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End-to-End System Test of the Relative Precision and Stability of the Photometric Method for Detecting Earth-Size Extrasolar Planets

We developed the CCD camera system for the laboratory test demonstration and designed the optical system for this test. The camera system was delivered to Ames in April, 1999 with continuing support mostly in the software area as the test progressed. The camera system has been operating successfully since delivery. The optical system performed well during the test. The laboratory demonstration activity is now nearly complete and is considered to be successful by the Technical Advisory Group, which met on 8 February, 2000 at the SETI Institute. A final report for the Technical Advisory Group and NASA Headquarters will be produced in the next few months. This report will be a comprehensive report on all facets of the test including those covered under this grant. A copy will be forwarded, if desired, when it is complete.

Dunham, Edward W.↗

Nasa's Search for Habitable Worlds

NASA's Kepler Mission launched in 2009 to scan a particular region of the sky for Earth-size planets transiting Sun-like stars in the habitable zone. After nearly ten years of observations, Kepler's mission ended, revealing over 2600 previously unknown exoplanets, most of which are smaller than 2X the size of Earth, and teaching us that small planets are common throughout the galaxy. NASA's TESS Mission launched in 2018 to continue NASA's quest for the search for life and is conducting a near all-sky survey for exoplanets orbiting stars 10X closer and 100X brighter than those observed by Kepler, permitting us to follow up many of the planetary discoveries to determine their masses, densities, and with future missions, to detect and characterize their atmospheres, and ultimately to potentially discover signs of life on these planets.

Jenkins, Jon M.↗

Mapping the Region in the Nearest Star System to Search for Habitable Planets

Circumstellar planets within the alpha Centauri AB star system have been suggested through formation models and recent observations, and ACESat (Belikov et al. AAS Meeting #225, #311.01, 2015) is a proposed space mission designed to directly image Earth-sized planets in the habitable zones of both of these stars. The alpha Centauri system is billions of years old, so planets are only expected to be found in regions where their orbits are long-lived. We evaluate the extent of the regions within the alpha Centauri AB star system where small planets are able to orbit for billion-year timescales and we map the positions in the sky plane where planets on stable orbits about either stellar component may appear. We confirm the qualitative results of Wiegert & Holman (Astron. J. 113, 1445, 1997) regarding the approximate size of the regions of stable orbits, which are larger for retrograde orbits relative to the binary than for prograde orbits. Additionally, we find that mean motion resonances with the binary orbit leave an imprint on the limits of orbital stability, and the effects of the Lidov-Kozai mechanism are also readily apparent. Overall, orbits in the habitable zones near the plane of the binary are stable, whereas high-inclination orbits are short-lived.

alpha Centauri AB star system↗

Overview and Status of the Kepler Mission

The Kepler Mission is a search for terrestrial planets with the design optimized for detecting Earth-size planets in the habitable zone (HZ) of solar-like stars. In addition, the mission has a broad detection capability for a wide range of planetary sizes, planetary orbits and spectral types of stars. The mission is in the midst of the development phase with good progress leading to the preliminary design review later this year. Long lead procurements are well under way. An overview in all areas is presented including both the flight system (photometer and spacecraft) and the ground system. Launch is on target for 2007 on a Delta II.

Koch, D.↗

Characterizing the Architectures, Diversity and Habitability of Nearby Planetary Systems: The HabEx Observatory

Ongoing research, upcoming developments in ground-based facilities, and the launch of new space missions (Transiting Exoplanet Survey Satellite [TESS], James Webb Space Telescope [JWST], and Wide Field Infrared Survey Telescope [WFIRST]) will continue to advance knowledge of the variety and nature of exoplanetary system components over the next decade and a half. However, many key questions will remain: What is the architecture and full diversity of mature planetary systems? What is the linkage between individual planet properties, planetary system architectures and circumstellar dust structures? How diverse are planetary atmospheres over the full range of planet sizes and stellar insulation levels? Are there Earth-sized planets orbiting in the habitable zone (HZ) of nearby sunlike stars, with water vapor in their atmospheres, evidence for surface oceans and signs of life? Are these signs of life really of biotic origin? Answering all of these questions requires direct imaging and spectroscopy from space in reflected light and/or thermal emission. We exclusively discuss reflected light (near ultraviolet [UV] to near infrared [IR]) investigations, identifying some of the observational, technological, and theoretical challenges that must be met to accomplish such a feat. This paper concentrates on one possible implementation strategy currently under study: the HabEx (Habitable Exoplanet) Observatory mission concept.

Mennesson, B.↗

The Habitable Exoplanet Observatory (HabEx): Science Goals and Projected Capabilities

Ongoing research, upcoming developments in ground-based facilities, and the launch of new space missions (Transiting Exoplanet Survey Satellite [TESS], James Webb Space Telescope [JWST], and Wide Field Infrared Survey Telescope [WFIRST]) will continue to advance knowledge of the variety and nature of exoplanetary system components over the next decade and a half. However, many key questions will remain: What is the architecture and full diversity of mature planetary systems? What is the linkage between individual planet properties, planetary system architectures, and circumstellar dust structures? How diverse are planetary atmospheres over the full range of planet sizes and stellar insulation levels? Are there Earth-sized planets orbiting in the habitable zone (HZ) of nearby sun-like stars, with water vapor in their atmospheres, evidence for surface oceans and signs of life? Are these really of biotic origin? Answering all of these questions requires direct imaging and spectroscopy from space in reflected light and/or thermal emission. We exclusively discuss reflected light (near ultraviolet [UV] to near infrared [IR]) investigations, identifying some of the observational, technological, and theoretical challenges that must be met to accomplish such a feat. This paper concentrates on one possible implementation strategy and mission concept currently under study: the HabEx (Habitable Exoplanet) Observatory.

Mennesson, Bertrand↗

From Pixels to Planets

The Kepler Mission was launched in 2009 as NASAs first mission capable of finding Earth-size planets in the habitable zone of Sun-like stars. Its telescope consists of a 1.5-m primary mirror and a 0.95-m aperture. The 42 charge-coupled devices in its focal plane are read out every half hour, compressed, and then downlinked monthly. After four years, the second of four reaction wheels failed, ending the original mission. Back on earth, the Science Operations Center developed the Science Pipeline to analyze about 200,000 target stars in Keplers field of view, looking for evidence of periodic dimming suggesting that one or more planets had crossed the face of its host star. The Pipeline comprises several steps, from pixel-level calibration, through noise and artifact removal, to detection of transit-like signals and the construction of a suite of diagnostic tests to guard against false positives. The Kepler Science Pipeline consists of a pipeline infrastructure written in the Java programming language, which marshals data input to and output from MATLAB applications that are executed as external processes. The pipeline modules, which underwent continuous development and refinement even after data started arriving, employ several analytic techniques, many developed for the Kepler Project. Because of the large number of targets, the large amount of data per target and the complexity of the pipeline algorithms, the processing demands are daunting. Some pipeline modules require days to weeks to process all of their targets, even when run on NASA's 128-node Pleiades supercomputer. The software developers are still seeking ways to increase the throughput. To date, the Kepler project has discovered more than 4000 planetary candidates, of which more than 1000 have been independently confirmed or validated to be exoplanets. Funding for this mission is provided by NASAs Science Mission Directorate.

supercomputers↗

Kepler Mission: A Discovery-Class Mission Designed to Determine the Frequency of Earth-Size and Larger Planets Around Solar-Like Stars

The first step in discovering the extent of life in our galaxy is to determine the number of terrestrial planets in the habitable zone (HZ). The Kepler Mission is designed around a 0.95 in aperture Schmidt-type telescope with an array of 42 CCDs designed to continuously monitor the brightness of 100,000 solar-like stars to detect the transits of Earth-size and larger planets. The photometer is scheduled to be launched into heliocentric orbit in 2007. Measurements of the depth and repetition time of transits provide the size of the planet relative to the star and its orbital period. When combined with ground-based spectroscopy of these stars to fix the stellar parameters, the true planet radius and orbit scale, hence the position relative to the HZ are determined. These spectra are also used to discover the relationships between the characteristics of planets and the stars they orbit. In particular, the association of planet size and occurrence frequency with stellar mass and metallicity will be investigated. At the end of the four year mission, hundreds of terrestrial planets should be discovered in and near the HZ of their stars if such planets are common. Extending the mission to six years doubles the expected number of Earth-size planets in the HZ. A null result would imply that terrestrial planets in the HZ occur in less than 1% of the stars and that life might be quite rare. Based on the results of the current Doppler-velocity discoveries, detection of a thousand giant planets is expected. Information on their albedos and densities of those giants showing transits will be obtained.

William Borucki↗

Exploring the Clouds of Venus: Science Driven Aerobot Missions to Our Sister Planet

Venus is essential to our understanding of the evolution and habitability of Earth-size planets throughout the galaxy. The selection of the VERITAS, EnVision, and DAVINCI missions by NASA and ESA in June 2021 is an important step in advancing the science. However, addressing many of the most challenging questions will require in situ platforms that can operate in the Venus environment for extended periods in order to capture the full complexity of our sister planet. Aerobots are aerial vehicles that exploit buoyancy to achieve long-duration operation in the Venus cloud layer where environmental conditions are comparatively benign. Buoyancy control, explained in more detail in a companion paper at this conference, allows aerobots to change altitude with little energy expenditure enabling new scientific measurement opportunities. These include atmospheric chemistry, dynamics, geophysical measurements of the crust and interior and geological investigations enabled by high resolution surface imaging. One aspect to our approach to defining missions that fit within the resource constraints of competitive missions is keeping the scale small. Today’s science-driven appetite for sophisticated measurements and large volumes of data is driving size upwards but advances in technology can enable aerobots that can be delivered to Venus at manageable costs. The other aspect is supporting the aerobot at Venus with orbiters providing data relay, localization and synergistic science. The recently selected orbiters, equipped with low-cost proximity relay systems routinely used at Mars may obviate the need for dedicated orbiters thereby enabling Discovery mission candidates. Four aerobot mission concepts have been defined which fit comfortably within the current New Frontiers (NF) cost cap ($900M in $FY22). One of these concepts would also be a candidate for a Discovery mission if that cost cap ($500M in $FY19) were raised. Raising the NF cost cap would enable more capable aerobot missions combining both altitude control with synergistic orbital observations. Investigations of surface geology at high resolution with subcloud NIR nightside imaging and dropsondes on the dayside of Venus could also benefit from collaborations with foreign contributions.

"O'Rourke, Joseph"↗

Educational And Public Outreach Software On Planet Detection For The Macintosh (TM)

The possibility of extra-solar planets has been a very popular topic with the general public for years. Considerable media coverage of recent detections has only heightened the interest in the topic. School children are particularly interested in learning about space. Astronomers have the knowledge and responsibility to present this information in both an understandable and interesting format. Since most classrooms and homes are now equipped with computers this media can be utilized to provide more than a traditional "flat" presentation. An interactive "stack" has been developed using Hyperstudio (TM). The major topics include: "1996 - The Break Through Year In Planet Detection"; "What Determines If A Planet Is Habitable?"; "How Can We Find Other Planets (Search Methods)"; "All About the Kepler Mission: How To Find Earth-Sized Planets"; and "A Mission Simulator". Using the simulator, the student records simulated observations and then analyzes and interprets the data within the program stacks to determine the orbit and planet size, the planet's temperature and surface gravity, and finally determines if the planet is habitable. Additional related sections are also included. Many of the figures are animated to assist in comprehension of the material. A set of a dozen lesson plans for the middle school has also been drafted.

Koch, David↗

The Impact of Stellar Variability on the Detection of Transiting Earth-like Planets

Stellar variability represents a key limitation on the detectability of weak transit signatures of small, Earth-size planets with space-based missions such as NASA's Kepler Mission or ESA's PLATO Mission. The expectations for the performance of the Kepler Mission in the face of solar-like variability were predicated on observations of the Sun with the Variability of Solar Irradiance and Gravity Oscillations (VIRGO) instrument aboard NASA and ESA's joint Solar and Heliospheric Observatory (SOHO) mission, which was launched in December 1995. Analyses of SOHO data indicated that solar-like variability would contribute approx.10 ppm to Kepler's noise budget at 6.5 ours, a typical grazing transit timescale. This proved to be optimistic as the typical 12th mag G2V star in the Kepler field of view exhibited 20 ppm of stellar variability-related noise at 6.5 hours, making the detection of true Earth-Sun analogs more difficult. While the consequent increase in the total noise at 6.5 hours from 20 ppm to 30 ppm could have been overcome by extending the mission to a total duration of 7 to 8 years. Unfortunately, a second reaction wheel failed in May 2013, ending the Kepler primary mission. Nevertheless, Kepler proved to be a veritable cornucopia of science results, both for exoplanets and for astrophysics. The phenomenal photometric precision and continuous observations required in order to identify small, rocky transiting planets enables the study of a large range of phenomena contributing to stellar variability for many thousands of solar-like stars in Kepler's field of view in exquisite detail. These effects range from less than 1 ppm acoustic oscillations on timescales from a few minutes and longward, to flares on timescales of hours, to spot-induced modulation on timescales of days to weeks to activity cycles on timescales of months to years. Kepler discovered over 2600 validated and confirmed exoplanets, and measured the pressure-mode oscillations of over 15000 stars over the course of its mission and the reconstituted K2 mission. We present the adaptive, wavelet-based matched filter used for both the Kepler and the TESS missions, and discuss the connections between this detection algorithm and fundamental detection theory, which allows the detector to function as a noise characterization engine. This provides a dynamical measurement of the photometric noise at transit timescales and thus, a key performance metric for missions like PLATO and Kepler. We give an overview of the stellar variability we see across the full range of spectral types observed by Kepler, from the cool, small red M stars to the hot, large late A stars, both in terms of amplitude as well as timescale.

transit surveys↗

The Impact of Stellar Variability on the Detection of Transiting Earth-Like Planets

Stellar variability represents a key limitation on the detectability of weak transit signatures of small, Earth-size planets with space-based missions such as NASA's Kepler Mission or ESA's PLATO Mission. The expectations for the performance of the Kepler Mission in the face of solar-like variability were predicated on observations of the Sun with the Variability of Solar Irradiance and Gravity Oscillations (VIRGO) instrument aboard NASA and ESA's joint Solar and Heliospheric Observatory (SOHO) mission, which was launched in December 1995. Analyses of SOHO data indicated that solar-like variability would contribute ~10 ppm to Kepler's noise budget at 6.5 ours, a typical grazing transit timescale. This proved to be optimistic as the typical 12th mag G2V star in the Kepler field of view exhibited 20 ppm of stellar variability-related noise at 6.5 hours, making the detection of true Earth-Sun analogs more difficult. While the consequent increase in the total noise at 6.5 hours from 20 ppm to 30 ppm could have been overcome by extending the mission to a total duration of 7 to 8 years. Unfortunately, a second reaction wheel failed in May 2013, ending the Kepler primary mission. Nevertheless, Kepler proved to be a veritable cornucopia of science results, both for exoplanets and for astrophysics. The phenomenal photometric precision and continuous observations required in order to identify small, rocky transiting planets enables the study of a large range of phenomena contributing to stellar variability for many thousands of solar-like stars in Kepler's field of view in exquisite detail. These effects range from <1 ppm acoustic oscillations on timescales from a few minutes and longward, to flares on timescales of hours, to spot-induced modulation on timescales of days to weeks to activity cycles on timescales of months to years. Kepler discovered over 2600 validated and confirmed exoplanets, and measured the pressure-mode oscillations of over 15000 stars over the course of its mission and the reconstituted K2 mission. We present the adaptive, wavelet-based matched filter used for both the Kepler and the TESS missions, and discuss the connections between this detection algorithm and fundamental detection theory, which allows the detector to function as a noise characterization engine. This provides a dynamical measurement of the photometric noise at transit timescales and thus, a key performance metric for missions like PLATO and Kepler. We give an overview of the stellar variability we see across the full range of spectral types observed by Kepler, from the cool, small red M stars to the hot, large late A stars, both in terms of amplitude as well as timescale.

exoplanets↗

Status of the Terrestrial Planet Finder Interferometer (TPF-I)

The interferometric version of the Terrestrial Planet Finder (TPF-I) has the potential to find and characterize earth-sized planets in the habitable zones of over 250 nearby stars and to search for life using biomarkers in the atmospheres of any planets found. The scientific case for such a mission continues to be strengthened by on-going progress in the detection of planets via indirect means. This paper summarizes the status of TPF-I, illustrative scientific requirements for the mission, and its enabling technologies.

Terrestrial Planet Finder (TPF)↗

Impact of Clouds and Hazes on the Simulated JWST Transmission Spectra of Habitable Zone Planets in the TRAPPIST-1 System

The TRAPPIST-1 system, consisting of an ultracool host star having seven known Earth-sized planets, will be a prime target for atmospheric characterization with the James Webb Space Telescope (JWST). However, the detectability of atmospheric molecular species may be severely impacted by the presence of clouds and/or hazes. In this work, we perform 3D general circulation model (GCM) simulations with the LMD-G model supplemented by 1D photochemistry simulations at the terminator with the Atmos model to simulate several possible atmospheres for TRAPPIST-1e, 1f, and 1g: (1) modern Earth, (2) Archean Earth, and (3) CO2-rich atmospheres. The JWST synthetic transit spectra were computed using the GSFC Planetary Spectrum Generator. We find that the TRAPPIST-1e, 1f, and 1g atmospheres, with clouds and/or hazes, could be detected using JWST's NIRSpec Prism from the CO2 absorption line at 4.3 μm in less than 15 transits at 3σ or less than 35 transits at 5σ. However, our analysis suggests that other gases would require hundreds (or thousands) of transits to be detectable. We also find that H2O, mostly confined in the lower atmosphere, is very challenging to detect for these planets or similar systems if the planets' atmospheres are not in a moist greenhouse state. This result demonstrates that the use of GCMs, self-consistently taking into account the effect of clouds and subsaturation, is crucial to evaluate the detectability of atmospheric molecules of interest, as well as for interpreting future detections in a more global (and thus robust and relevant) approach.

Thomas J. Fauchez↗

Adaptive Nulling for Interferometric Detection of Planets

An adaptive-nulling method has been proposed to augment the nulling-optical- interferometry method of detection of Earth-like planets around distant stars. The method is intended to reduce the cost of building and aligning the highly precise optical components and assemblies needed for nulling. Typically, at the mid-infrared wavelengths used for detecting planets orbiting distant stars, a star is millions of times brighter than an Earth-sized planet. In order to directly detect the light from the planet, it is necessary to remove most of the light coming from the star. Nulling interferometry is one way to suppress the light from the star without appreciably suppressing the light from the planet. In nulling interferometry in its simplest form, one uses two nominally identical telescopes aimed in the same direction and separated laterally by a suitable distance. The light collected by the two telescopes is processed through optical trains and combined on a detector. The optical trains are designed such that the electric fields produced by an on-axis source (the star) are in anti-phase at the detector while the electric fields from the planet, which is slightly off-axis, combine in phase, so that the contrast ratio between the star and the planet is greatly decreased. If the electric fields from the star are exactly equal in amplitude and opposite in phase, then the star is effectively nulled out. Nulling is effective only if it is complete in the sense that it occurs simultaneously in both polarization states and at all wavelengths of interest. The need to ensure complete nulling translates to extremely tight demands upon the design and fabrication of the complex optical trains: The two telescopes must be highly symmetric, the reflectivities of the many mirrors in the telescopes and other optics must be carefully tailored, the optical coatings must be extremely uniform, sources of contamination must be minimized, optical surfaces must be nearly ideal, and alignments must be extremely precise. Satisfaction of all of these requirements entails substantial cost.

Lay, Oliver P.↗

Autonomy Architectures for a Constellation of Spacecraft

Until the past few years, missions typically involved fairly large expensive spacecraft. Such missions have primarily favored using older proven technologies over more recently developed ones, and humans controlled spacecraft by manually generating detailed command sequences with low-level tools and then transmitting the sequences for subsequent execution on a spacecraft controller. This approach toward controlling a spacecraft has worked spectacularly on previous missions, but it has limitations deriving from communications restrictions - scheduling time to communicate with a particular spacecraft involves competing with other projects due to the limited number of deep space network antennae. This implies that a spacecraft can spend a long time just waiting whenever a command sequence fails. This is one reason why the New Millennium program has an objective to migrate parts of mission control tasks onboard a spacecraft to reduce wait time by making spacecraft more robust. The migrated software is called a "remote agent" and has 4 components: a mission manager to generate the high level goals, a planner/scheduler to turn goals into activities while reasoning about future expected situations, an executive/diagnostics engine to initiate and maintain activities while interpreting sensed events by reasoning about past and present situations, and a conventional real-time subsystem to interface with the spacecraft to implement an activity's primitive actions. In addition to needing remote planning and execution for isolated spacecraft, a trend toward multiple-spacecraft missions points to the need for remote distributed planning and execution. The past few years have seen missions with growing numbers of probes. Pathfinder has its rover (Sojourner), Cassini has its lander (Huygens), and the New Millenium Deep Space 3 (DS3) proposal involves a constellation of 3 spacecraft for interferometric mapping. This trend is expected to continue to progressively larger fleets. For example, one mission proposed to succeed DS3 would have 18 spacecraft flying in formation in order to detect earth-sized planets orbiting other stars. A proposed magnetospheric constellation would involve 5 to 500 spacecraft in Earth orbit to measure global phenomena within the magnetosphere. This work describes and compares three autonomy architectures for a system that continuously plans to control a fleet of spacecraft using collective mission goals instead of goals or command sequences for each spacecraft. A fleet of self-commanding spacecraft would autonomously coordinate itself to satisfy high level science and engineering goals in a changing partially-understood environment making feasible the operation of tens or even a hundred spacecraft (such as for interferometry or plasma physics missions). The easiest way to adapt autonomous spacecraft research to controlling constellations involves treating the constellation as a single spacecraft. Here one spacecraft directly controls the others as if they were connected. The controlling "master" spacecraft performs all autonomy reasoning, and the slaves only have real-time subsystems to execute the master's commands and transmit local telemetry/observations. The executive/diagnostics module starts actions and the master's real-time subsystem controls the action either locally or remotely through a slave. While the master/slave approach benefits from conceptual simplicity, it relies on an assumption that the master spacecraft's executive can continuously monitor the slaves' real-time subsystems, and this relies on high-bandwidth highly-reliable communications. Since unintended results occur fairly rarely, one way to relax the bandwidth requirements involves only monitoring unexpected events in spacecraft. Unfortunately, this disables the ability to monitor for unexpected events between spacecraft and leads to a host of coordination problems among the slaves. Also, failures in the communications system can result in losing slaves. The other two architectures improve robustness while reducing communications by progressively distributing more of the other three remote agent components across the constellation. In a teamwork architecture, all spacecraft have executives and real-time subsystems - only the leader has the planner/scheduler and mission manager. Finally, distributing all remote agent components leads to a peer-to-peer approach toward constellation control.

Barrett, Anthony↗

The Dependence of Signal-To-Noise Ratio (S/N) Between Star Brightness and Background on the Filter Used in Images Taken by the Vulcan Photometric Planet Search Camera

The Vulcan Photometric Planet Search is the ground-based counterpart of Kepler Mission Proposal. The Kepler Proposal calls for the launch of telescope to look intently at a small patch of sky for four year. The mission is designed to look for extra-solar planets that transit sun-like stars. The Kepler Mission should be able to detect Earth-size planets. This goal requires an instrument and software capable of detecting photometric changes of several parts per hundred thousand in the flux of a star. The goal also requires the continuous monitoring of about a hundred thousand stars. The Kepler Mission is a NASA Discovery Class proposal similar in cost to the Lunar Prospector. The Vulcan Search is also a NASA project but based at Lick Observatory. A small wide-field telescope monitors various star fields successively during the year. Dozens of images, each containing tens of thousands of stars, are taken any night that weather permits. The images are then monitored for photometric changes of the order of one part in a thousand. These changes would reveal the transit of an inner-orbit Jupiter-size planet similar to those discovered recently in spectroscopic searches. In order to achieve a one part in one thousand photometric precision even the choice of a filter used in taking an exposure can be critical. The ultimate purpose of an filter is to increase the signal-to-noise ratio (S/N) of one's observation. Ideally, filters reduce the sky glow cause by street lights and, thereby, make the star images more distinct. The higher the S/N, the higher is the chance to observe a transit signal that indicates the presence of a new planet. It is, therefore, important to select the filter that maximizes the S/N.

Mena-Werth, Jose↗

Direct IR Interferometric Detection of Extra Solar Planets

This paper describes a concept for the direct detection of extra solar planets. The concept is based on a decade old idea from Bracewell but expanded. A long baseline interferometer is examined with two three meter telescopes, cooled to 70K and a baseline of 30-50 meters. In space, this instrument would be able to detect an Earth sized planet around a solar like star at 10 parsec in approximately 1 hour of integration (5 sigma). The total number of candidate stars with detectable "Earths" number in the thousands.

Shao, Michael↗