Figure 1. Vesta, as photographed by Dawn on 23 July, 2011.

Home
___________

Sol
___________

Mercury
___________

Venus
___________

Earth &
Earth's Moon
___________

Mars
___________

Asteroids
___________

Jupiter
___________

Saturn
___________

Uranus
___________

Neptune
___________

Pluto &
Kuiper Belt
___________

Comets &
Oort Cloud
___________

Vesta's Violent Past

By F. E. Harris

July 30, 2011

Introduction

On July 23, 2011, the Dawn space probe's framing camera took an image of asteroid 4-Vesta's northern hemisphere.[1] This photo was intended primarily for navigation purposes. At the time, Dawn was still maneuvering into its first circular "science" orbit.

Before this photo, it was known that Vesta had suffered an enormous impact to its South pole. With these grooves, we have evidence that the asteroid fractured through and through from that impact, even into the high Northern latitudes. Probably the solid iron core focussed the shockwaves, so the fractures were concentrated in rings in the Northern hemisphere.

It will be a matter to calculate, whether this single impact blew away most of the ice that formerly clothed Vesta, and how much was lost due to momentum transfer, and how much was lost from heating, melting and boiling the ice off into space.

This picture ranks with some of the great first photos from Pioneer and Voyager, of Jupiter's and Saturn's moons. It's a scientific discovery all by itself.

---

Section 1: First Observations

You can see, by counting craters, that the ridges are the oldest geological features in the photo.[2] It is not clear whether the surface of Earth's moon can be used as a dating scale for asteroids, but if it can, then the oldest parts of the surface visible in this photo are well over a billion years old. More likely, over 2 billion years old.

You can tell that the 2 large craters toward the lower left, are among the youngest features visible: They have no smaller craters within them. This suggests an age of less than 10 million years.

There is a crater near the bottom of the picture, that looks a little funny. Look closely and you can see what are probably dust-landslides going down from the rim. This suggests the surface of Vesta is dust and rubble. Note that this is the only crater that shows rays, radiating from the center. On the Earth's Moon, rays are considered to be an indication that the crater is very young. The Moon has several ray craters, believed to be from a few thousand, to a few million years old.

Back to the 2 big craters toward the lower left. Not only are they very smooth, indicating youth, but the surrounding area is also smooth. This confirms to me that the surface is dusty. I think craters in the surrounding area were buried, by material ejected from the two large craters. The larger crater appears to be younger, and appears to have triggered landslides within its neighbor.

---

Section 2: Preliminary Calculations

The escape velocity of present day Vesta is about 0.35 km/s, and the asteroid's radius is about 265 km.[3] This means that the energy required to lift one kg from the surface to outside of Vesta's gravitational field is

E(e) = (1/2) m v2
= (1/2) 1 kg (3.5 x 102 m/s)2
= 6.125 x 104 J

The mass of Vesta is about

2.67 x 1020 kg

Assuming 10% to 20% of Vesta's mass was ice and rock that was lost during the South polar impact, that gives an energy of (for 20% mass lost)

E(total) = (1/2) 2.67 x 1020 kg (3.5 x 102 m/s)2
= 3.27 x 1024 J

If one includes the lost mass as part of the gravitational field of Vesta, then the energy required to escape from the asteroid rises by approximately 20% to 40%. So our lower bound for the energy of impact is about 1/2 of the above figure, E(min) = 1.64 x 1024 j, and our upper estimate is about 40% higher than the above figure, E(max) = 4.58 x 1024 J.

---

Section 3: Heat Considerations

If the lost mass of Vesta were water ice, and it was heated to the boiling point, how much energy would that require?[4]

Heat to melt ice = C(m) = 3.33 x 105 J/kg

Heat to boil water = C(v) = 2.26 x 106 J/kg

Heat to raise teperature of ice 1 degree C = C(p) = 2.05 x 103 J/(kg degree C)

Average temperature of Vesta = -90 degrees C.

Temperature rise needed to boil ice of Vesta ~ 190 degrees C.

Energy required to boil 1 Kg of ice on Vesta = E(b)

E(b) = (190 x 2.05 x 103 + 3.33 x 105 + 2.26 x 106) J/kg
= 2.97 x 106 j/kg

Now we multiply this number by 20% of the mass of Vesta.

E(t) = 2.97 x 106 J/kg x 2.67 x 1020 kg
= 7.93 x 1026 J

Interesting. The energy required to remove 20% of the mass from Vesta, is less than 1% of the energy required to boil that mass of water ice.

Saturn's moon Mimas
Figure 2 : Saturn's moon Mimas

---

Section 3: Limiting Values

Next, we turn to the question of the size and velocity of the impacting body that made Vesta's South polar crater, and Northern ridges. Saturn's moon Mimas[5],[6] is similar in size to Vesta, and posseses a large crater, though not as large as Vesta's. Dombard and Cheng[7], in their study of Saturn's moon Iapetus[8], suggest that a lower velocity, higher mass impact is more likely to produce ridges, like those seen on Vesta.

Saturn's moon Iapetus
Figure 3. Saturn's moon Iapetus

We can take the above-derived energies, for the upper and lower limits on the energy of collision. For the upper limit on the velocity of collision, we can take the volocity of a comet, falling from the Oort cloud. At Vesta's closest approach to the Sun, it is 321.82 x 109 m from the center of the sun,[3] The actual velocity could be slightly higher, if combined with the orbital velocity of Vesta in a head-on collision, so

V(es) ≥ (2GM/r)1/2
≥ (2 x 6.67 X 10 -11 m3/(kg s2) x 1.99 x 1030 kg/321.82 x 109 m)1/2
≥ 2.875 x 104 m/s

This is roughly 1/2 the velocity the same equation yields at Earth's orbit.

To derive a lower limit to the velocity of collision, I assume the mass of the colliding object was no more than 10% of the present mass of Vesta.[3]

M(cmax) = 0.1 x 2.67 x 1020 kg
= 2.67 x 1019 kg

The kinetic energy formula, E(k) = 1/2 mv2 can be rearranged to solve for velocity

v = (2E/m)1/2

Using values of E and M from above, this gives a minimum value of

v = 495 m/s.

Spreadsheet: Mass vs Velocity
Table 1. Spreadsheet: Mass vs Velocity

Putting these numbers into a spreadsheet with the formula for kinetic energy, we get the following graph.

Graph: Log plot of Mass vs. Velocity
Figure 4. Graph: Log plot of Mass vs. Velocity

The first thing that stands out from this graph, is that the velocity at the lower limit, V = 495 m/s, makes some sense. This is slightly above the escape velocity of Vesta V(e) = 350 m/s, and would correspond to a collision with another large asteroid, almost in the same orbit. However, such a low speed colision would probably not eject a great deal of material into space, since transfer of momentum would not be very elastic. The collision energy would be absorbed by Vesta, and released partly in the form of some ejected material, and partly in the form of melted ice, evaporating into space. One would not end up with modern Vesta, completely stripped of ice and showing a rocky crust over almost all of its surface. Instead, the resulting object would look like an ice cream cone, with the impactor sticking out a the South pole, and a fluffy crust of snow and ice, like a ball of ice cream, over the Northern hemisphere. Thus the lower limit for collision speed, is probably around 3000 m/s.

The ridges in the Northern hemisphere of Vesta are signs that the collision was not completely elastic. Considerable energy went into cracking rocks, creating faults, and moving large blocks of Vesta's crust Northward, without ejecting those rocks off of the surface. Thus, I believe a very high velocity collision would result in much material ejected several kilometers to hundred of kilometers above the surface, and falling back uniformly, creating a more spherical appearance to present-day Vesta.

Most likely masses, velocities, and energies for Vesta Impact Event.
Figure 5. Most likely masses, velocities, and energies for Vesta impact event.

---

Section 4: Conclusions

Disclaimer: The following conclusions are the result of back-of-the-envelope type calculations. The scientists at JPL and major universities have access to sophisticated computer models, and supercomputer time. I just have a calculator and spreadsheets. But the pictures are pretty, and some of my conclusions should prove to be close to the correct answers. Just watch for the real papers, when they come out in Icarus and AGU Abstracts in 6 months or so.

So there we have it. The colision that shaped Vesta was most likely 2 billion to 4 billion years ago, with a mass of 1017 kg to 1020 kg, and at a velocity of approximately 3500 m/s to 14,000 m/s.

That's about all I can deduce, from one photograph and a survey of the literature on large craters on moons. There is probably a paper I missed, that contains much better formulas, based on hundreds of hours of computer simulations. But I have some confidence that my results are substantially close to the mark.

Epilog:

NASA is still maneuvering Dawn into a circular orbit. Most of the time, the spacecraft has to point where the rocket engine needs it to point. We will get a lot more pictures after August 1.

References

1. The full-sized image:
http://dawn.jpl.nasa.gov/multimedia/dawn_vesta_image_072311.asp
2. "NASA's Dawn Spacecraft Views Dark Side of Vesta," JPL press release, 28 July, 2011.
http://dawn.jpl.nasa.gov/feature_stories/dawn_spacecraft_views_vesta.asp
3. "4 Vesta," Wikepedia, 3 July, 2011, with later edits.
http://en.wikipedia.org/wiki/4_Vesta
4. "Properties of water," Wikepedia, 25 April 2011, latest edit.
http://en.wikipedia.org/wiki/Properties_of_water
5. "Mimas (moon)," Wikepedia, 29 July 2011, latest edit.
http://en.wikipedia.org/wiki/Mimas_(moon)
6. "An Eye on Mimas: Endo- and Exogenic Effects on the Surface Evolution of Mimas (Invited),"
Schenk, P. AGU Fall Meeting Abstracts, Dec. 2010, http://adsabs.harvard.edu/abs/2010AGUFM.P21C..06S
7. "The Weirdest Topography in the Outer Solar System: The Ridge on Iapetus and its
Possible Formation via Giant Impact (Invited)," Dombard, A.~J., Cheng, A.~F., McKinnon, W.~B. and Kay, J.~P., AGU Fall Meeting Abstracts, Dec. 2010, http://adsabs.harvard.edu/abs/2010AGUFM.P31D..01D
8. "Iapetus (moon)," Wikepedia, 17 July 2011, latest edit.
http://en.wikipedia.org/wiki/Iapetus_(moon)
9. "Orbital mechanics," Wikepedia, 17 July 2011, latest edit.
http://en.wikipedia.org/wiki/Orbital_mechanics#Escape_velocity
Off TopicFunny Pictures from Orbit

© 2011 F. E. Harris for Hypertek Publications. All Rights Reserved.