#### Title

Extension of a Perturbation Analysis in Search of Exomoons in Planet-Pulsar Systems

#### List all Project Mentors & Advisor(s)

Dr. Maeve McCarthy

#### Presentation Format

Event

#### Abstract/Description

Perturbation theory studies the effect of small parameters on a given equation. Applied to orbital mechanics, these minute changes can be measured and used to detect changes in periodic phenomena. One such periodic phenomena is the time of arrival (TOA) of regularly detectable pulses from a pulsar, a rapidly rotating star. Perturbations can be modeled theoretically and then matched with experimental data in order to discern if it is likely that a given planet-pulsar system has an exomoon. The original mathematical analysis of this phenomenon was conducted out to order *O*(ε^{2}) and found that, for the case of a theoretical Jupiter-Jupiter system, a perturbation of 960 ns would occur. Our analysis expands the Maclaurin Series of the perturbed problem to order *O*(ε^{3}) and for the same system determines an additional perturbation of 46 ns, indicating an improved threshold for detectability of the exomoon. Computational software was also used to explore a general form for the terms of order ε^{4 }and higher to explore the limits of a useful approximation.

#### Location

Barkley Room, Curris Center

#### Start Date

April 2016

#### End Date

April 2016

#### Affiliations

Honors Thesis

Extension of a Perturbation Analysis in Search of Exomoons in Planet-Pulsar Systems

Barkley Room, Curris Center

Perturbation theory studies the effect of small parameters on a given equation. Applied to orbital mechanics, these minute changes can be measured and used to detect changes in periodic phenomena. One such periodic phenomena is the time of arrival (TOA) of regularly detectable pulses from a pulsar, a rapidly rotating star. Perturbations can be modeled theoretically and then matched with experimental data in order to discern if it is likely that a given planet-pulsar system has an exomoon. The original mathematical analysis of this phenomenon was conducted out to order *O*(ε^{2}) and found that, for the case of a theoretical Jupiter-Jupiter system, a perturbation of 960 ns would occur. Our analysis expands the Maclaurin Series of the perturbed problem to order *O*(ε^{3}) and for the same system determines an additional perturbation of 46 ns, indicating an improved threshold for detectability of the exomoon. Computational software was also used to explore a general form for the terms of order ε^{4 }and higher to explore the limits of a useful approximation.