Writeup Hack-A-Sat: Fiddlin' John Carson

Challenge description: Your spacecraft has provided its Cartesian ICRF position (km) and velocity (km/s). What is its orbit (expressed as Keplerian elements)?

The challenge is available at this address.

Let's connect to the challenge instance:

We need to determine the orbital parameters from the given Cartesian position and velocity. It’s important to understand what these orbital elements represent. For a refresher on orbital data, check out this lesson on [TLE basics](just here) :)

Below is a diagram illustrating the various parameters (note: the spacecraft’s placement is arbitrary for illustration):

The calculations to extract the orbital elements can be pretty involved. So instead, we’ll use the Python library poliastro to do the heavy lifting.

First, convert our lists for position and velocity into quantities with proper physical units:

Here, multiplying by u.km and u.km/u.s (from astropy) converts each coordinate into a Quantity with the appropriate units.

Next, we call the method Orbit.from_vectors to calculate the orbital elements:

Here, Earth provides the necessary gravitational parameters. And specifying the exact time is crucial since orbital parameters can change over time.

Once the orbit has been computed, we can extract the six Keplerian elements:

Using to_value(u.deg) (from astropy) converts the angles from radians to degrees.

Finally, print all the orbital parameters and verify: