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Gravity train

A gravity train is a theoretical transportation concept in which a vehicle travels between two points on Earth's surface through a straight-line tunnel bored through the planet, propelled solely by gravitational forces without the need for engines or fuel. The vehicle accelerates downward due to gravity as it descends toward the Earth's center and then decelerates symmetrically as it ascends to the destination, arriving with zero velocity under ideal conditions.^[1] This idea assumes a frictionless environment, evacuated air to eliminate drag, and a uniform Earth density for simplified calculations, resulting in a remarkably consistent travel time of approximately 42 minutes for any pair of antipodal or non-antipodal surface points.^[2]^[3] The concept originated in the late 17th century when English scientist Robert Hooke described it in a 1679 letter to Isaac Newton, predating Newton's publication of the law of universal gravitation and drawing on early ideas about motion through the Earth.^[4] Mathematically, the motion follows from Newton's shell theorem, which states that inside a uniform spherical shell, gravitational force is zero, while the net force within a solid sphere is proportional to the distance from the center, leading to simple harmonic motion along the tunnel.^[2] For a realistic, non-uniform Earth, advanced models adjust the travel time slightly to 37–40 minutes along optimal brachistochrone paths, such as hypocycloids, but straight-line tunnels remain the baseline for theoretical analysis.^[5] Despite its elegance, practical implementation faces insurmountable challenges, including the immense engineering feats required to drill tunnels through the mantle and core, extreme pressures and temperatures at depth, and the need for near-perfect vacuum conditions to minimize energy loss.^[1] The idea has inspired scientific discussions, educational projects like the Purdue Gravity Train initiative modeling routes from Indiana to France, and popular culture references, but it remains a thought experiment highlighting principles of classical mechanics rather than a feasible technology.^[2]

Definition and Concept

Basic Principle

A gravity train is a theoretical transportation system for moving a vehicle between two points on the surface of a spherical celestial body, such as Earth, via a straight-line tunnel excavated through its interior, with propulsion provided exclusively by the body's gravitational field and no external energy input required.^[4] The vehicle, assumed to be a point mass or low-friction capsule, is released from rest at the starting point on the surface.^[6] In operation, the vehicle experiences an initial acceleration along the tunnel due to the component of gravitational force parallel to the path, directed toward the tunnel's lowest point: the Earth's center for a diametric tunnel connecting antipodal points, or the geometric midpoint for shorter chordal tunnels between non-antipodal locations.^[4] This acceleration increases the vehicle's speed until it reaches maximum velocity at the bottom, after which the gravitational component reverses direction, causing symmetric deceleration as the vehicle ascends to the exit point, arriving with zero velocity.^[6] The motion is idealized as frictionless, ignoring air resistance, tunnel wall friction, and other dissipative effects that would occur in practice.^[4] The model further assumes the spherical body has uniform mass density throughout, which linearizes the gravitational restoring force along the tunnel and enables analytical solutions.^[6] Under these conditions, the vehicle's path exhibits simple harmonic motion, similar to that of a pendulum undergoing small oscillations or a mass attached to a spring, where the acceleration is directly proportional to the displacement from the equilibrium (lowest) point but opposite in direction.^[4] This oscillatory behavior ensures periodic motion if not damped, with the period independent of the tunnel's specific length for uniform density spheres.^[6] The term "gravity railroad" typically refers to 19th-century inclined-plane railways designed for freight transport, such as the Mauch Chunk Switchback Railway constructed in 1827 in Pennsylvania, which relied on gravity to propel loaded coal cars downhill along surface slopes while using mules or animal power to haul empty cars uphill.^[7] These systems were engineered for efficiency in mining operations but operated entirely on the Earth's surface, following contoured terrain rather than straight subsurface paths.^[8] In contrast, vacuum-tube transit concepts, such as the gravity-vacuum transit proposed by engineer Lawrence K. Edwards in the 1960s, envisioned underground low-pressure tubes to minimize air resistance, with vehicles propelled primarily by gravity along inclined routes but supported by additional infrastructure like dynamic airlocks and potentially magnetic suspension systems.^[9] Similarly, modern initiatives like the Hyperloop, as detailed in Elon Musk's 2013 conceptual whitepaper, utilize near-vacuum tubes for pods accelerated by linear electric motors and levitated via magnetic bearings, emphasizing engineered propulsion over unassisted gravitational motion.^[10] The theoretical gravity train differs fundamentally by positing straight-line tunnels bored directly through a planetary body's interior, such as from one surface point to its antipode, where motion arises solely from the conversion of gravitational potential energy into kinetic energy in a frictionless environment, resulting in simple harmonic oscillation without any post-launch energy input. Unlike surface-based gravity railroads or vacuum-assisted systems, which depend on inclines, pumps for pressure maintenance, or electromagnetic aids, gravity trains exploit the uniform gravitational field inside a spherical mass for bidirectional travel along chordal or diametric paths.^[11]

History and Development

Origin of the Concept

The concept of a gravity train, involving travel through tunnels bored through a planet under the influence of gravity alone, originated as a theoretical thought experiment in the late 17th century amid early explorations of universal gravitation. Robert Hooke, in a letter to Isaac Newton dated November 24, 1679, speculated on the motion of a body dropped into a hypothetical straight-line path through the Earth, suggesting it would accelerate toward the center and describing the trajectory as resembling an ellipse if gravity were constant inside the planet.^[12] This idea was part of Hooke's broader writings on gravity.^[13] Newton replied on November 28, 1679, engaging with the speculation by sketching a spiral path for the falling body in a rotating Earth frame and debating the deflection due to rotation, which he calculated as eastward.^[12] Their exchange, continuing through early 1680, highlighted disagreements—Hooke favoring an elliptical path under constant force, while Newton argued for precession based on varying gravity—but it marked the first detailed intellectual discussion of motion in subterranean channels.^[12] This correspondence occurred against the backdrop of the Hooke-Newton dispute over gravitational theory, with Hooke claiming priority in inverse-square ideas from his 1666 Royal Society lecture.^[14] Newton's Philosophiæ Naturalis Principia Mathematica (1687) provided implicit support for the concept through Proposition 12 of Book I, the shell theorem, which demonstrates that inside a spherically symmetric mass distribution, the gravitational field is zero for a hollow shell and proportional to distance from the center for a solid uniform sphere—enabling simple harmonic motion in a diametric tunnel without explicitly proposing travel applications.^[15] Though not directly addressing tunnels, this mathematical framework, derived from the inverse-square law of gravitation, established the physical feasibility of oscillatory paths through planetary interiors as a tool for illustrating gravitational principles.^[16]

Historical Proposals

The concept of gravity trains gained traction in the 19th century through practical engineering applications and speculative theoretical proposals. Early precursors emerged in the form of gravity railroads, which utilized inclines to harness gravitational force for transporting goods without continuous engine power. A prominent example is the Delaware and Hudson Canal Company's gravity railroad, completed in 1829 in Pennsylvania, USA, designed to haul anthracite coal from mines over the Moosic Mountains to canal boats; loaded cars descended under gravity while empty ones were pulled uphill by stationary engines or mules, demonstrating efficient use of terrain for industrial transport.^[17] Theoretical subsurface gravity trains were proposed around the same period, building on earlier mathematical explorations of motion through planetary interiors. In the 19th century, an anonymous group presented a detailed project for a straight-line gravity train tunnel through the Earth to the French Academy of Sciences, envisioning rapid global transit powered solely by gravity; however, the academy deferred consideration due to the era's technological constraints.^[18] These ideas were influenced by prior calculations, such as those by Robert Hooke in the late 17th century, who outlined the acceleration of objects falling through hypothetical Earth tunnels in correspondence with Isaac Newton, estimating transit times based on gravitational attraction.^[19] In the 20th century, renewed interest arose through scientific publications that analyzed gravity trains as potential future infrastructure. Physicist Paul Cooper's 1966 paper in the American Journal of Physics, titled "Through the Earth in Forty Minutes," rigorously modeled the dynamics of a frictionless train in a diametric tunnel, calculating a 42-minute journey from pole to pole and advocating for its consideration in long-term transportation planning, though it highlighted immense engineering barriers. Speculations like Cooper's were sometimes prompted by mentions in science fiction, which spurred physicists to verify the underlying orbital-like motion analogies. No full-scale gravity trains have been implemented, as proposals consistently stalled due to limitations in deep-drilling technology and the immense geological challenges of excavating straight-line tunnels through varying densities and high pressures.^[18] A brief modern analog appeared in 2022 when Australian mining firm Fortescue announced the "Infinity Train," a battery-electric system for iron ore haulage that recharges downhill via regenerative braking to power uphill segments, but the project was scaled back in September 2025 amid high costs^[20] and it remains a surface-based, non-subsurface design.^[21] Over time, the notion evolved from 19th-century incline-based systems for resource extraction to idealized subsurface concepts for passenger transit, continuing to inform debates on sustainable, gravity-assisted high-speed transport.

Physics Fundamentals

Gravitational Field Inside a Sphere

The gravitational field inside a spherical body of uniform density can be determined using Gauss's law for gravity, which relates the flux of the gravitational field through a closed surface to the enclosed mass.^[22] For a sphere of radius R and uniform mass density \rho, consider a Gaussian surface that is a concentric sphere of radius r < R. The enclosed mass is then \frac{4}{3}\pi r^3 \rho, and the symmetry implies a radial field uniform over this surface.^[22] Applying Gauss's law yields the magnitude of the gravitational acceleration g(r) at distance r from the center:

g(r) = \frac{4}{3} \pi G \rho r

directed toward the center, where G is the gravitational constant.^[22] This expression demonstrates that g(r) increases linearly with r, vanishing at the center (r = 0) and attaining its maximum value of \frac{4}{3} \pi G \rho R at the surface (r = R).^[22] At the center, the net field is zero, resulting in stable equilibrium for a test mass placed there, as contributions from all surrounding mass elements cancel out.^[23] In contrast, for points outside the sphere (r > R), the field behaves as if all mass were concentrated at the center, following the inverse-square law: g(r) = \frac{GM}{r^2}, where M = \frac{4}{3}\pi R^3 \rho is the total mass.^[23] Inside the sphere, however, the field is harmonic, meaning it is directly proportional to the displacement from the center, akin to a restoring force in simple harmonic motion.^[23] This analysis assumes a perfectly homogeneous density throughout the sphere, which simplifies the mathematics but approximates real planetary bodies like Earth only to a first order.^[24] In Earth's case, the denser iron-nickel core (surrounded by the less dense mantle) causes deviations: gravitational acceleration remains nearly constant through much of the mantle rather than increasing linearly, reaching a maximum at the core-mantle boundary before decreasing towards the center.^[24]^[25] The radial nature of the field inside a uniform sphere is often illustrated in diagrams showing field lines converging toward the center, with arrow lengths (representing field strength) starting from zero at the center and growing proportionally outward to the surface, emphasizing the linear variation and spherical symmetry.^[23]

Motion Dynamics in a Tunnel

In a straight tunnel bored through a spherically symmetric body such as Earth, modeled with uniform density, the motion of a frictionless object is governed by the component of the internal gravitational field along the tunnel axis. The gravitational acceleration at a distance r from the body's center is directed toward the center with magnitude g(r) = g \frac{r}{R}, where g is the surface gravity and R is the radius. For a position along the tunnel, the component of this vector onto the tunnel direction yields an effective acceleration a that acts as a restoring force toward the tunnel's midpoint, the point closest to the center. The component of the gravitational field along the tunnel direction results in a restoring acceleration exactly proportional to the displacement s from the midpoint, a = -\frac{g}{R} s.^[2] Under the frictionless assumption, this linear restoring force results in simple harmonic motion (SHM) for the object along any straight chord tunnel connecting two surface points. The equation of motion is \frac{d^2 s}{dt^2} = -\omega^2 s, where \omega = \sqrt{g/R} is the angular frequency, identical for all chords regardless of their length or orientation. The midpoint serves as the equilibrium point, where the net force along the tunnel vanishes, and the object oscillates symmetrically around it with amplitude equal to half the tunnel length. Energy conservation dictates that the object's gravitational potential energy converts to kinetic energy during descent, reaching maximum velocity at the lowest (midpoint) of the tunnel. The potential inside the body is quadratic, U(r) \propto r^2, ensuring the total mechanical energy remains constant and supporting the harmonic nature of the motion.^[26] For Earth, assuming uniform density, the full oscillation period—the time for a round trip through the tunnel and back—is approximately 84 minutes, equivalent to the orbital period of a hypothetical circular orbit at the surface. Consequently, a one-way transit from one surface endpoint to the other takes half this duration, about 42 minutes.

Mathematical Derivations

Diametric Path Through the Center

The diametric path for a gravity train consists of a straight-line tunnel extending through the center of a spherical body such as Earth, with a total length of $2R, where R is the radius of the sphere.^[26] For a body of uniform density, the gravitational force on a mass m at a displacement x from the center (along the tunnel axis) arises solely from the mass enclosed within radius |x|, leading to a restoring acceleration proportional to -x. Specifically, the equation of motion is \frac{d^2 x}{dt^2} = -\frac{GM}{R^3} x, where G is the gravitational constant and M is the total mass of the sphere.^[18] This follows from Gauss's law for gravity, as the field inside a uniform sphere is g(x) = -\frac{GM}{R^3} x.^[27] The differential equation describes simple harmonic motion with angular frequency \omega = \sqrt{\frac{GM}{R^3}}.^[18] The general solution for position is x(t) = A \cos(\omega t + \phi), where A is the amplitude and \phi is the phase constant; the corresponding velocity is v(t) = -A \omega \sin(\omega t + \phi).^[18] For a train released from rest at the surface (x(0) = R, v(0) = 0), the constants are A = R and \phi = 0, yielding x(t) = R \cos(\omega t) and v(t) = -R \omega \sin(\omega t).^[26] The time to traverse from one surface point to the antipode (x = R to x = -R) corresponds to half the oscillation period, t = \frac{\pi}{\omega} = \pi \sqrt{\frac{R}{g}}, where g = \frac{GM}{R^2} is the surface gravity; for Earth (R \approx 6371 km, g \approx 9.81 m/s²), this yields approximately 42 minutes.^[26] The maximum speed occurs at the center (x = 0, when \omega t = \frac{\pi}{2}), given by v_{\max} = R \omega = \sqrt{\frac{GM}{R}} = \sqrt{g R} \approx 7.9 km/s for Earth.^[18] At the center, the kinetic energy \frac{1}{2} m v_{\max}^2 = \frac{1}{2} m g R equals the loss in gravitational potential energy from the surface.^[18] For a uniform sphere, the potential at the surface is V(R) = -\frac{GM m}{R} and at the center is V(0) = -\frac{3 GM m}{2 R}, so the decrease \Delta V = V(0) - V(R) = -\frac{1}{2} \frac{GM m}{R} = -\frac{1}{2} m g R.^[27] This full conversion to kinetic energy assumes no dissipation, such as from air resistance or tunnel friction.^[26]

Chord Paths Between Arbitrary Points

In a gravity train along a straight-line chord connecting two arbitrary points on the surface of a uniform-density sphere of radius R, the geometry is defined by the central angle $2\alpha subtended by the chord at the sphere's center, where \alpha ranges from 0 (diametric path) to \pi/2 (surface tangent). The chord length is L = 2R \sin \alpha, and the radial distance from the center to the chord's midpoint is d = R \cos \alpha.^[18]^[28] The gravitational acceleration along the chord, with displacement s measured from the midpoint (where s = 0), is a = -\frac{GM}{R^3} s, where G is the gravitational constant and M is the sphere's mass; this linear restoring force confirms simple harmonic motion (SHM) with angular frequency \omega = \sqrt{GM / R^3}.^[29]^[30] The one-way travel time from one endpoint to the other corresponds to half the period of the SHM, given by t = \frac{\pi}{\omega} = \pi \sqrt{\frac{R^3}{GM}}, which is independent of \alpha and thus the same for all chord lengths—approximately 42 minutes for Earth.^[29]^[31] The maximum speed occurs at the midpoint and equals v_{\max} = \omega \cdot (L/2) = \sqrt{GM / R^3} \cdot R \sin \alpha = \sqrt{g R} \sin \alpha, where g = GM / R^2 is surface gravity; this decreases with shorter chords, for example reaching about 3 km/s for points separated by roughly 5000 km along the surface.^[29]^[18]

Dependence on Planetary Radius

The travel time for a gravity train along a diametric path through a spherically symmetric body of uniform density is half the period of simple harmonic motion, given by

\frac{T}{2} = \pi \sqrt{\frac{3}{4\pi G \rho}},

where G is the gravitational constant and \rho is the average density of the body.^[18] This formula reveals that the period T depends solely on the density \rho, independent of the body's radius R.^[18] Consequently, for any uniform-density sphere, the one-way transit time across the full diameter remains constant regardless of the planet's size, as the gravitational restoring force scales proportionally with displacement from the center, yielding identical oscillatory behavior.^[18] For Earth, with an average density of approximately 5514 kg/m³, this yields a one-way travel time of about 42 minutes.^[32]^[18] On the Moon, the lower average density of roughly 3340 kg/m³ results in longer transit times, approximately 53 minutes for a diametric journey.^[33]^[34] Gas giants like Jupiter, despite their much larger radii, have an average density of about 1326 kg/m³, leading to extended periods around 85 minutes due to the reduced gravitational strength per unit volume.^[35]^[18] In real celestial bodies with non-uniform density distributions, such as Earth—where denser material concentrates toward the core—the travel time for a diametric path is approximately 38 minutes, while for chord paths it ranges from about 38 to 42 minutes.^[36] For extremely high-density objects like neutron stars, with average densities on the order of $10^{17} kg/m³, the transit time would be extraordinarily brief, on the scale of milliseconds, highlighting the profound sensitivity to density.^[37]^[18] This density-dependent scaling implies that gravity train travel times are universal for uniform-density bodies of equivalent composition, enabling rapid inter-point transport across vastly different scales—from small asteroids to large planets—provided the density matches.^[18]

Feasibility and Challenges

Engineering and Technical Hurdles

Constructing a gravity train tunnel through Earth's interior poses insurmountable engineering challenges with current technology, primarily due to the vast scale and hostile subsurface environment. A straight-line tunnel connecting antipodal points would require excavating over 12,700 km, penetrating the crust, mantle, and core—depths more than 1,000 times greater than the deepest borehole ever drilled, the Kola Superdeep Borehole at 12.262 km.^[38] Drilling through such layers would encounter escalating temperatures exceeding 5,700°C in the core and pressures over 300 GPa, conditions that deform or melt conventional drill bits and equipment long before reaching significant depths. Maintaining structural integrity of the tunnel walls represents another critical barrier, as surrounding rock would undergo viscoelastic creep under gigapascal-level stresses, leading to gradual deformation and potential collapse over time.^[40] For efficient operation, the tunnel would need to operate in near-vacuum conditions to reduce aerodynamic drag at high velocities, but sustaining this vacuum against pervasive influxes of groundwater, magmatic fluids, and atmospheric gases through micro-fractures in the heterogeneous geology would demand unprecedented sealing technologies and continuous pumping systems.^[41] Vehicle design for a gravity train introduces further technical hurdles, requiring capsules capable of enduring peak speeds approaching 8 km/s while exposed to the intense heat, pressure, and corrosive chemistries of the deep interior.^[5] Passengers and cargo would face additional risks from residual radiation emanating from radioactive isotopes like uranium and thorium concentrated in the mantle and crust, which contribute to geothermal heat flux.^[42] Realistic Earth conditions exacerbate these issues beyond idealized models. The planet's non-uniform density profile, derived from seismic tomography, slightly reduces theoretical transit times (e.g., to about 38 minutes for a diametric path) but complicates the oscillatory motion, introducing perturbations that could destabilize vehicle guidance and tunnel alignment.^[5] Seismic activity, including earthquakes, would propagate amplified stresses through the tunnel structure, heightening the risk of fractures or catastrophic failure in an already fragile deep subsurface environment. Although gravity provides the primary propulsion, practical implementation demands supplemental energy inputs: a small initial impulse to counteract surface friction and Earth's rotation, plus robust braking mechanisms at endpoints to dissipate kinetic energy safely and prevent overshoot. These requirements underscore the gap between theoretical viability and engineering reality for gravity trains on Earth.

Economic and Practical Limitations

The construction of a gravity train network on Earth would entail enormous expenses, primarily due to the need for extensive, deep subterranean tunneling through challenging geological conditions. For instance, extrapolating from the Gotthard Base Tunnel's cost of approximately $12 billion for 57 kilometers—equating to about $210 million per kilometer—a single diametric tunnel spanning Earth's 12,742-kilometer diameter could exceed $2.6 trillion, while a global network connecting major cities might surpass $100 trillion in speculative analyses based on similar mega-projects like the Channel Tunnel, which cost $15 billion for 50 kilometers or roughly $300 million per kilometer.^[43]^[44] These figures dwarf even ambitious endeavors such as the International Thermonuclear Experimental Reactor (ITER), estimated at $22-45 billion, highlighting the prohibitive scale for infrastructure alone. Operational challenges further compound the impracticality, including high maintenance demands in inaccessible underground environments prone to seismic activity, geothermal heat, and structural degradation over time. Safety concerns are acute, as a single point of failure—such as a tunnel breach or system malfunction—could strand passengers in extreme conditions, with limited evacuation options and risks amplified by the high velocities involved. Moreover, gravity trains offer low passenger throughput compared to established systems; for example, they would handle far fewer travelers per hour than aviation or conventional rail, limiting economic returns despite zero propulsion energy needs.^[19] In comparison, alternatives like Hyperloop systems present more viable options for high-speed ground transport, with construction costs estimated at $75 million per kilometer for vacuum-tube designs—significantly lower than deep gravity tunnels—while enabling powered acceleration for shorter routes. Maglev trains, such as those in Japan, achieve speeds over 500 km/h at costs around $50-100 million per kilometer, offering reliable service without the depth-related hazards. For intercontinental distances, aviation remains superior, providing global connectivity at lower upfront infrastructure costs and higher capacity, rendering gravity trains obsolete for practical deployment.^[45] Applications on other celestial bodies, such as the Moon or Mars, appear marginally more feasible due to lower gravity, shallower tunneling requirements, and absence of a molten core, potentially reducing heat and pressure issues. However, even these remain economically unviable in the near term; NASA's Flexible Levitation on a Track (FLOAT) initiative for lunar rail transport emphasizes maglev over pure gravity systems, citing logistical benefits for resource hauling but underscoring high initial costs for extraterrestrial infrastructure. Analogous surface-based concepts, like Fortescue Metals Group's paused downhill electric "gravity train" for mining in 2025, demonstrate partial viability for specialized, non-subsurface uses but were halted due to escalating expenses, reinforcing the overall barriers.^[46]^[47] Ultimately, while gravity trains embody theoretical elegance in leveraging planetary physics for transit, their astronomical costs, operational risks, and inferiority to modern alternatives ensure they remain a conceptual curiosity rather than a practical solution.^[19]

Cultural and Modern References

In Fiction and Media

The concept of gravity trains has inspired various depictions in science fiction literature, often portraying them as efficient subsurface transportation systems powered by planetary gravity. In Hugo Gernsback's 1911 novel Ralph 124C 41+, a subterranean magnetic train links Europe to North America, envisioned as a high-speed marvel tunneling through the Earth to enable rapid intercontinental travel.^[48] This early portrayal highlights the allure of subsurface motion for futuristic commuting, blending scientific speculation with imaginative engineering, though powered by magnetism rather than gravity alone. In the late 20th century, John Varley's 1977 novel The Ophiuchi Hotline revisits and modernizes the underground gravity train idea, depicting advanced vessels that leverage gravitational forces for seamless subsurface journeys across planetary bodies.^[48] Varley's narrative uses the train as a narrative device to explore interstellar intrigue, emphasizing the technology's potential for covert and swift transit while incorporating elements of genetic engineering and alien contact. Film adaptations have further popularized gravity trains through dramatic visualizations of subsurface travel. The 2012 remake of Total Recall, directed by Len Wiseman, features "The Fall," a massive gravity train that bores through the Earth's core to connect the United Federation of Britain with The Colony (a post-apocalyptic Australia), completing the journey in just 17 minutes via free-fall acceleration.^[49] These cinematic elements dramatize the perils and thrills of gravity-driven paths, often amplifying speeds and simplifying physics for narrative tension. Such fictional representations frequently exaggerate achievable velocities—realistic calculations suggest a diametric gravity train would take approximately 42 minutes to traverse the Earth, not the shorter times depicted—or overlook challenges like uneven density and friction, thereby inspiring public interest in gravitational dynamics while prioritizing entertainment over strict scientific accuracy.^[49]

Contemporary Analogs and Proposals

In the realm of high-speed transportation, the Hyperloop concept, outlined in Elon Musk's 2013 white paper, proposes passenger pods traveling through low-pressure vacuum tubes using magnetic levitation and linear induction motors, achieving speeds up to 760 mph while minimizing air resistance in a manner reminiscent of early gravity train principles.^[10] This design, though powered, draws from vactrain ideas that leverage enclosed tunnels for efficient transit, with ongoing developments including test tracks worldwide.^[50] China's advancements in maglev technology serve as a partial analog, with a June 2025 test achieving 650 km/h (404 mph) for a 1.1-ton vehicle over a 600-meter vacuum tube track, demonstrating ultra-high-speed potential in controlled environments akin to gravity-assisted systems.^[51] Earlier trials in 2024 reached 623 km/h (387 mph) in a low-vacuum tube, highlighting engineering progress toward commercial hyperloop-like networks without full reliance on gravity alone.^[52] In mining operations, Fortescue Metals Group developed a battery-electric "gravity train" locomotive from 2022 to 2025, designed to haul iron ore downhill while recharging via regenerative braking, eliminating the need for external power and enabling zero-emission transport over Australia's Pilbara routes.^[53] The system, dubbed the Infinity Train, completed a 685-mile trial in June 2025 but was paused in October 2025 due to escalating costs and technical hurdles, despite its potential to move over 200 million tons of ore annually.^[47] Similar gravity-powered concepts appear in global mining, including downhill ore conveyance in regions like South America's Andean operations, where elevation gradients naturally assist loaded trains uphill-empty returns.^[54] For extraterrestrial applications, NASA has explored levitation-based transport in lunar and Martian contexts, such as the 2024 Flexible Levitation on a Track (FLOAT) system, which uses unpowered magnetic robots levitating over flexible tracks to navigate low-gravity environments without traditional propulsion.^[55] Proposals also leverage natural lava tubes—vast underground voids formed by ancient volcanism—for shielded transit networks, with studies indicating Martian tubes could span kilometers in diameter due to reduced gravity, potentially hosting rail systems for resource extraction or habitat connectivity.^[56] Related orbital ring concepts, involving rotating space elevators with track-like infrastructure, extend these ideas to near-Earth transport but remain theoretical.^[57] Recent academic research has advanced theoretical models of gravity trains, including a 2024 study on variable-mass systems where the train's payload affects oscillation periods in Earth-crossing tunnels, optimizing travel times under realistic mass variations.^[58] Published in the Revista Mexicana de Física E, this work analyzes energy and mass reduction during transit, confirming simple harmonic motion persists but with adjustments for practical implementation.^[59] As of 2025, no full-scale gravity train projects are operational worldwide, with efforts confined to prototypes, simulations, and niche applications like mining trials.

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When this is analyzed in detail, you find that the gravity at any radius r less than REarth will be linearly proportional to the distance from the center.
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Jan 10, 2020 · A classical result by Cooper1 asserts that a gravity train has a simple harmonic motion and always needs a constant amount of time (roughly 42 ...Missing: arbitrary | Show results with:arbitrary
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Earth's mass is about 5.97 ⨉ 1024 kilograms. Dividing this mass by Earth's volume results in an average density of approximately 5,517 kilograms per cubic meter ...
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AVERAGE ORBIT DISTANCE. Average of minimum and maximum distances from an ... DENSITY. 3.344g/cm3. oz/in3. g/cm3. 5.513g/cm3. oz/in3. g/cm3. MASS.
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By crisscrossing the earth with subterranean tunnels, the freewheeling mathematician proposes in the current issue of the American Journal of Physics, man could ...Missing: Émilie du Châtelet<|control11|><|separator|>
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[PDF] Jupiter Fact Sheet - Radio Jove - NASA
Jupiter's mass is 1,898.6 x 10^24 kg, its equatorial radius is 71,492 km, and its mean density is 1,326 kg/m^3. Its orbit period is 4,332.589 days.
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Numerically, it is found that the time taken to fall along the diameter is 38 min, compared to 42 min for a planet with uniform density.Missing: train | Show results with:train
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Jan 24, 2020 · In the drill core of the Kola super-deep borehole (SG-3, 12,262 m depth) gold-bearing rocks of Archaean age have been located at depths of 9,500 ...
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Oct 10, 2024 · The pressure at Earth's core measures about three million times the pressure of the atmosphere at the surface, and the temperature of Earth's ...
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DEM simulation of rock creep in tunnels using Rate Process Theory
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Key vacuum technology issues to be solved in evacuated tube ...
Aug 10, 2025 · This pa-per lists some key vacuum technology issues in ETT: (1) how to construct ultra-large-scale vacuum chamber with lower cost and high ...
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Jun 1, 2016 · The project, which cost more than $12bn (£8.3bn) to build, was endorsed by Swiss voters in a referendum in 1992. Voters then backed a proposal ...
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Jan 17, 2024 · The USD $15BN undersea mega-tunnel connected two of the world's most important cities. It drew in 1,300 workers, stretched 50 kilometres under ...
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A Critical Review of Hyperloop (Ultra-High Speed Rail) Technology
The technology significantly builds on a much older idea variously known as “gravity vacuum tube,” “gravity vacuum transit,” or “high-speed tube transportation, ...
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We want to build the first lunar railway system, which will provide reliable, autonomous, and efficient payload transport on the Moon.
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The steam train was a quantum leap in how humans could harness the ...<|control11|><|separator|>
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Aug 13, 2012 · The point of the tunnel is that gravity does the hard work of accelerating passengers from one end to the other.
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Jun 9, 2003 · A CGI disaster film about a journey to the centre of the Earth to restart the magnetic core that is construed as a series of spectacular ...
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Hyperloop for High-Speed Passenger Transport
Nov 4, 2020 · Implementation: Published in August 2013, Elon Musk's paper proposed a route running from the Los Angeles region to the San Francisco Bay Area.
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China breaks record with maglev train hitting 650 km/h in 7 seconds
Jun 18, 2025 · The test data showed that the vehicle reached the remarkable speed in about 7 seconds with a running distance of 600 meters, Li Weichao, ...
[52]
Record-smashing Chinese maglev hyperloop train hits 387 mph and ...
Feb 28, 2024 · China says its maglev hyperloop train has broken the world speed record in a test run, reaching a blistering 387 mph (623 km/h).
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A Mining Company Built A Battery-Electric Train That Never Has To ...
Jun 23, 2025 · Its beast has a 1.4 MWh battery, recharges on down slopes, and can reportedly fast-charge in as quickly as 30 minutes, and the idea of using ...
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Electric vehicles tease a new energy source: Gravity - NBC News
May 23, 2022 · One of Fortescue's ore trains near the Eliwana mine in the Pilbara region of Western Australia. The route is nearly 100 miles long.
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May 1, 2024 · The FLOAT system employs unpowered magnetic robots that levitate over a 3-layer flexible film track.
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Jul 16, 2024 · A new study adds to the evidence that lunar caves are a viable plan to shelter future permanent outposts on the Moon.
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[PDF] Technologies Enabling Exploration of Skylights, Lava Tubes and ...
Due to the lesser gravity, it is predicted that lava tubes on Mars or the Moon may be much larger in diameter than those found on Earth (Coombs & Hawke ...
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Jul 2, 2024 · We discuss the mass and energy reduction of the gravity train during travel and find the optimal conditions for economical travel. This study is ...Missing: seminal | Show results with:seminal
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Jul 1, 2024 · The gravity train is a virtual vehicle that travels in a tunnel across Earth, and its motion due to only gravity is a simple harmonic oscillator ...Missing: seminal | Show results with:seminal<|control11|><|separator|>