MODELING THE NEOs ORBITAL DISTRIBUTION AND NEO DISCOVERY STRATEGIES

A. Morbidelli (OCA)

R. Jedicke (Spacewatch)

W.F. Bottke (SWRI)

P. Michel (OCA)

P. Tanga (OCA, Obs. Turin)

ESA Contract No. 14018/2000/F/TB

ASTEROIDS CAN ESCAPE FROM THE MAIN BELT AND BECOME NEOs

By numerically integrating the dynamics of a large number of particles we can quantify the statistics of the orbital evolutions

WE HAVE DEVELOPED A NEO DISTRIBUTION MODEL BY:

1. USING NUMERICAL INTEGRATIONS

2. CALIBRATING THE FREE PARAMETERS USING THE OBSERVATIONAL DATA

Our approach consists of 5 steps.

Step 1: Find “Primary” NEO Source Regions

Nu6

Each source produces NEOs with a distinctive orbital distribution

MCMC

OB 3:1

JFC

PRINCIPLE:

The distribution of the residence times is equal to the steady-state orbital distribution of the NEOs coming from the considered source.

Step 1 (continued): Determine the orbital distribution of NEOs coming from each Source

Nu6

Step 2: Combine NEO Sources

IMC 3:1 Outer MB JFC

n u 6 IM C 3:1 O u ter M B JF Cs

C om b in e N E O S ou rcesR (a ,e,i)

Step 3: Create Model NEO Distribution

C om b in e N E O S ou rcesR (a ,e,i)

A b s. M ag. D is trib u tionN (H)

D eb iased N E O O rb its M odel (a ,e,i,H ) = R (a ,e,i) N (H )

We cannot compare our NEO model with data until we account for observational biases!

Step 4: Create Biased NEO Distribution

O b servation al B iasesB (a ,e,i,H)

D eb iased N E O O rb its M odel (a ,e,i,H)

" O b served " N EO D istrib u tionn (a ,e,i,H ) = B (a ,e,i,H ) M odel (a ,e ,i,H)

Combine NEO model with the probability than an object with given (a,e,i,H) with be discovered by Spacewatch.

Step 5: Compare Biased Model with NEO Data

O b servation al B iasesB (a ,e,i,H )

n u 6 IM C 3:1 O u ter M B JF Cs

C om b in e N E O S ou rcesR (a ,e,i)

A b s. M ag. D is trib u tionN (H)

D eb iased N E O O rb its M odel (a ,e,i,H )

" O b served " N EO D istrib u tionn (a ,e,i,H )

C om p are w ith S p acew atch N E O D atan (a ,e ,i,H ) = "K now n N E O s"?

Continue U

ntil “Best-F

it” Found

(4)

(3)

(1)

(2)

(5)

Comparison Between NEOs and Best-Fit Model

Source contributions

6 0.37 ± 0.08

IMC 0.25 ± 0.03

3:1 0.23 ± 0.08

Outer MB 0.08 ± 0.01

JFC 0.06 ± 0.04

Model fit to 138 Spacewatch NEOs

with H < 22

Debiased Orbital and Size Distribution of NEOs

There are ~ 970 NEOs with H < 18 and a < 7.4 AU.

~50% of them have been found so far.

60% come from the inner main belt (a < 2.5 AU).

Amor: 32%; Apollo: 62%; Aten:6%; IEO: 2%

A SPECTRAL DISTRIBUTION MODEL

From the spectral distribution of the bodies in/close the 5 main NEO sources we compute the spectral distribution of NEOs as a function of their orbital distribution.

We estimate that:

1) the C/S ratio for an H-limited sample of the NEO population is 0.25 +/- 0.02

2) The C/S ratio for a size-limited sample of the NEO population is 0.87+/- 0.05

Using our NEO albedo distribution model we predict 834 bodies with D>1km, against 963 with H<18

To obtain a mass distribution we assume, in agreement with recent determinations by flyby missions or satellite detections, that:

1) C-type NEOs have density 1.3 g/cm

2) S-type NEOs have density 2.7 g/cm

With this, we have all ingredients to estimate the frequency of NEO collisions with the Earth as a function of impact energy:

ENERGY

(MT)

AV. INT.

(Y) H D

(M)

COMPLET.

(%)

1,000 63,000 20.5 277 18

10,000 241,000 19.0 597

37

100,000 925,000 17.3 1287 49

3

3

WE PREDICT 4X LESS IMPACTS THAN PREVIOUSLY ESTIMATED

Difference is likely due to an estimated smaller number of NEOs, different orbital distribution, improved bulk densities etc.

The « measured » formation rate of 4 km craters on the Moon is: 3.3+/-1.7x10 -14 km2/y; our NEO model predicts : 2.73x10-14km2/y

NEO DISCOVERY STRATEGIES

How to achieve the Spageguard goal (90% of H<18 NEOs within 2008) and beyond (90% of H<20.5 NEOs)?

• Characterization of existing major surveys (LINEAR)

• How to achieve the Spaceguard goal with a LINEAR-esque

strategy

•Space-based strategies

We have constructed a pseudoLINEAR simulator, that simulates the average sky coverage of LINEAR and its average limiting magnitude V=18.5

QUALITY TEST I:

In 2 years LINEAR increased the detected population of the NEOs with H<18 from 273 to 449.

Our pseudoLINEAR simulator takes 2.14 years

QUALITY TEST II:

The orbital-magnitude distribution of the first 469 NEOs with H<18 discovered by our pseudoLINEAR simulator mimics very well that of the 469 objects discovered so far by LINEAR and other surveys

PROSPECTS FOR ACHIEVING THE SPACEGUARD GOAL WITH A GROUND BASED SURVEY

LINEAR

LSST?

Current completeness

Current time

SPACE BASED SURVEYS

A space-based survey that duplicates the strategy of ground-based surveys will never be competitive in term of cost.

A space-based survey must take advantage of the location of the instrument in space by either:

•Observe at small solar elongation or,

•Search for NEOs from a point closer to the Sun than the Earth

NEO sky density viewed from 1 AU

Discovery efficiency of satellites with V=18.5 on NEOs with H<18

(Ideal situation with daily full sky coverage, except 45deg close to the Sun)

WARNING: the fact that a space-based survey detects NEOs that are not visible from the ground, implies that one cannot count on ground-based recoveries for follow-up and orbital determination

Ground-based ecliptic coordinates of NEOs at the time of their discovery form a space observatory inside Venus’ orbit

A space-based survey must be able to do its own follow-up

CONCLUSIONS

• We have a model of the (a,e,i,H) NEO distribution

• We estimate 963 NEOs with H<18 and 855 with D>1km

• Our model predicts 4x less collisions than Shoemaker’s

• We predict one 1,000MT collision every 63 Kyear

• These collisions are caused in average by H ~ 20.5

• The Spaceguard goal should be extended to H=20.5 NEOs

CONCLUSIONS

• We have a model of the (a,e,i,H) NEO distribution

• We estimate 963 NEOs with H<18 and 855 with D>1km

• Our model predicts 4x less collisions than Shoemaker’s

• We predict one 1,000MT collision every 63 Kyear

• These collisions are caused in average by H ~ 20.5

• The Spaceguard goal should be extended to H=20.5 NEOs

CONCLUSIONS

• We have a model of the (a,e,i,H) NEO distribution

• We estimate 963 NEOs with H<18 and 855 with D>1km

• Our model predicts 4x less collisions than Shoemaker’s

• We predict one 1,000MT collision every 63 Kyear

• These collisions are caused in average by H ~ 20.5

• The Spaceguard goal should be extended to H=20.5 NEOs

CONCLUSIONS

• We have a model of the (a,e,i,H) NEO distribution

• We estimate 963 NEOs with H<18 and 855 with D>1km

• Our model predicts 4x less collisions than Shoemaker’s

• We predict one 1,000MT collision every 63 Kyear

• These collisions are caused in average by H ~ 20.5

• The Spaceguard goal should be extended to H=20.5 NEOs

CONCLUSIONS

• We have a model of the (a,e,i,H) NEO distribution

• We estimate 963 NEOs with H<18 and 855 with D>1km

• Our model predicts 4x less collisions than Shoemaker’s

• We predict one 1,000MT collision every 63 Kyear

• These collisions are caused in average by H ~ 20.5

• The Spaceguard goal should be extended to H=20.5 NEOs

CONCLUSIONS

• We have a model of the (a,e,i,H) NEO distribution

• We estimate 963 NEOs with H<18 and 855 with D>1km

• Our model predicts 4x less collisions than Shoemaker’s

• We predict one 1,000MT collision every 63 Kyear

• These collisions are caused in average by H ~ 20.5

• The Spaceguard goal should be extended to H=20.5 NEOs

CONCLUSIONS (2)

• To achieve a satisfactory completeness on the H<20.5 NEO population, ground based surveys should be pushed to V=24

• Spaced-based surveys can be effective only if– They observe at small solar elongation– They observe from a point placed a smaller

heliocentric distance than the Earth

• Space-based surveys must do their own follow-up work

CONCLUSIONS (2)

• To achieve a satisfactory completeness on the H<20.5 NEO population, ground based surveys should be pushed to V=24

• Spaced-based surveys can be effective only if– They observe at small solar elongation– They observe from a point placed a smaller

heliocentric distance than the Earth

• Space-based surveys must do their own follow-up work

CONCLUSIONS (2)

• To achieve a satisfactory completeness on the H<20.5 NEO population, ground based surveys should be pushed to V=24

• Spaced-based surveys can be effective only if– They observe at small solar elongation– They observe from a point placed a smaller

heliocentric distance than the Earth

• Space-based surveys must do their own follow-up work