to create a NumPy array or list first. This works as long as the size of the array matches the shape of the DataFrame:

rows = df.shape[0]
df['thrust'] = np.zeros(rows)

If you re-assign to an existing column, the old column gets replaced.

Modify the contents of a Column#

Now we need to switch on the thrusters.

Fill up the bottom part of the thrust column with the thruster strength. The df.loc allows you to access a part of a column:

activation_time = 500  # after 500 seconds
strength = 50.0        # must be between 10.0-100.0
df.loc[activation_time:, 'thrust'] = strength

Column Arithmetics#

We can create new columns using math equations:

df['acceleration'] = df['gravity'] - df['thrust']

To calculate the speed, we need to add all acceleration values up to a given row:

df['speed'] = df['acceleration'].cumsum()

Any calculation may include constant values. They are applied to every row.

df['altitude [km]'] = 500 - (df['speed'].cumsum() / 1000)

Remove a Column#

The seconds column was useful in the beginning, so that the DataFrame was not empty. But we do not really need it for the calculation. To remove it, use:

df.drop('seconds', axis=1, inplace=True)

The argument axis=1 refers to columns (axis=0 deletes rows). The inplace=True modifies the DataFrame.

Visualize the Descent#

Let's plot the outcome of the simulation. A simple line plot is sufficient. We add a horizontal line to indicate the surface.

from matplotlib import pyplot as plt

df['altitude [km]'].plot()
plt.hlines(xmin=0, xmax=1500, y=0.0, color="red")

To debug the descent, it may help to see the speed as well. We can show both columns in a line plot, but need to switch to a log-scale (both for comparability and precision).

ax = df[['altitude [km]', 'speed']].plot()
ax.set_yscale('log')

When you see that your altitude goes through the floor of the log plot, it means that the spaceship would crash into the planet.

Challenge#

Once you reach an altitude of less than 100 m and a speed of less than 100 m/s, you can activate the anti-gravitational landing gear that will finish the landing automatically.

Find out values for activation_time and strength.