# Example Moon-forming Synestia Cases Created via Giant Impact¶

The various post-giant-impact synestias used throughout this document as examples are the same three potential Moon-forming impact cases used in (Lock et al., 2018). All three cases are Earth-mass synestias created shortly after (within 48 hours of) their respective giant impact. The synestia cases are all thermally equilibrated and have not yet begun to cool.

M\(_t\) is the mass of the target body (body being impacted in the impact reference frame) and M\(_p\) is the mass of the *projectile* (the impactor in the impact reference frame). Both masses are described in terms of the present-day mass of Earth. The velocity v is the relative velocity with which the projectile impacts the target. The angle of the impact is described in terms of b, where b = sin\(\theta\) and \(\theta\) is the angle between the centers of the target and projectile at first contact, such that b = 0 is a direct impact (at 0\(^\circ\)) and b = 1 is a glancing impact (at 90\(^\circ\)). Q\(_s\) is the *specific impact energy* developed by (Leinhardt & Stewart, 2012); these three cases are high energy giant impacts. M\(_{bnd}\) is the mass of the material gravitationally bound to the system in terms of the present-day mass of Earth. M\(_{seed}\) is the mass of the lunar seed (in terms of the present-day mass of the Moon) created from the impact.

## Synestia Case 1¶

This case is based on a giant impact proposed by (Canup, 2012), and is example A used in (Lock et al., 2018). Near two half-Earth-mass bodies collide near head on at a relative velocity close to that of the escape velocity for the system (11 km/s). The impact parameters are as follows:

M\(_t\) = 0.572 M\(_{Earth}\)

M\(_p\) = 0.468 M\(_{Earth}\)

v = 12.33 km s\(^{-1}\)

b = 0.4

Q\(_s\) = 1.62 \(\times\) 10\(^7\) J kg\(^{-1}\)

M\(_{bnd}\) = 0.895 M\(_{Earth}\)

M\(_{seed}\) = 0.4 M\(_{Moon}\)

## Synestia Case 2¶

This case is based on a giant impact proposed by (Ćuk & Stewart, 2012), and is example B used in (Lock et al., 2018). A relatively small impactor quickly collides with a rapidly rotating protoplanet at a near head on angle. The impact parameters are as follows:

M\(_t\) = 0.99 M\(_{Earth}\)

M\(_p\) = 0.1 M\(_{Earth}\)

v = 15 km s\(^{-1}\)

b = 0.4

Q\(_s\) = 7.2 \(\times\) 10\(^6\) J kg\(^{-1}\)

M\(_{bnd}\) = 0.9929 M\(_{Earth}\)

M\(_{seed}\) = 0.5 M\(_{Moon}\)

## Synestia Case 3¶

This case is based on a giant impact proposed by (Quintana et al., 2016), and is example C used in (Lock et al., 2018). A medium-size impactor collides with a proto-Earth (with twice the mass of the impactor) at a less-than-head-on angle and velocity near escape velocity of the system (11 km/s). The impact parameters are as follows:

M\(_t\) = 0.75 M\(_{Earth}\)

M\(_p\) = 0.3 M\(_{Earth}\)

v = 11.3 km s\(^{-1}\)

b = 0.6

Q\(_s\) = 3.9 \(\times\) 10\(^6\) J kg\(^{-1}\)

M\(_{bnd}\) = 0.9977 M\(_{Earth}\)

M\(_{seed}\) = 0.8 M\(_{Moon}\)

## References¶

Canup, R. M. (2012). Forming a Moon with an Earth-like Composition via a Giant Impact. *Science (American Association for the Advancement of Science)*, 338 (6110), 1052-1055.

Ćuk, M., & Stewart, S. T. (2012). Making the Moon from a fast-spinning Earth: A giant impact followed by resonant despinning. *Science (American Association for the Advancement of Science)*, 338 (6110), 1047-1052.

Leinhardt, Z. M., & Stewart, S. T. (2012). Collisions between gravity-dominated bodies. I. Outcome regimes and scaling laws. *The Astrophysical Journal*, 745 (79), 1-27.

Lock, S. J., Stewart, S. T., Petaev, M. I., Leinhardt, Z. M., Mace, M. T., Jacobsen, S. B., & Ćuk, M. (2018). The origin of the Moon within a terrestrial synestia. *Journal of Geophysical Research: Planets (American Geophysical Union)*, 123 (4), 910-951.

Quintana, E. V., Barclay, T., Borucki, W. J., Rowe, J. F., & Chambers, J. E. (2016). The frequency of giant impacts on Earth-like worlds. *The Astrophysical Journal*, 821 (126), 1-13.