Search

We present initial results of an ongoing engineering study on the feasibility of a space mission to the focal region of the solar gravitational lens (SGL). The mission goal is to conduct exoplanet imaging operations at heliocentric distances in the range ~548-900 astronomical units (AU). Starting at 548 AU from the Sun, light from an exoplanet located behind the Sun is greatly amplified by the SGL. The objective is to capture this light and use it for multipixel imaging of an exoplanet up to 100 light years distant. Using a meter-class telescope one can produce images of the exoplanet with a surface resolution measured in tens of kilometers and to identify signs of habitability. The data are acquired pixel-by-pixel while moving an imaging spacecraft within the image. Given the long duration of the mission, decades to 900 AU, we address an architecture for the fastest possible transit time while reducing mission risk and overall cost. The mission architecture implements solar sailing technologies and in-space aggregation of modularized functional units to form mission capable spacecraft. The study reveals elements of such a challenging mission, but it is nevertheless found to be feasible with technologies that are either extant or in active development., Comment: 43 pages, 8 figures, and 9 tables

The solar gravitational lens (SGL) provides a factor of $10^{11}$ amplification for viewing distant point sources beyond our solar system. As such, it may be used for resolved imaging of extended sources, such as exoplanets, not possible otherwise. To use the SGL, a spacecraft carrying a modest telescope and a coronagraph must reach the SGLs focal region, that begins at $\sim$550 astronomical units (AU) from the Sun and is oriented outward along the line connecting the distant object and the Sun. No spacecraft has ever reached even a half of that distance; and to do so within a reasonable mission lifetime (e.g., less than 25 years) and affordable cost requires a new type of mission design, using solar sails and microsats ($<100$~kg). The payoff is high -- using the SGL is the only practical way we can ever get a high-resolution, multi-pixel image of an Earth-like exoplanet, one that we identify as potentially habitable. This paper describes a novel mission design starting with a rideshare launch from the Earth, spiraling in toward the Sun, and then flying around it to achieve solar system exit speeds of over $20$ AU/year. A new sailcraft design is used to make possible high area to mass ratio for the sailcraft. The mission design enables other fast solar system missions, starting with a proposed very low cost technology demonstration mission (TDM) to prove the functionality and operation of the microsat-solar sail design and then, building on the TDM, missions to explore distant regions of the solar system, and those to study Kuiper Belt objects (KBOs) and the recently discovered interstellar objects (ISOs) are also possible., Comment: 18 pages, 10 figures

A solar sail propelled small satellite mission concept to intercept and potentially rendezvous with newly discovered transient interstellar objects (ISOs) is described. The mission concept derives from the proposal for a technology demonstration mission for exiting the solar system at high velocity, eventually to reach the focal region of the solar gravitational lens. The ISO mission concept is to fly a solar sail toward a holding orbit around the Sun and when the ISO orbit is confirmed, target the sailcraft to reach an escape velocity of over 6 AU/year. This would permit rapid response to a new ISO discovery and an intercept within 10 AU from the Sun. Two new proven interplanetary technologies are utilized to enable such a mission: i) interplanetary smallsats, such as those demonstrated by the MarCO mission, and ii) solar sails, such as demonstrated by LightSail and IKAROS missions and developed for NEA Scout and Solar Cruiser missions. Current technology work suggests that already within this decade such a mission could fly and reach an ISO moving through the solar system. It might enable the first encounter with an ISO to allow for imaging and spectroscopy, measurements of size and mass, potentially giving a unique information about the object's origin and composition. A similar approach may be used to allow for a sample return., Comment: 17 pages, 9 figures

We examined the solar gravitational lens (SGL) as the means to produce direct high-resolution, multipixel images of exoplanets. The properties of the SGL are remarkable: it offers maximum light amplification of ~1e11 and angular resolution of ~1e-10 arcsec. A probe with a 1-m telescope in the SGL focal region can image an exoplanet at 30 pc with 10-kilometer resolution on its surface, sufficient to observe seasonal changes, oceans, continents, surface topography. We reached and exceeded all objectives set for our study: We developed a new wave-optical approach to study the imaging of exoplanets while treating them as extended, resolved, faint sources at large but finite distances. We properly accounted for the solar corona brightness. We developed deconvolution algorithms and demonstrated the feasibility of high-quality image reconstruction under realistic conditions. We have proven that multipixel imaging and spectroscopy of exoplanets with the SGL are feasible. We have developed a new mission concept that delivers an array of optical telescopes to the SGL focal region relying on three innovations: i) a new way to enable direct exoplanet imaging, ii) use of smallsats solar sails fast transit through the solar system and beyond, iii) an open architecture to take advantage of swarm technology. This approach enables entirely new missions, providing a great leap in capabilities for NASA and the greater aerospace community. Our results are encouraging as they lead to a realistic design for a mission that will be able to make direct resolved images of exoplanets in our stellar neighborhood. It could allow exploration of exoplanets relying on the SGL capabilities decades, if not centuries, earlier than possible with other extant technologies. The architecture and mission concepts for a mission to the strong interference region of the SGL are promising and should be explored further., Comment: Final Report for the NASA's Innovative Advanced Concepts (NIAC) Phase II proposal. 91 pages, 50 figures, 5 tables

The goal of the paper "A new graph over semi-direct products of groups" is to define a graph \Gamma(G) on a group G when G splits over a normal subgroup. We demonstrate herein that the graph is ill-defined. We also attempt to ascertain causes for the discrepancies., Comment: 2 pages, 3 sections

Given a Mersenne prime $q$ and a positive even integer $e$, let $F$ and $E$ be the fields of orders $q$ and $q^e$ respectively. Let $C$ be a cyclic subgroup of $E^\times$ whose index in $E^\times$ is divisible only by primes dividing $q - 1$. We compute the character degrees of the group $C \rtimes {\rm Gal} (E/F)$ by using the Galois connection between the subfields of $E$ and the Galois group ${\rm Gal} (E/F)$.