1. The projectile shape and material effect on the momentum transfer for asteroid orbit change
Daisuke Yokoo, Masashi Tanaka, Masaya Ikeda, Takao Koura and Yausuhiro Akahoshi
Department of Mechanical and Control Engineering, Kyushu Institute of Technology
1-1 Sensui, Tobata, Kitakyushu, Fukuoka, , Japan
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IAA-PDC P INTRODUCTION
In this study, we will discuss about momentum transfer in which the kinetic impact is used for an asteroid orbit change. An effect of the kinetic impact is evaluated by β, where this ratio β is defined as comparison between the asteroid output momentum and the impactor input momentum shown in Eq. (1).
The β ratio is affected by various factors. In this poster, we focused on two factors: There are projectile shape and the material effect. The purpose of this study is to reveal the projectile shape and material effect tendency and identify the respective shape and material from experiments using different projectiles.
𝑴 𝑨 ∆ 𝑽 𝑨 = 𝑴 𝑰 𝑽 𝑰 −∑ 𝒎 𝒆 − 𝒗 𝒆 𝒄𝒐𝒔𝜽
= 𝟏+ ∑ 𝒎 𝒆 𝒗 𝒆 𝒄𝒐𝒔𝜽 𝑴 𝑰 𝑽 𝑰 𝑴 𝑰 𝑽 𝑰
=𝜷 𝑴 𝑰 𝑽 𝑰 ···(1)
𝑴 𝑨 ∆ 𝑽 𝑨
𝒎 𝒆 𝒗 𝒆
𝑴 𝑰 𝑽 𝑰 𝜽
𝜷 SCALING
SHAPE EFFECT
𝛽−1~ 𝑣 p ∙ 𝜌 𝑡 𝑌 𝑡 3𝜇−1 ∙ 𝜌 𝑡 𝜌 𝑝 1−3𝜈
Cylinder
Cone
Punch
Cup
Sphere
shape
𝑣 𝑝 ⋯ Impact velocity
𝜌 𝑡 ⋯ Target density
𝑌 𝑡 ⋯ Target strength
𝜌 𝑝 ⋯ Projectile density
K. A. Holsapple, “Momentum transfer in asteroid impact. I. Theory and scaling”, Icarus 221 p , 2012
where μ and ν are called “scaling parameter”.
The ν is about 0.4 for most materials. So, we chose ν=0.4 and plot data obtained from experiments in order to calculated C and μ from an approximate curve.
The projectile shapes does not affect the ejecta mass
MATERIAL EFFECT Cu
Chromium steel Ti
Aluminum alloy
Appearance
We compare the β ratio at an actual impact velocity range using scaling law.
The β difference was caused by the spread angle of the ejecta emission
less than 15 km/s
the Cup shape has the highest β ratio
more than 15 km/s
the Sphere shape has the highest β ratio
The aluminum alloy has the best β ratio, followed by copper
CONCLUSION
Projectile shape does not affect the ejecta mass
Projectile shape affects the ejecta emission direction
The Cup shape has the best β less than 15 km/s and Sphere shape has the best more than 15 km/s.
The aluminum alloy has the best value for β