Using Modeling and Simulation to solve Lambert’s problem to enable space travel

Spaceflight involves finding a path between an origin and a destination. In spaceflight mechanics, position and velocity are important because mathematically they determine the coordinates for both the origin and destination. The path between is called the orbit.

The determination of an orbit given two position vectors and the time of flight is known in celestial mechanics as Lambert’s problem, also known as two point boundary value problem. This contrasts with Kepler’s problem or propagation, which is rather an initial value problem.

The package poliastro.iod allows as to solve Lambert’s problem, provided the main attractor’s gravitational constant, the two position vectors and the time of flight. As you can imagine, being able to compute the positions of the planets as we saw in the previous section is the perfect complement to this feature!

For instance, this is a simplified version of the example Going to Mars with Python using poliastro, where the orbit of the Mars Science Laboratory mission (rover Curiosity) is determined:

ate_launch = time.Time(‘2011-11-26 15:02′, scale=’utc’)
date_arrival = time.Time(‘2012-08-06 05:17′, scale=’utc’)
tof = date_arrival – date_launch

ss0 = Orbit.from_body_ephem(Earth, date_launch)
ssf = Orbit.from_body_ephem(Mars, date_arrival)

from poliastro import iod
(v0, v), = iod.lambert(Sun.k, ss0.r, ssf.r, tof)

And these are the results:

>> v0
<Quantity [-29.29150998, 14.53326521, 5.41691336] km / s>
>>> v
<Quantity [ 17.6154992 ,-10.99830723, -4.20796062] km / s>

Welcome to Redmoon Systems, LLC.

Aerospace, Analysis, Modeling, Simulation, and Design

Redmoon Systems specializes in innovation and research in aerospace consulting. Our clients consist of major aerospace firms as well as diverse corporate and privately funded interests.

We leverage research and innovation across aerospace domains with experience to provide a unique blend of consulting services that meet the client’s needs in product development, project management, and business planning. Redmoon provides capabilities to bridge knowledge gaps in aerospace, security, and defense.

Cutting-edge industries employ a wide range of tools to enable technologies for military and civilian mission objectives. We specialize in computer aided design, modeling, and simulation across the multiple disciplines:

  • Mission Modeling and Control Systems
  • Situational analysis for space platforms  
  • Electro-optical systems for military, civilian, and scientific
  • End-to-end artificial intelligence solutions integrating algorithm development for tracking, discrimination, and analysis
  • Data fusion and graphical display of strategic information
  •  Space policy
  • Geopolitical analysis through application of space situational awareness systems to complex geospatial environments

Redmoon Systems remains uniquely positioned through its high-value innovation and consulting services for its clients. We provide the customer with advanced and effective knowledge-based tools for mission-driven pragmatic solutions.

A Picture is worth a Thousand Words

In ancient military strategy, it was seen as advantageous to occupy the high ground during a battle. Today, the high ground is provided by computer-assisted technologies such as virtual reality, simulation, automated analysis, and data fusion. In addition technologies using space for peaceful purposes contribute to advanced situational awareness of the battlefield. 

Data Analytics in Complex Space Environments

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