PhD Research Fellow on Newtonian Gravitational calculations for the Extended N-Body Problem

Closing date: 15.09.18

University of Agder

The University of Agder has more than 1200 employees and 12000 students. This makes us one of the largest workplaces in Southern Norway. Our staff research, teach and disseminate knowledge from a variety of academic fields. Co-creation of knowledge is our common vision. We offer a broad range of study programmes in many fields. We are situated at two modern campuses in Kristiansand and Grimstad respectively.

We are an open and inclusive university marked by a culture of cooperation. The aim of the university is to further develop education and research at a high international level.

The University of Agder invites applications for a PhD fellowship in applied mathematics within “Newtonian gravity calculations” for a period of 3 years. The position is linked to The Department of Engineering Sciences. The starting date is late 2018 or as negotiated with the faculty.

The Department of Engineering Sciences has more than 100 employees in scientific positions and more than 1600 students at all levels. A variety of research is conducted within mechatronics, renewable energy, civil engineering and industrial economy, and we also welcome interdisciplinary projects within the department or with other research groups. We have a broad international cooperation and close collaboration with industrial partners and public services in the region. Partners contribute with assignments, competence, and resources.

Information about why University of Agder provides an excellent environment for PhD studies and more about working at UiA.

About the project

Newtonian gravity calculations are still standard for the gravitational interaction of two or more irregular bodies such as asteroids and small moons, and especially for asteroid binaries. Recently a new method has been developed by Conway [1] for calculating the gravitational field and scalar potential of a general polyhedron of uniform density. This method is based on a gravitational vector potential formulation and has already been applied to gravitational calculations of dust flow around Comet 67p/Churyumov-Gerasimenko by Kramer and Noach [2-3]. This comet was recently visited by the European Space Agency Rosetta spacecraft and its Philae lander, and this work is directly relevant to future space missions to the asteroid belt or to small moons.

The method has been further developed, Conway [4], to give the force and torque acting between two irregular bodies in terms of surface integrals of the fields induced by one body over the surface of the second body. As yet, analytical solutions have not been found for these integrals for fully three-dimensional irregular bodies, although numerical surface integrations are certainly possible. However, an analytical solution of the force and torque between two circular disks was also presented in [4], and this seems to be the first analytical solution for the extended two body problem, when neither of the bodies is a sphere. This theory can be extended to bodies of variable density, and many of the applications of work of this kind are in geophysics, for modelling of the gravitational fields of ore bodies and other geophysical features. There are also direct applications to gravimetric laboratory experiments.

The mathematics developed in [1] and [4] is applicable to many other areas involving potential field theory, especially in electromagnetics, and has already been applied to solve for the mutual inductance of electrical coils at arbitrary relative position and orientation, Conway [5]. It has also been identified as similar to that used to introduce inclusions into a crystal lattice by Nenashev and Dvurechenskii [6].

The PhD project will consist primarily of numerical implementation and validation of the two-body (and possibly N-body) theory given in [4], together with orbit calculations using the mutual forces and torques between the two bodies. The project will also involve developing software to visualize the gravitational interaction between the two (or more) bodies. It is likely that the analytical theory will be further developed during the timescale of the project, and if time permits, extensions or validations based on new results can be incorporated into the project.


(1) J. T. Conway. Analytical solutions from vector potentials for the gravitational field of a general polyhedron. Celest Mech Dyn Astr, Vol 121, pp 17-38, 2015.

(2) Kramer, T. and Noack M. Prevailing dust transport directions on Comet 67P/Churyumov-Gerasimenko. ApJL, Vol 813, L33, 2015.

(3) Kramer T. and Noack M. On the origin of inner coma structures observed by Rosetta during a diurnal rotation of Comet 67P/Churyumov-Gerasimenko. ApJL, Vol 823, L11, 2016.

(4) J. T. Conway. Vector potentials for the gravitational interaction of extended bodies and laminas with analytical solutions for two disks. Celest Mech Dyn Astr, Vol 125, pp 161-194, 2015.

(5) J. T. Conway. Mutual inductance of thick coils for arbitrary relative orientation and position. PIERS Singapore, 19-22 Nov 2017.

(6) A. V. Nenashev and A. V. Dvurechenskii. Elastic strain field due to an inclusion of a polyhedral shape with a non-uniform lattice misfit. Journal of Applied Physics, Vol 121, issue 12, 2017.

Admission requirements

The candidate will be enrolled in the PhD programme at the Faculty of Engineering and Science and the applicant must qualify for admission to this PhD Programme. More information about the programme and a complete list of admission requirements for the PhD programme can be found here.

Proficiency in oral and written English is required. Knowledge of Norwegian or another Scandinavian language is an advantage.

Regarding English skills, please check here to see if an English test is required. An additional assessment of English may be undertaken at the time of interview.

Further provisions relating to the position as PhD Research Fellow can be found in the Regulations Concerning Terms and Conditions of Employment for the Posts of Post-Doctoral Research Fellow, Research Fellow, Research Assistant, and Resident.

Additional requirements

The successful applicant should hold a master’s degree from a Norwegian or an accredited foreign university in applied mathematics, physics or astrophysics.

In addition, the following additional requirements will be prioritized:

  • Strong academic credentials, written and spoken English proficiency
  • Experience in modeling and simulation by using numerical tools
  • Publications in the related and relevant field

The applicant must submit an approved project description within three months of appointment. The PhD dissertation must be written in English.

Personal suitability will be emphasized in the evaluation as well as relevant practical experience. Research Fellows are expected to contribute to the active research community at the University. The position places great demands on the applicant’s capacity for independent goal-oriented work, their ability to concentrate, and on attention to detail. Applicants will be assessed on the basis of academic background and results, and any previous research and development work.

Short-listed applicants will be invited for interviews. With the applicant’s permission, UiA will also conduct a reference check before the appointment.


The position is remunerated according to the State Salary Scale, code 1017 Research Fellow, salary NOK 449 400 gross per year. A 2 % compulsory pension contribution to the Norwegian Public Service Pension Fund is deducted from the pay according to current statutory provisions.

The Norwegian Public Service is committed to reflecting the diversity of society, and the personnel policy of the University of Agder aims to achieve a balanced workforce. All qualified persons are therefore encouraged to apply for the position, irrespective of cultural background, gender, age, or disability.

The appointment is made by the University of Agder’s Appointments Committee for Teaching and Research Positions. The successful applicant will have rights and obligations in accordance with the current regulations for the Public Service.


Submit your application and CV online. Please click on the link “Apply for this job”. The following documentation should be submitted as attachments to the online application:

  • Certificates and grades for all post-secondary education, up to and including the bachelor's level; master's degree/higher degree certificate, with a summary of the courses/subjects included in the degree
  • Applicants with a foreign higher education must attach an official description of the grading system used at the issuing institution
  • Applicants who are required to document their English proficiency must submit their TOEFL or IELTS test results (these may be forwarded after the closing date). An additional assessment of English may be undertaken at the time of interview
  • Summary and links to the applicant's scientific publications if produced
  • All applicants should submit a description of their PhD project, not longer than 2 pages in font size 10. Applications that lack such a description will not be considered for the position

Please do not submit large documents, like e.g. thesis or publications. If any additional information is required, the applicant will be informed later.

Original documents must be presented for verification to the University of Agder. Successful candidates will be asked, normally during the interview, to ensure that the issuing university submits documents in a sealed envelope directly to UiA or provide access to their documents online, which allows UiA to verify the authenticity of these electronic documents via a secure website hosted by the issuing university (contact person at UiA will be provided later for certain candidates).

The applicant is fully responsible for submitting complete documentation. Without complete documentation we cannot, unfortunately, include you in the assessment process.

All documentation of education must be in the original language and in English, Norwegian, Swedish, or Danish (if the original language is not one of these). The application should include a translation, which should preferably be from the issuing university. Additional documentation must be in English, Norwegian, Swedish or Danish.

Closing date: 15.09.18

For further information please contact:

In accordance with §25(2) of the Freedom of Information Act, applicants may request that they are not identified on the open list of applicants. The University, however, reserves the right to publish the name of applicants. Applicants will be advised of the University’s intention to exercise this right.


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