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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

UPDATED ANALYSIS OF THE UPWIND INTERPLANETARY HYDROGEN VELOCITY AS OBSERVED BY THE HUBBLE SPACE TELESCOPE DURING SOLAR CYCLE 23

The interplanetary hydrogen (IPH), a population of neutrals that fill the space between planets inside the heliosphere, carries the signature of the interstellar medium (ISM) and the heliospheric interface. As the incoming ISM-ionized component deflects at the heliopause, charge exchange reactions decelerate the bulk motion of the neutrals that penetrate the heliosphere. Inside the heliosphere, the IPH bulk velocity is further affected by solar gravity, radiation pressure, and ionization processes, with the latter two processes dependent on solar activity. Solar cycle 23 provided the first partial temporal map of the IPH velocity, including measurements from the Hubble Space Telescope (HST) spectrometers (Goddard High Resolution Spectrograph (GHRS) and Space Telescope Imaging Spectrograph (STIS)) and the Solar and Heliospheric Observatory/Solar Wind ANisotropies (SWAN) instrument. We present an updated analysis of IPH velocity measurements from GHRS and STIS and compare these results with those of SWAN and two different time-dependent models. Our reanalysis of STIS data reveals a significant change in IPH velocity relative to earlier reports, because of the contamination by geocoronal oxygen that was not accounted for. While current models of the heliospheric interface predict the observed IPH velocity for solar maximum, they are not consistent with data covering solar minimum. With updates to the HST data points, we now find that all data can be fit by the existing models to within 1{sigma}, with the exception of SWAN observations taken at solar minimum (1997/1998). We conclude that the current data lack the temporal coverage and/or precision necessary to determine the detailed characteristics of the solar cycle dependence. Hence, new observations are merited.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A new detection of LYα absorption from the heliotail

We present new Hubble Space Telescope observations of H I Lyα absorption toward the F8 V star HD 35296. This line of sight is only a few degrees from the downwind direction of the local interstellar medium flow vector. As a consequence, Lyα absorption from the heliotail is detected in the spectrum, consistent with three previous downwind detections of heliotail absorption. The clustering of the heliotail absorption detections around the downwind direction demonstrates that the heliotail is pointed close to that direction, limiting the extent to which the interstellar magnetic field might be distorting and deflecting the heliotail. We explore this issue further using three-dimensional MHD models of the global heliosphere. The three computed models represent the first three-dimensional MHD models with both a kinetic treatment of neutrals and an extended grid in the tail direction, both of which are necessary to model Lyα absorption downwind. The models indicate only modest heliotail asymmetries and deflections, which are not large enough to be inconsistent with the clustering of heliotail absorption detections around the downwind direction. The models are reasonably successful at reproducing the observed absorption, but they do overpredict the Lyα opacity by a factor of 2-3. We discuss implications of these results in light of observations of the heliotail region from the Interstellar Boundary Explorer mission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

SPITZER OBSERVATIONS OF LONG-TERM INFRARED VARIABILITY AMONG YOUNG STELLAR OBJECTS IN CHAMAELEON I

Infrared variability is common among young stellar objects, with surveys finding daily to weekly fluctuations of a few tenths of a magnitude. Space-based observations can produce highly sampled infrared light curves, but are often limited to total baselines of about 1 month due to the orientation of the spacecraft. Here we present observations of the Chameleon I cluster, whose low declination makes it observable by the Spitzer Space Telescope over a 200-day period. We observe 30 young stellar objects with a daily cadence to better sample variability on timescales of months. We find that such variability is common, occurring in ∼80% of the detected cluster members. The change in [3.6]–[4.5] color over 200 days for many of the sources falls between that expected for extinction and fluctuations in disk emission. With our high cadence and long baseline we can derive power spectral density curves covering two orders of magnitude in frequency and find significant power at low frequencies, up to the boundaries of our 200-day survey. Such long timescales are difficult to explain with variations driven by the interaction between the disk and stellar magnetic field, which has a dynamical timescale of days to weeks. The most likely explanation is either structural or temperature fluctuations spread throughout the inner ∼0.5 au of the disk, suggesting that the intrinsic dust structure is highly dynamic.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The P( 4 S) + NH( 3 Σ – ) and N( 4 S) + PH( 3 Σ – )reactions as sources of interstellar phosphorus nitride

Phosphorus nitride (PN) is believed to be one of the major reservoirs of phosphorus in the interstellar medium (ISM). For this reason, understanding which reactions produce PN in space and predicting their rate coefficients is important for modelling the relative abundances of P-bearing species and clarifying the role of phosphorus in astrochemistry. Here, in this work, we explore the potential energy surfaces of the $\textrm{P}(^4\textrm{S}) + \textrm{NH}(^3\Sigma^-)$ and $\textrm{N}(^4\textrm{S}) + \textrm{PH}(^3\Sigma^-)$ reactions and the formation of $\textrm{H}(^2\textrm{S}) + \textrm{PN}(^1\Sigma^+)$ through high accuracy ab initio calculations and the variable reaction coordinate transition state theory (VRC-TST). We found that both reactions proceed without an activation barrier and with similar rate coefficients that can be described by a modified Arrhenius equation ( $k(T)=\alpha\!\left( T/300 \right)^{\beta} \exp\!{(\!-\!\gamma/T)})$ with $\alpha=0.93\times 10^{-10}\rm cm^3\,s^{-1}$ , $\beta=-0.18$ and $\gamma=0.24\, \rm K$ for the $\textrm{P} + \textrm{NH} \longrightarrow \textrm{H} + \textrm{PN}$ reaction and $\alpha=0.88\times 10^{-10}\rm cm^3\,s^{-1}$ , $\beta=-0.18$ and $\gamma=1.01\, \rm K$ for the $\textrm{N} + \textrm{PH} \longrightarrow \textrm{H} + \textrm{PN}$ one. Both reactions are expected to be relevant for modelling PN abundances even in the cold environments of the ISM. Given the abundance of hydrogen in space, we have also predicted rate coefficients for the destruction of PN via H + PN collisions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

QUANTIFYING THE HEATING SOURCES FOR MID-INFRARED DUST EMISSIONS IN GALAXIES: THE CASE OF M 81

With the newly available photometric images at 250 and 500 μm from the Herschel Space Observatory, we study quantitative correlations over a sub-kiloparsec scale among three distinct emission components in the interstellar medium of the nearby spiral galaxy M 81 (NGC 3031): (1) I {sub 8} or I {sub 24}, the surface brightness of the mid-infrared emission observed in the Spitzer Space Telescope 8 or 24 μm band, with I {sub 8} and I {sub 24} being dominated by the emissions from polycyclic aromatic hydrocarbons (PAHs) and very small grains (VSGs) of dust, respectively; (2) I {sub 500}, that of the cold dust continuum emission in the Herschel Space Observatory 500 μm band, dominated by the emission from large dust grains heated by evolved stars; and (3) I {sub Hα}, a nominal surface brightness of the Hα line emission, from gas ionized by newly formed massive stars. The results from our correlation study, free from any assumption on or modeling of dust emissivity law or dust temperatures, present solid evidence for significant heating of PAHs and VSGs by evolved stars. In the case of M 81, about 67% (48%) of the 8 μm (24 μm ) emission derives its heating from evolved stars, with the remainder attributed to radiation heating associated with ionizing stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Lyα EMISSION FROM GREEN PEAS: THE ROLE OF CIRCUMGALACTIC GAS DENSITY, COVERING, AND KINEMATICS

We report Hubble Space Telescope/Cosmic Origins Spectrograph observations of the Lyα emission and interstellar absorption lines in a sample of 10 star-forming galaxies at z ∼ 0.2. Selected on the basis of high equivalent width optical emission lines, the sample, dubbed “Green Peas,” make some of the best analogs for young galaxies in an early universe. We detect Lyα emission in all ten galaxies, and 9/10 show double-peaked line profiles suggestive of low H i column density. We measure Lyα/Hα flux ratios of 0.5–5.6, implying that 5%–60% of Lyα photons escape the galaxies. These data confirm previous findings that low-ionization metal absorption (LIS) lines are weaker when Lyα escape fraction and equivalent width are higher. However, contrary to previously favored interpretations of this trend, increased Lyα output cannot be the result of a varying H i covering: the Lyman absorption lines (Lyβ and higher) show a covering fraction near unity for gas with N{sub H} {sub i} ≳ 10{sup 16} cm{sup −2}. Moreover, we detect no correlation between Lyα escape and the outflow velocity of the LIS lines, suggesting that kinematic effects do not explain the range of Lyα/Hα flux ratios in these galaxies. In contrast, we detect a strong anticorrelation between the Lyα escape fraction and the velocity separation of the Lyα emission peaks, driven primarily by the velocity of the blue peak. As this velocity separation is sensitive to H i column density, we conclude that Lyα escape in these Green Peas is likely regulated by the H i column density rather than outflow velocity or H i covering fraction.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2015

Propulsion Technology Assessment: Science & Enabling Technologies to Explore the Interstellar Medium

As part of a larger effort led by the Keck Institute for Space Studies at the California Institute of Technology, the Advanced Concepts Office at NASA's George C. Marshall Space Flight Center conducted a study to assess what low-thrust advanced propulsion system candidates, existing and near term, could deliver a small, Voyager-like satellite to our solar system's heliopause, approximately 100 AU from the center of the sun, within 10 years and within a 2025 to 2035 launch window. The advanced propulsion system trade study consisted of three candidates, including a Magnetically Shielded Miniature (MaSMi) Hall thruster, a solar sail and an electric sail. Two aerial densities, and thus characteristic accelerations, 0.426 mm/s2 and 0.664 mm/s2, were analyzed for the solar sail option in order understand the impact of near and long term development of this technology. Similarly, two characteristic accelerations, 1 mm/s2 and 2 mm/s2, were also analyzed for the electric sail option in addition to tether quantities of 10 and 20, respectively, and individual tether length of 20 km. A second analysis was conducted to determine what existing solid rocket motor kick stage(s) would be required to provide additional thrust at various points in the trajectory, assuming an earth departure characteristic energy capability provided by a Space Launch System (SLS) Block 1B vehicle architecture carrying an 8.4 meter payload fairing. Two trajectory profiles were considered, including an escape trajectory using a Jupiter gravity assist (E-Ju), and an escape trajectory first performing a Jupiter gravity assist followed by an Oberth maneuver around the sun and an optional Saturn gravity assist (E-Ju-Su-Sa). The Oberth maneuver would need to be performed very close to the sun, wherein this study assumed a perihelion distance of approximately 11 solar radii, or 0.05 AU, away from the surface. The heat shield technology required to perform this type of ambitious maneuver was assumed to be similar to that of NASA's Solar Probe Plus mission, which is slated to launch in July 2018. With respect to a SLS Block 1B earth departure characteristic energy capability of 100 sq km/s2 for the E-Ju trajectory option, results indicated that compared to having no advanced propulsion system onboard, both the MaSMi Hall thruster and solar sail options subtract approximately 8 to 10 years from the total trip time while the electric sail outperforms all options by subtracting up to 20 years. With respect to an average kick stage velocity capability of 2.5 to 3.5 km/s at perihelion, the most sensitive segment of the E-Ju-Su-Sa trajectory option, results indicated that both the MaSMi Hall thrust and solar sail options only subtract 1 to 3 years from the total trip time whereas the electric sail again outperforms all other options by subtracting up to 5 years. In other words, if the Technology Readiness Level of an electric sail could be increased in time, this propulsion technology could not only enable a satellite to reach 100 AU in 10 years but it could potentially do so even faster. Completing such an ambitious mission in that short of a timespan would be very attractive to many as it would be well within the average career span of any of those involved.

Hopkins, Randall C.↗
NASA NTRS2016

Propulsion Technology Assessment: Science and Enabling Technologies to Explore the Interstellar Medium

As part of a larger effort led by the Keck Institute for Space Studies at the California Institute of Technology, the Advanced Concepts Office at NASA’s George C. Marshall Space Flight Center conducted a study to assess what low-thrust advanced propulsion system candidates, existing and near term, could deliver a small, Voyager-like satellite to our solar system’s heliopause, approximately 100 AU from the center of the sun, within 10 years and within a 2025 to 2035 launch window. The advanced propulsion system trade study consisted of three candidates, including a Magnetically Shielded Miniature (MaSMi) Hall thruster, a solar sail and an electric sail. Two aerial densities, and thus characteristic accelerations, 0.426 mm/s(exp 2) and 0.664 mm/s(exp 2), were analyzed for the solar sail option in order understand the impact of near and long term development of this technology. Similarly, two characteristic accelerations, 1 mm/s(exp 2) and 2 mm/s(exp 2), were also analyzed for the electric sail option in addition to tether quantities of 10 and 20, respectively, and individual tether length of 20 km. A second analysis was conducted to determine what existing solid rocket motor kick stage(s) would be required to provide additional thrust at various points in the trajectory, assuming an earth departure characteristic energy capability provided by a Space Launch System (SLS) Block 1B vehicle architecture carrying an 8.4 meter payload fairing. Two trajectory profiles were considered, including an escape trajectory using a Jupiter gravity assist (E-Ju), and an escape trajectory first performing a Jupiter gravity assist followed by an Oberth maneuver around the sun and an optional Saturn gravity assist (E-Ju-Su-Sa). The Oberth maneuver would need to be performed very close to the sun, wherein this study assumed a perihelion distance of approximately 11 solar radii, or 0.05 AU, away from the surface. The heat shield technology required to perform this type of ambitious maneuver was assumed to be similar to that of NASA’s Solar Probe Plus mission, which is slated to launch in July 2018. With respect to a SLS Block 1B earth departure characteristic energy capability of 100 km(exp 2)/s(exp 2) for the E-Ju trajectory option, results indicated that compared to having no advanced propulsion system onboard, both the MaSMi Hall thruster and solar sail options subtract approximately 8 to 10 years from the total trip time while the electric sail outperforms all options by subtracting up to 20 years. With respect to an average kick stage velocity capability of 2.5 to 3.5 km/s at perihelion, the most sensitive segment of the E-Ju-Su-Sa trajectory option, results indicated that both the MaSMi Hall thrust and solar sail options only subtract 1 to 3 years from the total trip time whereas the electric sail again outperforms all other options by subtracting up to 5 years. In other words, if the Technology Readiness Level of an electric sail could be increased in time, this propulsion technology could not only enable a satellite to reach 100 AU in 10 years but it could potentially do so even faster. Completing such an ambitious mission in that short of a timespan would be very attractive to many as it would be well within the average career span of any of those involved.

Hopkins, Randall C.↗
NASA NTRS1996

GAuche-Ethyl Alcohol: Laboratory Assignments and Interstellar Identification

Ethyl alcohol (ethanol) is known to possess a pair of closely-spaced excited torsional substates (gauche +, gauche -) at an energy of approximately 57 K above the ground (trans) torsional substrate. We report an extended analysis of some gauch- - gauch+ Q branch (delta J=0) transitions witha three-substrate fixed frame axis method (FFAM) Hamilton.

ISM↗
DOE OSTI2014

The structure of the local interstellar medium. VI. New Mg II, Fe II, and Mn II observations toward stars within 100 pc

We analyze high-resolution spectra obtained with the Space Telescope Imaging Spectrograph onboard the Hubble Space Telescope toward 34 nearby stars (≤100 pc) to record Mg II, Fe II, and Mn II absorption due to the local interstellar medium (LISM). Observations span the entire sky, probing previously unobserved regions of the LISM. The heavy ions studied in this survey produce narrow absorption features that facilitate the identification of multiple interstellar components. We detected one to six individual absorption components along any given sight line, and the number of absorbers roughly correlates with the pathlength. This high-resolution near-ultraviolet (NUV) spectroscopic survey was specifically designed for sight lines with existing far-UV (FUV) observations. The FUV spectra include many intrinsically broad absorption lines (i.e., of low atomic mass ions) and are often observed at medium resolution. The LISM NUV narrow-line absorption component structure presented here can be used to more accurately interpret the archival FUV observations. As an example of this synergy, we present a new analysis of the temperature and turbulence along the line of sight toward ε Ind. The new observations of LISM velocity structure are also critical in the interpretation of astrospheric absorption derived from fitting the saturated H I Lyα profile. As an example, we reanalyze the spectrum of λ And and find that this star likely does have an astrosphere. Two stars in the sample that have circumstellar disks (49 Cet and HD141569) show evidence for absorption due to disk gas. Finally, the substantially increased number of sight lines is used to test and refine the three-dimensional kinematic model of the LISM and search for previously unidentified clouds within the Local Bubble. We find that every prediction made by the Redfield and Linsky kinematic model of the LISM is confirmed by an observed component in the new lines of sight.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2001

A Comprehensive Investigation of the Structuring of the Interstellar Medium of Massive Stars

We proposed to use the International Ultraviolet Explorer (IUE), ROSAT (X-ray satellite), Advanced Spacecraft for Cosmology Astrophysics (ASCA), and Hubble Space Telescope (HST) archival data, complemented by data obtained from ground-based observatories, to study the physical structure of the interstellar medium as a result of interactions between massive stars and the ambient medium. During the granting period, we have carried out the major tasks proposed originally and reported the results in a large number of papers. The papers published during the last two years below. We conclude that this program has been highly successfully.

Chu, You-Hua↗
NASA NTRS1985

The kinematics of cool metal-line white dwarfs and accretion in the local interstellar medium

The data base of spectroscopically identified white dwarfs is used to isolate a sample of cool degenerates with trace metals. The spatial distribution and space velocity components of the white dwarfs projected onto and perpendicular to the galactic plane are compared with the distribution of local interstellar hydrogen. The results are consistent with the metals having been accreted during recent encounters with local density enhancements. However, the limited availability of radial velocities, coupled with uncertainties in the derived abundances, the diffusion times, and in the three-dimensional structure of the local medium, prevent a definitive test of the accretion hypothesis at this time.

Aannestad, P. A.↗
DOE OSTI2026

The Interstellar Mapping And Acceleration Probe High Energy (IMAP-Hi) Neutral Atom Imager

The IMAP-Hi Energetic Neutral Atom (ENA) Imager on NASA’s Interstellar Mapping and Acceleration Probe (IMAP) mission (McComas et al. 2018a, 2025) is designed to measure ENAs from the global interaction between the heliosphere and the local interstellar medium (LISM). These ENAs are initially plasma ions of solar wind origin that are neutralized by charge exchange with the cold neutral atoms of LISM that freely flow through the heliosphere-LISM interaction region. IMAP-Hi consists of two identical single-pixel sensors, each covering the ENA spectral range from 0.44 keV to 15.6 keV over nine contiguous energy passbands and having an approximately conical field-of-view (FOV) of 4.1o full width at half maximum (FWHM). The Hi-45 sensor points 45o relative to the spacecraft spin axis from the antisunward direction; each spacecraft spin, it measures ENA intensity over a circular swath with half-cone angle 45o centered on the ecliptic plane. The Hi-90 sensor points 90o relative to the spin axis; each spacecraft spin, it measures ENA intensity over a great circle in the sky, sampling both the north and south ecliptic poles. As the IMAP spin vector is re-pointed daily toward the Sun, the ecliptic longitude of the swaths moves daily by ∼1o such that a full sky map is acquired by Hi-90 every six months and a complete low latitude (−45o to +45o) map is acquired by Hi-45 annually. The IMAP-Hi sensor design has direct heritage from the IBEX-Hi imager on the Interstellar Boundary Explorer (IBEX) mission, with substantial improvements in energy range, energy resolution, angular resolution, signal-to-noise ratio, and, for ecliptic latitudes within ±45o, temporal resolution and exposure time. The global ENA maps acquired by IMAP-Hi partially overlap in energy and viewing with the ENA maps acquired by the IMAP-Lo and IMAP-Ultra ENA imagers, which we combine to answer fundamental questions about the structure and dynamics of the interaction of the heliosphere and the LISM.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1984

Radio interferometry from space platforms

While current VLBI observations are limited in their resolution by the earth diameter magnitude, which is the largest antenna separation available, as well as in their information content, because of the small number of antennas in use at a given time, the extension of VLBI to include one or more antennas in space will relieve both constraints and help to map distant radio sources with the highest possible resolution. Attention is given to the implementation of such an orbital VLBI system extension through (1) a Shuttle-launch mission, (2) a six-month to one-year near earth orbit mission based on a space platform associated with the Space Station, (3) a large orbit free flyer platform mission of more than 2-year duration, and (4) lunar and/or deep space orbits, aimed at reaching the resolution limits set by interstellar scattering.

Roberts, D. H.↗
NASA NTRS2003

The Lifetimes of Nitriles (-C*N) and Acids (-COOH) during Ultraviolet Photolysis and Their Survival in Space

Nitriles are one of the most common classes of molecules observed in the gas phase in space, with over a dozen having been positively identified in interstellar and circumstellar environments through the detection of their rotational transitions. Acids, in contrast, are much less common. In this paper we present laboratory data comparing the stability of two structurally related acid-nitrile pairs to ultraviolet (UV) photolytic destruction: acetic acid vs. acetonitrile (CH3-COOH vs. CH3-CN) and glycine vs. aminoacetonitrile (H2N-CH2-COOH vs. H2N-CH2-CN). We find that the nitriles are destroyed ten and five times more slowly (respectively) by UV photolysis than are the corresponding acids. This suggests that whatever their relative formation rates, acids may be less abundant than nitriles in interstellar environments in part because they are more rapidly destroyed by photolysis. The results of this infrared (IR) spectral matrix isolation study indicate that during the lifetime of a typical interstellar cloud, even in its darkest regions, a population of acids in the gas phase will likely be diminished by at least half. Since aminoacetonitrile is a precursor to the amino acid glycine, and far more stable, presolar aminoacetonitrile may be a contributor to the deuterium enriched glycine detected in meteorites. It would clearly be informative to search for aminoacetonitrile (the nitrile corresponding to glycine) in the regions where the amino acid glycine has been reported.

Bernstein, Max P.↗
NASA NTRS2003

The Petrography of Meteoritic Nano-Diamonds

At least some meteoritic nanodiamonds are likely of presolar origin because of their association with anomalous Xe-HL and Te isotopic components indicative of a supernova (SN) origin. But the abundance of Xe is such that only approx. 1 in 10(exp 6) nano-diamonds contains a Xe atom, and the bulk C-13/C-12 composition of nano-diamond acid residues is chondritic (solar). Therefore, it is possible that a significant fraction of meteoritic nano-diamonds formed within the solar nebula. Nano-diamonds have recently been detected for the first time within the accretion discs of young stars by the Infrared Space Observatory (ISO). No comparable evidence of nanodiamonds in the interstellar medium has yet been found. We have identified nano-diamonds in acid etched thin-sections of meteorites, polar micrometeorites, and interplanetary dust particles (IDPs) with the goal of determining their distribution as a function of heliocentric distance. (It is assumed the meteorites and the polar micrometeorites are from asteroids at 2-4 AU and at least some of the IDPs are from comets at >50AU). We found that nano-diamonds are heterogeneously distributed throughout carbon-rich meteoritic materials (we identified them in some IDPs and not in others), and that their abundance may actually decrease with heliocentric distance, consistent with the hypothesis that some of them formed within the inner solar system and not in a presolar (SN) environment. In order to gain further insight about the origins of meteoritic nano-diamonds we are currently investigating their distribution in unetched thin-sections. We have examined a chondritic cluster IDP (U220GCA), fragments of the Tagish Lake (CM1) meteorite, and a SN graphite spherule (KE3d8) isolated from the Murchison (CM) meteorite. We selected U220GCA because its nano-diamond abundance (in acid etched thin-sections) appears to be as much as approx. 10X higher than in Murchison matrix, Tagish Lake because it has a higher reported nano-diamond abundance than other carbonaceous chondrites (approx. 3650-4330 ppm), and KE3d8 because it is a carbon spherule with an isotopic composition suggesting that it is a bone fide presolar SN grain.

Dai, Z. R.↗
NASA NTRS2000

The Merits of Multi-Hop Communication in Deep Space

The physics of communication give an advantage to multi-hop systems, because the ratio of power received to power transmitted on a telecommunications link over a fixed distance S increases by a factor of n(sup 2) if the link is divided in to n equal hops of length S/n.

interstellar interplanetary↗