Switching to the Moon’s gravity

This figure, created a few days ago, shows the Earth- and Moon-centered orbit estimates.  It also shows the uncertainty in these estimates.  The uncertainty is very small, although it's hard to see the scale in this picture.

This figure, created a few days ago, shows the Earth- and Moon-centered orbit estimates. It also shows the uncertainty in these estimates. The uncertainty is very small, although it’s hard to see the scale in this picture since we zoomed in to show it.  The uncertainty is shown as a 3 dimensional region in space that represents where LADEE is most likely to be.  The region in the picture is only a few hundred meters long, using the estimate from several days ago (it’s smaller now).

As we mentioned previously, we’re not quite within the Moon’s sphere of influence yet.  (LADEE will be within most definitions of the Moon’s sphere of influence by 19:30 UTC today, October 5th.)  Even so, we’ve been modeling the significant effects of the Moon’s gravity on our trajectory since we launched.  The way we modeled it, as is standard, was as if the Moon is a perfect sphere.  In reality, however, we know from all the previous lunar missions that the Moon’s gravity field is quite “lumpy” and when we are in orbit around the Moon, we will model the Moon’s gravity with many more equations than we did when LADEE was close to Earth.  As we approach the Moon, we have to transition from considering the Earth’s gravity as dominant to the Moon’s gravity as the primary effect.  For trajectory design purposes we’ve been switching from an Earth-centered orbit propagation to a Moon-centered orbit propagation when LADEE gets within 50,000 km of the Moon’s center.   (Our analysis has shown that this number doesn’t have to be very precise to meet the accuracy requirements.  On the Clementine lunar mission we didn’t switch to a Moon-centered orbit propagation until we captured at Lunar Orbit Insertion.)

In addition to calculating the trajectories, we also have to track LADEE and estimate the orbit, using a technique called “Orbit Determination.”  Fellow Astrogators Lisa Policastri, Ryan Lebois, and Craig Nickel work with us on this.  The method we use is an Extended Kalman Filter, which processes tracking data sequentially as we receive the data from the tracking stations around the world.  Orbit Determination is sort of like curve fitting, and one of our jobs is to estimate the trajectory that best fits the tracking data.  As you can see from the pictures we’ve posted previously, LADEE’s trajectory bends a lot as it goes from the Earth’s influence to the Moon’s.  To model the changing gravity for Orbit Determination, we decided to do something different than we do for trajectory design.  Instead of switching from Earth-Centered to Moon-centered at a specified point, a few days ago we started running two algorithms side-by-side; one Earth-centered, and one Moon-centered.  We trend the two different orbit estimates, and by the time we reach the LOI1 maneuver (6 Oct 2013 10:57 UTC), which is just past periselene, we will be ready to transition to using the Moon-centered algorithm for the rest of the mission.

IBEX Lunar Synchronous Orbit

For the whole story, check out the June 24th, 2011 mission update by Dave McComas on the Official IBEX Web Site (ibex.swri.edu) .

The real challenge was to find an orbit that we could control for a long time. The original orbit could only be predicted for about 3 years. Cislunar space is a crazy place to try and fly a long-term trajectory; the slightest change in initial conditions can cause completely different trajectories years later. Because IBEX’s original orbit was often closer to the Moon than to the Earth, it was performing gravity assists regularly. The uncertainty in our initial conditions from orbit estimation knowledge and attitude re-pointing maneuvers would cause nearly identical trajectory predictions to eventually experience different gravity assist geometries, and the slightest change in that geometry during the encounter causes huge differences in the subsequent trajectory. Some predictions would hit the Earth (not a good thing for most space missions, by the way) and others would escape the Earth-Moon system (great for science, but not so good for communicating with a spacecraft designed to stay close to Earth.) Our new orbit keeps the apogee away from the Moon and has reduced the sensitivities. We can now predict this trajectory well beyond 11 years now so we can get the full Solar Cycle.

Here is our original trajectory in an Earth-centered Inertial (Mean Earth Equator and Mean Equinox of J2000.0) Coordinate system:

Original IBEX orbit

Original IBEX orbit at the beginning of nominal operations

The Earth is hard to see, but it is in the center, and the white circle is the Moon’s orbit. Now here it is in the Earth-Moon Rotating coordinate system; note the apogees that come close to the Moon:

The Original IBEX orbit shown in the Earth-Moon Rotating System

The Original IBEX orbit shown in the Earth-Moon Rotating System

In this rotating system the Earth and the Moon are both pretty much fixed (although the Moon moves up and down a bit because of its orbit’s eccentricity). The Earth is still in the center, and the Moon at the top of the white circle. The white line connects the Earth to the Moon (Don’t look for that with your telescope).
Here is our new orbit in Earth Inertial – not really all that different from the original (just a slightly larger semi-major axis and higher radius of perigee):

The new IBEX Orbit in Earth-centered Inertial coordinates

The new IBEX Orbit in Earth-centered Inertial coordinates

And here it is in the Earth-Moon rotating frame:

The new IBEX orbit in Earth-Moon Rotating Coordaintes

The new IBEX orbit in Earth-Moon Rotating Coordaintes

Note that the apogees stay far away from the Moon, so the gravity assists are much weaker. The spacecraft is always very near perigee when it crosses the Earth-Moon line. (And, no, the spacecraft trajectory is not perturbed by that big white line.)

For more information on the IBEX Flight Dynamics, check out the white papers at the Applied Defense Solutions website.

Astrogator swings past Jupiter

If you hadn’t heard, the entire trajectory to Pluto (New Horizons) was planned and is being flown by Astrogator. They just passed Jupiter (gravity assist) and are on their way to Pluto. They took a ton on of images as they passed.
Good job everyone!

Also remember, it’s the fastest thing ever built by man! only nine hours from the Earth to the Moon when it launched!

After they plan a maneuver they check it with JPL trajectory software and things are going perfectly!

Here’s the home page with a screen snap from STK:

Jupiter Swingby With Gator

New Horizons home page

New Horizons animation

Some links from the New Horizons home page:

Pluto-Bound New Horizons Spacecraft Gets a Boost from Jupiter

Tvashtar’s Plume


Little Red Spot

Fyi, they also do the maneuver planning for Messenger with Astrogator. JPL’s CATO is used for the multiple gravity assist trajectory design, and the high-fidelity maneuver planning and gravity assists are planned with Astrogator. See Messenger

There are lot’s of STK animations there, too!