To download 50,000 pictures using the Google Static Maps API, you can follow these steps:

1.Obtain an API Key**: Before using the Google Static API, you'll need to obtain an API key from the Google Cloud Platform Console. This key will authenticate your requests.

2. Construct the URL: Use the following URL format to construct a request for each image: https://maps.com/maps/api/staticmap?parameters

   Replace "parameters" with the specific parameters for each image, including the location (center), image size, zoom level, and any optional markers.

3. Loop Through Cluster Centroids: Utilize the mean latitude and longitude of the households, defined by the cluster centroids in your dataset. Loop through these centroids to form the center parameter for each image request.

4. Set Image Size and Resolution: Ensure you set the size of each image to 400x400 pixels to match the area covered by a single pixel of your nighttime image data.

5. Adjust Zoom Level: Determine the appropriate zoom level to achieve a pixel resolution of approximately 2.5 meters per pixel.

6. Make HTTP Requests: Use a programming language (such as Python, JavaScript, or others) to automate the generation of URLs and make HTTP requests to download the images. You can use libraries like Requests (in Python) to handle the HTTP requests.

7. Save the Images: After making the requests, save the images to your local storage or a cloud storage service for further processing.

8. Consider API Limits and Billing: Be mindful of the API usage and billing information. Ensure compliance with any usage limits and billing requirements, as downloading a large number of images may have cost implications.

By following these steps, you should be to programmatically download 50,000 pictures using the Google Static Maps API while matching the specifications outlined in your project report.

It should be noted that while Google Maps API is a powerful tool, using it as you described may accumulate significant costs as the API isn't completely free. However, you can consider using alternative open-source satellite imaging services that are free, such as Sentinel Hub operated by the European Space Agency (ESA).

Here is a Python-based procedure on how to download satellite images using the library Sentinel Hub, in combination with tools like GeoPandas and Shapely for downloading an image based on cluster's centroids. You will need to install these libraries if you do not have them already1. Install Packages: If not already installed, you will need to install the following Python packages:

pip install sentinelhub geopandas shapely

2. Importing Required Libraries: In your Python script, import the necessary libraries:

from sentinelhub import SHConfig, SentinelHubRequest, MimeType, CRS, BBox, constants
import geopandas as gpd
from shapely.geometry import Point

3. Setting Up Hub Configuration: Replace 'YOUR-INSTANCE-ID' with Sentinel Hub instance ID.

INSTANCE_ID = 'YOUR-INSTANCE-ID' 

config = SHConfig()
config.instance_id = INSTANCE_ID

4. Define Function to Download Images:

def download_images(lat, long, config):
    # Define bounding box of the images to be downloaded.
    bbox = BBox(bbox=[long-0.001, lat-0.001, long0.001, lat+0.001], crs=CRS.WGS84)

    # Define the request for images.
    img_request = SentinelHubRequest(
        evalscript=constants.Evalscript.RAW_UINT8,
        input_data=[
            SentinelHubRequest.input_data(
                data_source=DataSource.SENTINEL2_L1C,
                time_interval=("2022-01-01T00:00:00", "2022--31T23:59:59"),
            )],
        responses=[
            SentinelHubRequest.output_response('default', MimeType.PNG)
        ],
        bbox=bbox,
        config=config
    )
    img_name = f"{lat}_{long}_image.png"
    with open(img_name, 'wb') as file:
        file.write(img_request.get_data()[0])

5. Load Cluster Centroids Data: Load your data containing cluster centroids. This example assumes you have a pandas DataFrame df with latitude and longitude columns.

centroids =pd.GeoDataFrame(df, geometry=gpd.points_from_xy(df.Longitude, df.Latitude))

6. Batch Download Images: Iterate over the centroid points data and download images.

for idx, row in centroids.iterrows():
    download_images(row['latitude'], row['longitude'], config)

The above python code will download Sentinel-2 images, of locations specified in your DataFrame, to your local directory. Remember to adjust the parameters as per your exact use case (like box size, time interval, and image resolution). Make sure to replace 'YOUR-INSTANCE-ID' with your actual instance ID from Sentinel Hub.

For acquiring Hub's instance ID:

• Go to the Sentinel Hub Dashboard (https://apps.sentinel-hub.com/dashboard/#/)
• Create a new account or sign in.
• Navigate to the "Configurations" segment.
• If necessary make a new configuration. Your instance ID is listed here.

Please note that this approach still requires access to Sentinel Hub's services. While their services are not free, they do offer a 30-day free trial, which could be beneficial for small-scale projects or academic research.

Be aware that while large scale data download is possible with Sentinel Hub, their free trial and free tier have limitations on the number of requests and the amount of data you can retrieve. As such, to download extensive, you may need to look into their pricing options.

Disclaimer: Please make sure you adhere to the terms and conditions of the chosen API. Data usage could have restrictions regarding distribution or commercial use.