Collision

A **collision** occurs between two objects when Universe Sandbox detects that the objects are overlapping in space during a time step. Most object types in Universe Sandbox cannot occupy the same point in space at the same time, and as a result, they may break apart or merge together. Objects involved in a collision will also have their velocities changed, due to the conservation of momentum, and will heat up due to the impacts.

## Related Properties & Settings

### Properties

* The mass and velocity of each colliding object will influence the outcome of the collision, and determine whether fragmentation occurs.

### Settings

* Collisions can be turned off using the Collide toggle in the Sim menu in the bottom bar, or using the Detect Collisions toggle in the full Sim Settings Menu.
* The production of all fragments can be turned off using the Fragment toggle in the Sim menu or the Create Fragments toggle in the full Sim Settings Menu. Collision fragmentation (as opposed to Roche fragmentation or friction fragmentation can be individually controlled in the Sim Settings Menu.

## Models

### Mass Transfer

When two objects collide, mass is transferred from the smaller to the larger object. This transferred mass, *M*trans, is equal the the mass contained in the volume of the region where the two objects overlap, *V*overlap:

M

t
r
a
n
s

=
ρ

V

o
v
e
r
l
a
p

,

{\displaystyle M\_{trans}=\rho V\_{overlap},}

where ρ is the density of the smaller object. In other words, the part of the smaller object that is inside the larger object will be transferred to the larger object. The kinetic energy, *E*trans, carried by this transferred mass depends on the relative velocity of the colliding objects, *V*rel:

E

t
r
a
n
s

=

1
2

M

t
r
a
n
s

V

r
e
l

2

.

{\displaystyle E\_{trans}={\frac {1}{2}}M\_{trans}V\_{rel}^{2}.}

### Momentum Conservation

Collisions must obey the laws of conservation of momentum, for both linear momentum and angular momentum. After calculating the transfer of mass from the smaller object to the larger object, Universe Sandbox calculates what the new velocities of each object must be in order to keep the total linear momentum of the objects constant. This change in the velocity vectors will alter the objects' orbital angular momentum vectors, so Universe Sandbox then adjusts the angular speed of each object to keep the total angular momentum of the objects constant.

### Merging

If the volume overlap between the colliding objects is equal to the volume of the smaller object, the smaller object will be completely absorbed into the larger object, and the two objects will merge into one. The remaining object will maintain its original name and other properties, but will have a mass equal to the combined masses of the original colliding objects.

### Craters

To simulate the effect of an impact on the surface of an object, Universe Sandbox changes the appearance of the larger object to show an impact crater on its surface. The diameter of the crater is calculated from the parameters of the collision, including the densities of the larger and smaller objects, ρ1 and ρ2, the radius of the smaller object, *R*2, the relative velocity of the colliding objects, *V*rel, and the surface gravity of the larger object, *g*1, using

D

c
r
a
t
e
r

=
1.161

(

ρ

2

ρ

1

)

1

/

3

(
2

R

2

)

0.78

V

r
e
l

0.44

g

1

−
0.22

.

{\displaystyle D\_{crater}=1.161\left({\frac {\rho \_{2}}{\rho \_{1}}}\right)^{1/3}(2R\_{2})^{0.78}V\_{rel}^{0.44}g\_{1}^{-0.22}.}

For collisions in which the radius of the smaller object is less than 5% of the radius of the larger object, Universe Sandbox uses a simpler equation for calculating the diameter of the crater, based on the mass of the smaller object, *M*2, and the relative velocity of the colliding objects, using

D

c
r
a
t
e
r

=
0.0195
(

M

2

V

r
e
l

2

/

2

)

1

/

3.4

.

{\displaystyle D\_{crater}=0.0195(M\_{2}V\_{rel}^{2}/2)^{1/3.4}.}

### Fragmentation

Besides visually changing the surface of an impacted object, Universe Sandbox also simulates the creation of impact craters by producing fragments to simulate the ejection of material from the crater site. Impact fragmentation is triggered when the radius of the intersection ring (the circle outlining the area where the two bodies overlap) is larger than 1/10 the radius of the smaller object.

The energy of an impact will melt a portion of the larger body at the impact site. The volume of the melted material is calculated based on the kinetic energy of the transferred mass, *Etrans*, and the impact angle, θ, using

V

m
e
l
t

=
8.9
×

10

−
12

E

t
r
a
n
s

sin
⁡

θ

.

{\displaystyle V\_{melt}=8.9\times 10^{-12}E\_{trans}\sin {\theta }.}

The melt volume is then increased by a factor of

1
0.8

R

s
m
a
l
l

R

l
a
r
g
e

,

{\displaystyle 1+0.8{\frac {R\_{small}}{R\_{large}}},}

where *R*small and *R*large are the radii of the smaller and larger object, respectively. This increase in melt volume simulates the additional effects of shear forces on crater formation.

The amount of melted mass, calculated from the melt volume and the density of the larger object, is subtracted from the larger object and used to produce fragments. The number of fragments is constrained by performance and calculated automatically by Universe Sandbox. Each fragment is given a random mass, such that the total mass of the fragments equals the mass of the melted material. Each fragment is also given a random rotation period around a randomly oriented rotation axis.

Fragments are produced at the intersection ring. The average kinetic energy of the fragments is calculated from the mass of melted material, *M*melt, the relative velocity of the two colliding objects, *V*rel, and the number of fragments, *N*frag:

E

a
v
g

=

1
2

M

m
e
l
t

V

r
e
l

2

N

f
r
a
g

.

{\displaystyle E\_{avg}={\frac {{\frac {1}{2}}M\_{melt}V\_{rel}^{2}}{N\_{frag}}}.}

Each fragment is given a velocity, *V*frag, based on this average kinetic energy and the fragment's individual mass, *M*frag, such that

E

a
v
g

=

1
2

M

f
r
a
g

V

f
r
a
g

2

.

{\displaystyle E\_{avg}={\frac {1}{2}}M\_{frag}V\_{frag}^{2}.}

The direction of the velocity vector of each fragment is randomly chosen from within a cone whose angle depends on the impact angle of the collision. For example, if the impact was head-on, the fragments will mostly be reflected backwards in the direction the smaller object came from. If the impact was more of a grazing collision, the fragments will create a spray in roughly the direction of the smaller object's original motion.

Each fragment is given a radius that varies randomly from what would be expected from the fragment's mass and the density of the larger body. The density of each fragment is then adjusted accordingly based on its radius and mass.

In order to prevent a large number of collisions being detected immediately after an impact when the fragments are close together, collisions with other objects are ignored until a fragment has moved a distance of twice its radius away from its place of origin.

### Energy Conservation

Simulated collisions also conserve energy. Some of the kinetic energy of a collision is used to heat the colliding objects.

## Limitations

* Collisions are not affected by an object's atmosphere.
* Objects always assumed to be spheres.

## References

1. ↑ 1.0 1.1 Collins, G.S.; Melosh, H.J.; Marcus, R.A. (2005).Earth Impact Effects Program: A Web-based computer program for calculating the regional environmental consequences of a meteoroid impact on Earth. *Meteoritics & Planetary Science*. **40** (6):817-849
2. ↑ Strobel, N. (2019). Effects of an Asteroid Impact on Earth. *Astronomy Notes*.