To develop a computational model of the velocity of a satellite based on the distance from Earth and the time elapsed, we can use the formula given:
\[ V = \frac{2nX}{Y} \]
Where:
- \( V \) is the velocity,
- \( n \) is a constant (in this case, it's not specified but we can assume \( n = 1 \) for simplicity in calculations),
- \( X \) is the distance from Earth,
- \( Y \) is the time elapsed.
Given the dataset:
- Distances (X): 100, 20, 15, 29, 67, 5
- Time elapsed (Y): 31, 44, 27, 22, 36, 52
We can develop a simple Python script that calculates the velocity for each pair of distance and time. Here's how you can implement it:
# Define the constants
n = 1 # Assuming n = 1 for simplicity
# Dataset
X = [100, 20, 15, 29, 67, 5]
Y = [31, 44, 27, 22, 36, 52]
# Calculate the velocities
V = [2 * n * x / y for x, y in zip(X, Y)]
# Print the results
for distance, time, velocity in zip(X, Y, V):
print(f"Distance: {distance} km, Time: {time} seconds, Velocity: {velocity:.2f} km/s")
Explanation of the Code:
- We define a constant \( n \) that determines the factor in the velocity calculation.
- We create lists \( X \) and \( Y \) holding the corresponding distances and times.
- We then utilize a list comprehension to calculate the velocity \( V \) for each distance-time pair and store these results in the list \( V \).
- Finally, we print out each distance, corresponding time, and calculated velocity.
Running the Code:
To run this code, you can use an online tool like Trinket, Repl.it, or your local Python environment. Simply copy the code, paste it into the tool, and execute it.
This will output the velocities for the given pairs of distance and time, all organized neatly for you to review. The output will show each distance, the time elapsed, and the computed velocity, formatted to two decimal places.