Deep Impact Ejecta Plume Behavior

James E. Richardson, Jr.

Research Associate

Early Deep Impact Ejecta Plume Simulations:

Determining Comet Mass via Impact Ejecta Behavior

by James Richardson and H. Jay Melosh

Objectives

As part of the Deep Impact Discovery mission, the purpose of this project is to investigate the possibility of determining the mass of a target comet by monitoring the expansion and behavior of an impact ejecta plume emanating from that target comet. If all goes as planned, in July of 2005, a small, 370 kg impactor will be intentionally collided with comet Tempel 1 at a closing speed of 10.2 km/sec. In the most likely scenario, this collision will produce a small impact crater on the surface of the comet (probably a few hundred meters in diameter and taking a few miniutes to form) and a corresponding ejecta plume which will be observed by the flyby spacecraft for a period of about 20 minutes following the impact.

The expansion and behavior of this ejecta plume can potentially be used to estimate the strength of the gravity field of the target comet -- allowing us to also estimate the mass and density of the comet. Under the best of circumstances this will be a difficult measurement to make, but given the circumstances of this flyby mission, it will provide us with one of our only methods for measuring the comet's mass.

A More Realistic Ejecta Curtain Simulation

To more realistically simulate the actual appearance of an impact ejecta curtain resulting from an impact on a small target body, the models previously developed (shown in the sections below) have been expanded to model the ejecta curtain as a three-dimensional shape, rather than randomly generated tracer particles. Additionally, the opacity of each polygon of the ejecta curtain is calculated at each time step, and rendered appropriately. This model mode will be used along with the random tracer particle simulations to create a more visually realist appearance for use in image sequence simulations. Note that while the ejecta curtain is more realistically portrayed in these simulations, the ejecta blanket (that portions which was "landed") is only generally represented in a rather "patchy" fashion -- in reality, the ground coverage would appear more uniform.

Example 1: This figure show the ejecta curtain behavior resulting from a "Deep Impact" style impact on a small comet-density body having the shape of the asteroid Eros, but scaled down to the size of Comet Tempel 1 (average radius = 3 km). This simulation is viewed a stationary spacecraft range of 8.15 km (30 degree field-of-view), and is shown here at ~8 minutes after impact. A time-lapse MPEG movie (5.1 MB) can be downloaded here.

Other Examples (longer format AVI video clips):

Gravity-dominated plume behavior (12.7 MB)
Strength-dominated plume behavior (13.3 MB)

Advanced Impact Simulations: Complex Target Bodies with Rotation

To better simulate a true collision on a small target body, the simple model previously developed has been expanded to model the ejecta plume (shown as white tracer particles), the ejecta blanket (shown as yellow tracer particles), and the impact crater area (shown in blue) resulting from a specified impact on an irregularly shaped target body (modeled in 3-dimensional polygon fashion). Additionally, the target body can also be placed in a simple rotation state about one of its principal axes.

The below two figures show the results of two Deep Impact style impacts on a "test" comet having the shape of the asteroid Eros, but scaled down to the size of Comet Tempel 1 (average radius = 3 km) and given a fast rotation period of 6 hours about it's principal C axis (Tempel 1 has a much slower rotation period of 41 hours).

Example 1: This simulation shows the result of an impact on the northern portion of the smaller lobe of the test comet at a stationary spacecraft range of 35 km (30 degree field-of-view), and is shown here at 20 minutes after impact. A time-lapse MPEG movie (6.7 MB) or long-format AVI video clip (11.8 MB) showing a full 6-hour rotation can be downloaded here.

Example 2: This simulation shows the result of an impact on the extreme end of the larger lobe of the test comet at a stationary spacecraft range of 3041 km (shown here at 10 minutes after impact). A time-lapse MPEG movie (5.2 MB) showing a full 6-hour rotation can be downloaded here.

Simple Impact Simulations: Gravity vs. Strength Dominated Cratering

Below are two simulation animations, showing the ejecta plume behavior which results from a Deep Impact like collision on a triaxial-ellipsoid body of density 1.5 g/cc and having a 6 km long major axis and 3 km long minor axis (about the size of comet Tempel 1). Two different cratering regimes are depicted: a "gravity-domimated" cratering regime, where the comet material is inherently weak and the comet's gravity domimates the crater and ejecta plume formation process, and a "strength-dominated" cratering regime, where the comet material is strong enough to dominate the crater and ejecta plume formation process.

Gravity-dominated Ejecta Plume Behavior: This animation tracks the paths of 1000 test particles ejected from the target comet in accordance with the gravity-dominated cratering scaling laws. The left image shows the ejecta plume at the end of the crater formation process (about 5 minutes) with all test particles ejected from the comet. The right image shows the ejecta plume 20 minutes after impact, at about the time that the flyby spacecraft will have to cease observations and go into a protective mode. After about 24 hours, about 75% of the plume particles will have re-impacted with the the target comet while about 25% of the plume particles will have escaped from the comet's gravity. A Windows Media AVI video clip (2.9 MB) of the full 10 second animation is avaiable here.

Strength-dominated Ejecta Plume Behavior: This animation tracks the paths of 1000 test particles ejected from the target comet in accordance with the strength-dominated cratering scaling laws. The left image shows the ejecta plume at the end of the crater formation process (about 1 minute) with all test particles ejected from the comet. The right images shows the ejecta plume 20 minutes after impact, at about the time that the flyby spacecraft will have to cease observations and go into a protective mode. Note that at this stage, NONE of the ejected particles have re-impacted with the target comet (about 50% will ultimately escape from the comet's gravity in this particular simulation). A Windows Media AVI video clip (3.9 MB) of the full 10 second animation is avaiable here.

Measuring Comet Mass / Density

The below two figures demonstrate how the mass / density of target comet can be determined by monitoring the behavior of the impact ejecta plume. Each graph shows curves for a Tempel 1 sized comet having three different densities: blue = 1.0 g/cc, magenta = 1.5 g/cc, and yellow = 2.0 g/cc. The upper graph shows the ejecta plume position as a function of time while the bottom graph shows the ejecta plume velocity as a function of time.

Note that in the case of measuring the ejecta plume position, the curves produced by the different comet densities do not significantly begin to seperate until near the end of the 20 minute observing period, making this the more difficult method to use. However, in the case of measuring the ejecta plume velocity, the curves produced by the different comet densities begin to seperate relatively early in the plume expansion process -- providing us with a reasonable method for determining the comet mass / density (provided that these measurements can be made).

Early Model Testing: Orbiting Particles

Three particles in orbit around a small spherical asteroid: This figure shows the paths followed by three particles in orbit about a small, spherical, 3.0 km diameter asteroid, having a Carbonaceous Chondrite like density of 2000 kg/m^3 (distances shown in meters). This model asteroid has a mass of 2.87E+13 kg, and a surface gravity of only g = -0.8 mm/sec^2. Two particles orbit in nearly circular orbits, with periapses only 100 m above the surface -- one in an equatorial orbit and one in a polar orbit. The third particle's path is tilted at 45 degrees to these two planes and is more eccentric. All three particles travel at 1.1 m/sec at their periapse points. The prupose of this test was to check the results of the numerical integration routines against the analytically known solutions for central-force motion (Kepler's Laws, etc.).

Three particles in orbit around a small ellipsoidal asteroid: Another title for this figure might be "What happens when you try to orbit a water-melon." The asteroid in this case is ellipsoidal in shape and is 3.0 km long along its major axis, but only 1.5 km long along its minor axes (distances shown in meters). Using the same 2000 kg/m^3 density as before, the model asteroid has a mass of 7.06E+12 kg and an average surface gravity of g = -0.4 mm/sec^2. The three particles were initially set up in a similar configuration to Figure 1 (only with lower speeds of 0.7 m/sec), but the instability of the resulting orbits is readily apparent after just a handful of revolutions. The equatorial and polar orbits remain in their respective planes, but the periaps/apoaps locations precess in spirograph fashion. The particle initially placed at 45 degrees to the planes of the first two particles here wanders wildly up and down the length of the asteroid over the short time period of the test run (15 hours).

The paths of six particles ejected from the poles of a small ellipsoidal asteroid: Unlike the previous two figures, in this test the particles are ejected ballistically from the surface of the asteroid, rather than being placed in orbit. The asteroid in this case is the same as in the second figure: it is ellipsoidal in shape, is 3.0 km long along its major axis, and 1.5 km long along its minor axes (distances shown in meters). Using a 2000 kg/m^3 density, the model asteroid has a mass of 7.06E+12 kg and an average surface gravity of g = -0.4 mm/sec^2. Three particles are launched from the "north" pole of the asteroid, having speeds of 0.28, 0.35, and 0.52 m/sec respectively, and all follow ballistic trajectories -- landing back on the northern half of the asteroid. Three other particles are launched from the "south" pole of the asteroid, having speeds of 0.57, 0.87, and 1.0 m/sec, with different results. The first particle follows a typical ballistic path and lands back on the southern half of the asteroid; the second particle follows a large looping trajectory and lands on the opposite northern half of the asteroid; and the third particle reaches escape velocity and leaves the asteroid's influence.