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NASA NTRS1977

An introduction to orbit dynamics and its application to satellite-based earth monitoring systems

The long term behavior of satellites is studied at a level of complexity suitable for the initial planning phases of earth monitoring missions. First-order perturbation theory is used to describe in detail the basic orbit dynamics of satellite motion around the earth and relative to the sun. Surface coverage capabilities of satellite orbits are examined. Several examples of simulated observation and monitoring missions are given to illustrate representative applications of the theory. The examples stress the need for devising ways of maximizing total mission output in order to make the best possible use of the resultant data base as input to those large-scale, long-term earth monitoring activities which can best justify the use of satellite systems.

Brooks, D. R.↗

NASA NTRS2019

A Proposal for Standardized MMOD Shielding for Robotic Spacecraft

NASA robotic spacecraft are required to assess the potential for small debris induced failure for all disposal-critical components. Additional shielding might then be necessary in order to meet the acceptable risk requirement for the overall mission. Traditionally this requirement had been met with little or no additional shielding. Since the introduction of a high density debris population in ORDEM 3.0, some missions, especially those in higher portions of Low Earth Orbit, have needed additional MMOD-specific shielding in order for the mission to meet the requirement. This is a costly design effort when performed late in the project life cycle, which adds unexpected mass to the spacecraft components during the integration phase, and could disrupt thermal management.A proposal is discussed to develop a more cost-effective approach to MMOD-shielding, which can be employed earlier in the hardware design phase. The development and adoption of standardized shielding assemblies allows early tailoring of the shielding around a component, so that the mass is accounted for, as well as the small particle penetration risk, at a point in the design phase when the cost and schedule impact are more manageable. A set of several assemblies can be developed with a range of protection thresholds, in order to control mass where less shielding is needed. Such shielding assemblies would be developed in collaboration with blanket assembly specialists and thermal control engineers to ensure manufacturability and thermal performance challenges are known and acceptable. One clear benefit of such an approach is that hypervelocity testing can be performed on each of the standard shield assemblies to refine and confirm their performance prior to use.The challenges inherent in designing supplemental MMOD shielding will be discussed, including variations in the orbital debris environment and performance prediction. The benefits of a standardized shielding approach and example applications will also be presented.

Hull, Scott M.↗

NASA NTRS2019

A Proposal for Standardized MMOD Shielding for Robotic Spacecraft

NASA robotic spacecraft are required to assess the potential for small debris induced failure for all disposal-critical components. Additional shielding might then be necessary in order to meet the acceptable risk requirement for the overall mission. Traditionally this requirement had been met with little or no additional shielding. Since the introduction of a high density debris population in ORDEM 3.0, some missions, especially those in higher portions of Low Earth Orbit, have needed additional MMOD-specific shielding in order for the mission to meet the requirement. This is a costly design effort when performed late in the project life cycle, which adds unexpected mass to the spacecraft components during the integration phase, and could disrupt thermal management. A proposal is discussed to develop a more cost-effective approach to MMOD-shielding, which can be employed earlier in the hardware design phase. The development and adoption of standardized shielding assemblies allows early tailoring of the shielding around a component, so that the mass is accounted for, as well as the small particle penetration risk, at a point in the design phase when the cost and schedule impact are more manageable. A set of several assemblies can be developed with a range of protection thresholds, in order to control mass where less shielding is needed. Such shielding assemblies would be developed in collaboration with blanket assembly specialists and thermal control engineers to ensure manufacturability and thermal performance challenges are known and acceptable. One clear benefit of such an approach is that hypervelocity testing can be performed on each of the standard shield assemblies to refine and confirm their performance prior to use.The challenges inherent in designing supplemental MMOD shielding will be discussed, including variations in the orbital debris environment and performance prediction. The benefits of a standardized shielding approach and example applications will also be presented.

Hull, Scott M.↗

NASA NTRS2002

Design, Development, and Integration of A Space Shuttle Orbiter Bay 13 Payload Carrier

Bay 13 of the Space Shuttle Orbiter has been limited to small sidewall mounted payloads and ballast. In order to efficiently utilize this space, a concept was developed for a cross-bay cargo carrier to mount Orbital Replacement Units (ORU's) for delivery to the International Space Station and provide additional opportunities for science payloads, while meeting the Orbiter ballast requirements. The Lightweight Multi-Purpose Experiment Support Structure (MPESS) Carrie (LMC) was developed and tested by NASA's Marshall Space Flight Center and the Boeing Company. The Multi-Purpose Experiment Support Structure (MPESS), which was developed for the Spacelab program was modified, removing the keel structure and relocating the sill trunnions to fit in Bay 13. Without the keel fitting, the LMC required a new and innovative concept for transferring Y loads into the Orbiter structure. Since there is no keel fitting available in the Bay 13 location, the design had to utilize the longeron bridge T-rail to distribute the Y loads. This concept has not previously been used in designing Shuttle payloads. A concept was developed to protect for Launch-On-Need ORU's, while providing opportunities for science payloads. Categories of potential ORU's were defined, and Get-Away Special (GAS) payloads of similar mass properties were provided by NASA's Goddard Space Flight Center. Four GAS payloads were manifest as the baseline configuration, preserving the capability to swap up to two ORU's for the corresponding science payloads, after installation into the Orbiter cargo bay at the pad, prior to closeout. Multiple configurations were considered for the analytical integration, to protect for all defined combinations of ORU's and GAS payloads. The first physical integration of the LMC war performed by Goddard Space Flight Center and Kennedy Space Center at an off-line facility at Kennedy Space Center. This paper will discuss the design challenges, structural testing, analytical and physical integration for the LMC's successful maiden flight on STS-108/ISS UF-1 mission in December 2001.

Spencer, Susan H.↗

NASA NTRS2011

Aerospace News: Space Shuttle Commemoration. Volume 2, No. 7

The complex space shuttle design was comprised of four components: the external tank, two solid rocket boosters (SRB), and the orbiter vehicle. Six orbiters were used during the life of the program. In order of introduction into the fleet, they were: Enterprise (a test vehicle), Columbia, Challenger, Discovery, Atlantis and Endeavour. The space shuttle had the unique ability to launch into orbit, perform on-orbit tasks, return to earth and land on a runway. It was an orbiting laboratory, International Space Station crew delivery and supply replenisher, satellite launcher and payload delivery vehicle, all in one. Except for the external tank, all components of the space shuttle were designed to be reusable for many flights. ATK s reusable solid rocket motors (RSRM) were designed to be flown, recovered, and the metal components reused 20 times. Following each space shuttle launch, the SRBs would parachute into the ocean and be recovered by the Liberty Star and Freedom Star recovery ships. The recovered boosters would then be received at the Cape Canaveral Air Force Station Hangar AF facility for disassembly and engineering post-flight evaluation. At Hangar AF, the RSRM field joints were demated and the segments prepared to be returned to Utah by railcar. The segments were then shipped to ATK s facilities in Clearfield for additional evaluation prior to washout, disassembly and refurbishment. Later the refurbished metal components would be transported to ATK s Promontory facilities to begin a new cycle. ATK s RSRMs were manufactured in Promontory, Utah. During the Space Shuttle Program, ATK supported NASA s Marshall Space Flight Center whose responsibility was for all propulsion elements on the program, including the main engines and solid rocket motors. On launch day for the space shuttle, ATK s Launch Site Operations employees at Kennedy Space Center (KSC) provided lead engineering support for ground operations and NASA s chief engineer. It was ATK s responsibility to have a representative in Firing Room 2 at KSC in case of potential motor problems. However, the last time ATK was responsible for a space shuttle launch slip was 1989. During launch, engineers were also stationed in Promontory on teleconference with counterparts at KSC in the event their support was required.

Source record↗

NASA NTRS1973

Long-term motion in a restricted problem of rotational motion

A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the long-term effects of gravity-gradient torque and orbital evolution on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is constrained to precess and spin with constant rates. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order in n/omega sub 0, where n is the orbital mean motion of the center of mass and omega sub 0 is a reference value of the magnitude of the satellite's rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable, and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed, and a comparison of theoretical results with observations is made.

Cochran, J. E.↗

NASA NTRS1991

ASPEC: Solar power satellite

The solar power satellite (SPS) will provide a clean, reliable source of energy for large-scale consumption. The system will use satellites in geostationary orbits around the Earth to capture the Sun's energy. The intercepted sunlight will be converted to laser beam energy that can be transmitted to the Earth's surface. Ground systems on the Earth will convert the transmissions from space into electric power. The preliminary design for the SPS consists of one satellite in orbit around the Earth transmitting energy to a single ground station. The SPS design uses multilayer solar cell technology arranged on a 20 km squared planar array to intercept sunlight and convert it to an electric voltage. Power conditioning devices then send the electricity to a laser, which transmits the power to the surface of the Earth. A ground station will convert the beam into electricity. Typically, a single SPS will supply 5 GW of power to the ground station. Due to the large mass of the SPS, about 41 million kg, construction in space is needed in order to keep the structural mass low. The orbit configuration for this design is to operate a single satellite in geosynchronous orbit (GEO). The GEO allows the system to be positioned above a single receiving station and remain in sunlight 99 percent of the time. Construction will take place in low Earth orbit (LEO); array sections, 20 in total, will be sailed on solar wind out to the GEO location in 150 days. These individual transportation sections are referred to as solar sailing array panels (SSAP's). The primary truss elements used to support the array are composed of composite tubular members in a pentahedral arrangement. Smart segments consisting of passive and active damping devices will increase the control of dynamic SPS modes.

Source record↗

NASA NTRS1993

Very-long-baseline-interferometry measurements of planetary orbiters at Mars and Venus

The first attempts to use radio interferometric techniques to measure the positions of planetary orbiters were made in 1980 with the Viking Mars orbiter and again in 1993 using the Pioneer Venus orbiter. The angular accuracy of these early measurements was on the order of 200 nrad. This work describes more recent very-long baseline interferometry (VLBI) measurements made in 1989 of the Soviet Martian orbiter, Phobos 2, and several measurements made since September of 1990 of the Magellan spacecraft orbiting Venus. Both the Phobos and Magellan measurements recorded data with the Mark 3 VLBI systems located at antennas of NASA's Deep Space Network (DSN). The much wider bandwidth of this recording system and the availability of ionospheric calibrations should allow angular accuracy approaching 5 nrad to be achieved with these measurements.

Kroger, Peter M.↗

NASA NTRS1981

Crew activities in space

One of the mission requirements of the Space Shuttle is to serve as a working platform for experiments in space. Many of these experiments will be performed by crewmembers (mission specialists and payload specialists) in a general purpose laboratory called Spacelab. All nonexperiment-related activities or housekeeping activities will be done in the Orbiter, while most of the mission-related activities (experiments) will be done in Spacelab. In order for experimenters to design their experiments to best utilize the capabilities of the Orbiter, the Spacelab, and the crew, the working environment in the Orbiter and in Spacelab is described. In addition, the housekeeping activities required of the crew are summarized.

Bluford, G. S., Jr.↗

DOE OSTI2022

Giant resonances in topological spin Hall effect due to electron-skyrmion scattering in two-dimensional Rashba spin-orbit ferromagnets

Here we study a topological spin Hall effect where conduction electrons are scattered by Néel-type skyrmions in two-dimensional Rashba spin-orbit ferromagnets. We find the resonance structures in direct and Hall electric conductivities. The resonances strongly depend on the skyrmion size, the Rashba spin-orbit coupling vector value, and the relative direction between magnetization and Rashba vectors. The antiparallel arrangement of the Rashba spin-orbit coupling vector with respect to the magnetization determines the resonance structure and increases the direct conductivity by about two orders of magnitude. For the parallel arrangement the electric conductivities decrease by one to three orders of magnitude and the Hall conductivity changes the sign. The Rashba spin-orbit coupling also modifies electron bands depending on the ratio ε R /J, where ε R is Rashba energy and J is an exchange integral between conduction and localized electrons. If ε R /J ≤ 1, each energy band has the single minimum while for ε R /J > 1 the lower band has the “Mexican-hat” shape with the maximum at k = 0. We focus on the dependencies of direct and Hall electric conductivities on Fermi energy, ε F , skyrmion sizes, and Rashba spin-orbit coupling constant values and its relative direction with the magnetization. Analyzing both types of the energy bands, in general, we find two types of resonances: at the minimum of the upper band and behaviors, we employ the scattering pattern analysis. The resonance dependencies on skyrmion sizes and Rashba, a spin-orbit coupling contestant, can be qualitatively explained in terms of the Ramsauer-Townsend scattering of the upper band electrons by the skyrmion quantum well. The resonance properties can be used in spin transistors. To discover the resonances it is necessary to know the specific range of the parameters. At some values of the parameters the electric conductivity changes by about two orders of magnitude in the narrow range of ε F (< 0.01 eV). To detect the resonances it is also important to identify the relative direction of the Rashba spin-orbit coupling vector with respect to the magnetization.

36 MATERIALS SCIENCE↗

NASA NTRS2010

Active Debris Removal - A Grand Engineering Challenge for the Twenty-First Century

The collision between Iridium 33 and Cosmos 2251 in 2009 underlined the potential of an ongoing collision cascade effect (the Kessler Syndrome ) in the near-Earth orbital debris environment. A 2006 NASA analysis of the instability of the debris population in the low Earth orbit (LEO, the region below 2000 km altitude) shows that the environment has reached a point where the debris population will continue to increase in the next 200 years, even without any future launches. The increase is driven by fragments generated via collisions among existing objects in LEO. In reality, the situation will be worse than this prediction because satellite launches will continue and unexpected major breakups may continue to occur. Mitigation measures commonly adopted by the international space community (such as the 25-year rule) will help, but will be insufficient to stop the population growth. To better preserve the near-Earth space environment for future generations, active debris removal (ADR) should be considered. The idea of active debris removal is not new. However, due to the monumental technical, resource, operational, legal, and political challenges associated with removing objects from orbit, it has not yet been widely considered feasible. The recent major breakup events and the environment modeling efforts have certainly reignited the interest in using active debris removal to remediate the environment. This trend is further highlighted by the National Space Policy of the United States of America, released by the White House in June 2010, where the President explicitly directs NASA and the Department of Defense to pursue research and development of technology and techniques, to mitigate and remove on-orbit debris, reduce hazards, and increase understanding of the current and future debris environment. A 2009 modeling study by the NASA Orbital Debris Program Office has shown that, in order to maintain the LEO debris population at a constant level for the next 200 years, an active debris removal of about five objects per year is needed. The targets identified for removal are those with the highest mass and collision probability products. Analyses from the study indicate that the majority of those objects are spent upper stages with masses ranging from 1 to more than 8 metric tons, residing in several altitude regions and concentrated in about 10 inclination bands. To remove five of those objects per year in a cost-effective manner truly represents a grand challenge in engineering and technology development. An end-to-end debris removal operation includes, in general terms, launches orbit rendezvous, precision tracking, stabilization (of the tumbling motion), capture, and deorbit of the targets. An ADR system deigned to remove a single object is not very cost-effective. Therefore, the repeatability of the removal system is almost a requirement. Some of the technologies involved in the ADR process do exist, but the difficulty is to make them more cost effective. Other technologies, such as ways to stabilize a massive tumbling upper stage and the capture mechanisms, are new and will require major innovative research and development efforts. This paper summarizes an updated assessment of the environment, including what needs to be done to control the population growth, and outlines the major engineering and technology challenges to carry out active debris removal to preserve the environment.

Liou, Jer-Chyi↗

NASA NTRS1989

Real-time approximate optimal guidance laws for the advanced launch system

An approach to optimal ascent guidance for a launch vehicle is developed using an expansion technique. The problem is to maximize the payload put into orbit subject to the equations of motion of a rocket over a rotating spherical earth. It is assumed that the thrust and gravitational forces dominate over the aerodynamic forces. It is shown that these forces can be separated by a small parameter epsilon, where epsilon is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in a series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The zeroth-order problem is that of putting maximum payload into orbit subject to the equations of motion of a rocket in a vacuum over a flat earth. The neglected inertial and aerodynamic terms are included in higher order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only quadrature integrations. These quadrature integrations can be performed rapidly, so that real-time approximate optimization can be used to construct the launch guidance law.

Speyer, Jason L.↗

NASA NTRS1980

A study of the effects of state transition matrix approximations

The effects of using an approximate state transition matrix in orbit estimation are investigated. The approximate state transition matrix results when higher order geopotential terms in the equations of motion are ignored in the formation of the variational equations. Two methods of orbit estimation are considered: the differential correction procedure (DC) and the extended Kalman filter (EKF). The system used for the study is the Research & Development version of the Goddard Trajectory Determination System. The effects of the approximation are analyzed on a number of orbits. These orbits of various inclinations and semimajor axes. Other parameters studied include geopotential models and DC arc length.

May, J. A.↗

NASA NTRS1996

Orbital debris removal using ground-based lasers

Orbiting the Earth are spent rocket stages, non-functioning satellites, hardware from satellite deployment and staging, fragments of exploded spacecraft, and other relics of decades of space exploration: orbital debris. The United States Space Command tracks and maintains a catalog of the largest objects. The catalog contains over 7000 objects. Recent studies have assessed the debris environment in an effort to estimate the number of smaller particles and the probability of a collision causing catastrophic damage to a functioning spacecraft. The results of the studies can be used to show, for example, that the likelihood of a collision of a particle larger than about one centimeter in diameter with the International Space Station during a 10-year period is a few percent, roughly in agreement with earlier estimates for Space Station Freedom. Particles greater than about one centimeter in diameter pose the greatest risk to shielded spacecraft. There are on the order of 105 such particles in low Earth orbit. The United States National Space Policy, begun in 1988, is to minimize debris consistent with mission requirements. Measures such as venting unused fuel to prevent explosions, retaining staging and deployment hardware, and shielding against smaller debris have been taken by the U.S. and other space faring nations. There is at present no program to remove debris from orbit. The natural tendency for upper atmospheric drag to remove objects from low Earth orbit is more than balanced by the increase in the number of debris objects from new launches and fragmentation of existing objects. In this paper I describe a concept under study by the Program Development Laboratory of Marshall Space Flight Center and others to remove debris with a ground-based laser. A longer version of this report, including figures, is available from the author.

Taylor, Charles R.↗

NASA NTRS2016

Transit Timing Variations for Planets Near Eccentricity-Type Mean Motion Resonances

We derive the transit timing variations (TTVs) of two planets near a second-order mean motion resonance (MMR) on nearly circular orbits. We show that the TTVs of each planet are given by sinusoids with a frequency of jn(sub 2) - ( j - 2)n(sub 1), where j ≽ 3 is an integer characterizing the resonance and n(sub 2) and n(sub 1) are the mean motions of the outer and inner planets, respectively. The amplitude of the TTV depends on the mass of the perturbing planet, relative to the mass of the star, and on both the eccentricities and longitudes of pericenter of each planet. The TTVs of the two planets are approximated anti-correlated, with phases of ϕ and ≈ϕ + π, where the phase ϕ also depends on the eccentricities and longitudes of pericenter. Therefore, the TTVs caused by proximity to a second-order MMR do not in general uniquely determine both planet masses, eccentricities, and pericenters. This is completely analogous to the case of TTVs induced by two planets near a first-order MMR. We explore how other TTV signals, such as the short-period synodic TTV or a first-order resonant TTV, in combination with the second-order resonant TTV, can break degeneracies. Finally, we derive approximate formulae for the TTVs of planets near any order eccentricity-type MMR; this shows that the same basic sinusoidal TTV structure holds for all eccentricity-type resonances. Our general formula reduces to previously derived results near first-order MMRs.

Celestial mechanics↗

NASA NTRS2005

Accurate Determination of Comet and Asteroid Orbits Leading to Collision With Earth

Movements of the celestial bodies in our solar system inspired Isaac Newton to work out his profound laws of gravitation and motion; with one or two notable exceptions, all of those objects move as Newton said they would. But normally harmonious orbital motion is accompanied by the risk of collision, which can be cataclysmic. The Earth s moon is thought to have been produced by such an event, and we recently witnessed magnificent bombardments of Jupiter by several pieces of what was once Comet Shoemaker-Levy 9. Other comets or asteroids may have met the Earth with such violence that dinosaurs and other forms of life became extinct; it is this possibility that causes us to ask how the human species might avoid a similar catastrophe, and the answer requires a thorough understanding of orbital motion. The two red square flags with black square centers displayed are internationally recognized as a warning of an impending hurricane. Mariners and coastal residents who know the meaning of this symbol and the signs evident in the sky and ocean can act in advance to try to protect lives and property; someone who is unfamiliar with the warning signs or chooses to ignore them is in much greater jeopardy. Although collisions between Earth and large comets or asteroids occur much less frequently than landfall of a hurricane, it is imperative that we learn to identify the harbingers of such collisions by careful examination of an object s path. An accurate determination of the orbit of a comet or asteroid is necessary in order to know if, when, and where on the Earth s surface a collision will occur. Generally speaking, the longer the warning time, the better the chance of being able to plan and execute action to prevent a collision. The more accurate the determination of an orbit, the less likely such action will be wasted effort or, what is worse, an effort that increases rather than decreases the probability of a collision. Conditions necessary for a collision to occur are discussed, and warning times for long-period comets and near-Earth asteroids are presented.

Roithmayr, Carlos M.↗

NASA NTRS2007

EVA Hazards due to TPS Inspection and Repair

Tile inspection and repair activities have implicit hazards associated with them. When an Extra Vehicular Activities (EVA) crewmember and associated hardware are added into the equation, additional hazards are introduced. Potential hazards to the Extravehicular Mobility Unit (EMU), the Orbiter or the crew member themselves are created. In order to accurately assess the risk of performing a TPS inspection or repair, an accurate evaluation of potential hazards and how adequately these hazards are controlled is essential. The EMU could become damaged due to sharp edges, protrusions, thermal extremes, molten metal or impact with the Orbiter. Tools, tethers and the presence of a crew member in the vicinity of the Orbiter Thermal Protection System (TPS) pose hazards to the Orbiter. Hazards such as additional tile or Reinforced Carbon-Carbon (RCC) damage from a loose tool, safety tethers, crewmember or arm impact are introduced. Additionally, there are hazards to the crew which should be addressed. Crew hazards include laser injury, electrical shock, inability to return to the airlock for EMU failures or Orbiter rapid safing scenarios, as well as the potential inadvertent release of a crew member from the arm/boom. The aforementioned hazards are controlled in various ways. Generally, these controls are addressed operationally versus by design, as the majority of the interfaces are to the Orbiter and the Orbiter design did not originally account for tile repair. The Shuttle Remote Manipulator System (SRMS), for instance, was originally designed to deploy experiments, and therefore has insufficient design controls for retention of the Orbiter Boom Sensor System (OBSS). Although multiple methods to repair the Orbiter TPS exist, the majority of the hazards are applicable no matter which specific repair method is being performed. TPS Inspection performed via EVA also presents some of the same hazards. Therefore, the hazards common to all TPS inspection or repair methods will be addressed.

Stewart, Christine E.↗

DOE OSTI2022

Orbital-induced crossover of the Fulde-Ferrell-Larkin-Ovchinnikov phase into Abrikosov-like states.

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can emerge in superconductors for which the orbital critical field exceeds the Pauli limit. Here, we present angular-resolved specific-heat data of the quasi-two-dimensional organic superconductor ??-(ET)2Cu(NCS )2 , with a focus on high fields in the regime of the FFLO transition. For an increasing out-of-plane tilt of the applied magnetic field, which leads to an increase of orbital contributions, we found that the nature of the superconducting transition changes from second to first order and that a further transition appears within the high-field superconducting phase. However, the superconducting state above the Pauli limit is stable for field tilt of several degrees. Since any finite perpendicular component of the magnetic field necessarily leads to quantization of the orbital motion, the resulting vortex lattice states compete with the modulated order parameter of the FFLO state leading to complex high-field superconducting phases. By solving the linearized self-consistency equation within weak-coupling BCS theory, we show that our results are clear experimental evidence of an orbital-induced transformation of the FFLO order parameter into Abrikosov-like states of higher Landau levels.

Kotte, Tommy↗