On Asteroid Engineering

1
Olaf Lechtenfeld
Olaf Lechtenfeld
1 Leibniz University Hannover

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I pose the question of maximal Newtonian surface gravity on a homogeneous body of a given mass and volume but with variable shape. In other words, given an amount of malleable material of uniform density, how should one shape it in order for a microscopic creature on its surface to experience the largest possible weight? After evaluating the weight on an arbitrary cylinder, at the axis and at the equator and comparing it to that on a spherical ball, I solve the variational problem to obtain the shape which optimizes the surface gravity in some location. The boundary curve of the corresponding solid of revolution is given by (x 2 + z 2 ) 3 -(4 z) 2 = 0 or r(θ) = 2√cos θ, and the maximal weight (at x = z = 0) exceeds that on a solid sphere by a factor of 35√3 5, which is an increment of 2.6%. Finally, the values and the achievable maxima are computed for three other families of shapes.

5 Cites in Articles

References

  1. O Lechtenfeld (2000). Remainder Term.
  2. O Lechtenfeld (1986). Mathematical methods for physicists II, summer term 2009.
  3. Y Kantor Physics Questions/Problems.
  4. D Morin (2007). Introduction to Classical Mechanics.
  5. Xiao-Wei Wang,Yue Su (2015). The optimal shape of an object for generating maximum gravity field at a given point in space.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Olaf Lechtenfeld. 2016. \u201cOn Asteroid Engineering\u201d. Global Journal of Science Frontier Research - A: Physics & Space Science GJSFR-A Volume 16 (GJSFR Volume 16 Issue A2): .

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Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-A Classification: FOR Code: 020109
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v1.2

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March 29, 2016

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English

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I pose the question of maximal Newtonian surface gravity on a homogeneous body of a given mass and volume but with variable shape. In other words, given an amount of malleable material of uniform density, how should one shape it in order for a microscopic creature on its surface to experience the largest possible weight? After evaluating the weight on an arbitrary cylinder, at the axis and at the equator and comparing it to that on a spherical ball, I solve the variational problem to obtain the shape which optimizes the surface gravity in some location. The boundary curve of the corresponding solid of revolution is given by (x 2 + z 2 ) 3 -(4 z) 2 = 0 or r(θ) = 2√cos θ, and the maximal weight (at x = z = 0) exceeds that on a solid sphere by a factor of 35√3 5, which is an increment of 2.6%. Finally, the values and the achievable maxima are computed for three other families of shapes.

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On Asteroid Engineering

Olaf Lechtenfeld
Olaf Lechtenfeld Leibniz University Hannover

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