question: How is Earth's gravity strong enough to keep the moon in orbit but not strong enough to pull the ISS or satellites back to the ground?
comment: The ISS is travelling at just the right speed and is falling towards the earth but the earth , as the ISS travels forward, curves away under the ISS , this curvature matches exactly the free fall distance that the ISS falls during any period and therefore ISS maintains the same distance from the earth and as there is virtually no atmosphere at that height to slow ISS it continues to constantly fall to earth but never reaching it and therefore is in orbit .
passages: Although the forces balance at these points, the first three points (the ones on the line between a certain large mass, e.g. a star, and a smaller, orbiting mass, e.g. a planet) are not stable equilibrium points. If a spacecraft placed at the Earth–Moon point is given even a slight nudge away from the equilibrium point, the spacecraft's trajectory will diverge away from the point. The entire system is in motion, so the spacecraft will not actually hit the Moon, but will travel in a winding path, off into space. There is, however, a semi-stable orbit around each of these points, called a halo orbit. The orbits for two of the points, and , are stable, but the halo orbits for through are stable only on the order of months.
   In the Earth example, the Earth (5.97×10 kg) orbits the Sun (1.99×10 kg) at a distance of 149.6 million km, or one astronomical unit (AU). The Hill sphere for Earth thus extends out to about 1.5 million km (0.01 AU). The Moon's orbit, at a distance of 0.384 million km from Earth, is comfortably within the gravitational sphere of influence of Earth and it is therefore not at risk of being pulled into an independent orbit around the Sun. All stable satellites of the Earth (those within the Earth's Hill sphere) must have an orbital period shorter than seven months.
   A perfectly stable geostationary orbit is an ideal that can only be approximated. In practice the satellite drifts out of this orbit because of perturbations such as the solar wind, radiation pressure, variations in the Earth's gravitational field, and the gravitational effect of the Moon and Sun, and thrusters are used to maintain the orbit in a process known as station-keeping.
  
  Section::::Other geosynchronous orbits.
   Since gravity is inversely proportional to the square of the distance, a space station 400 km above the Earth feels almost the same gravitational force as we do on the Earth's surface. The reason a space station does not plummet to the ground is not that it is not subject to gravity, but that it is in a free-fall orbit.
  
  Section::::Gas giants.
  
  For gas giant planets such as Jupiter, Saturn, Uranus, and Neptune, where the surfaces are deep in the atmosphere and the radius not known, the surface gravity is given at the 1 bar pressure level in the atmosphere. 
   There are two points in space where an elevator's docking port could maintain a stable, lunar-synchronous position: the Earth-Moon Lagrange points and . is 56,000 km away from the Earth-facing side of the Moon, (at the lunar equator) and is 67,000 km from the center of the Moon's far side, in the exact opposite direction. At these points, the effect of the Moon's gravity and the effect of the centrifugal force resulting from the elevator system's synchronous, rigid body rotation cancel each other out. The gravitational stability of these Lagrange points are not permanent, ( and are in unstable equilibrium along a straight line between Earth and Moon,) but so long as small inertial adjustments are made to account for minor gravitational perturbations, any object positioned there can remain stationary.
   For spacecraft in a halo orbit around a Lagrangian point station-keeping is even more fundamental, as such an orbit is unstable; without an active control with thruster burns the smallest deviation in position/velocity would result in the spacecraft leaving the orbit completely.
  
  Section::::Station-keeping in low Earth orbit.
  
  For a spacecraft in a very low orbit the atmospheric drag is sufficiently strong to cause a re-entry before the intended end of mission if orbit raising manoeuvres are not executed from time to time.
   Until Shenzhou 8, the orbital module of the Shenzhou was equipped with its own propulsion, solar power, and control systems, allowing autonomous flight. It was possible for Shenzhou to leave an orbital module in orbit for redocking with a later spacecraft, something which the Soyuz cannot do, since the only hatch between orbital and reentry modules is a part of reentry module, and the orbital module is depressurised after separation. In the future it might be possible for the orbital module(s) to be left attached to the station as additional station modules. Small modules for the ISS are launched by Soyuz spacecraft in this way. In unmanned test flights, the orbital module of each Shenzhou was left functioning on orbit for several days after the return of the reentry modules, and the Shenzhou 5 orbital module continued to operate for six months after launch.
   If the moon's mass is not too low compared to the planet, it may in turn stabilize the planet's axial tilt, i.e. its obliquity against the orbit around the star. On Earth, the Moon has played an important role in stabilizing the axial tilt of the Earth, thereby reducing the impact of gravitational perturbations from the other planets and ensuring only moderate climate variations throughout the planet. On Mars, however, a planet without significant tidal effects from its relatively low-mass moons Phobos and Deimos, axial tilt can undergo extreme changes from 13° to 40° on timescales of to .
   Both of these positions are substantially farther up than the 36,000 km from Earth to geostationary orbit. Furthermore, the weight of the limb of the cable system extending down to the Moon would have to be balanced by the cable extending further up, and the Moon's slow rotation means the upper limb would have to be much longer than for an Earth-based system, or be topped by a much more massive counterweight. To suspend a kilogram of cable or payload just above the surface of the Moon would require 1,000 kg of counterweight, 26,000 km beyond . (A smaller counterweight on a longer cable, e.g., 100 kg at a distance of 230,000 km — more than halfway to Earth — would have the same balancing effect.) Without the Earth's gravity to attract it, an cable's lowest kilogram would require 1,000 kg of counterweight at a distance of 120,000 km from the Moon. The average Earth-Moon distance is 384,400 km.
   The International Telecommunications Union (ITU) and United Nations (UN) recommend that satellites in geosynchronous orbit be designed to move themselves to a disposal orbit some above the GEO belt, and then remove internally stored energy. Most GEO satellites conform to these recommendations, although there are no enforcement mechanisms.
  
  Section::::Standard practices.
  
  Within national regimes, where national governments can control the launch licenses of launch vehicles and spacecraft, there are some enforceable requirements for passivation. 
   To a modern physicist working with Einstein's general theory of relativity, the situation is even more complicated than is suggested above. Einstein's theory suggests that it actually is valid to consider that objects in inertial motion (such as falling in an elevator, or in a parabola in an airplane, or orbiting a planet) can indeed be considered to experience a local loss of the gravitational field in their rest frame. Thus, in the point of view (or frame) of the astronaut or orbiting ship, there actually is nearly-zero proper acceleration (the acceleration felt locally), just as would be the case far out in space, away from any mass. It is thus valid to consider that most of the gravitational field in such situations is actually absent from the point of view of the falling observer, just as the colloquial view suggests (see equivalence principle for a fuller explanation of this point). However, this loss of gravity for the falling or orbiting observer, in Einstein's theory, is due to the falling motion itself, and (again as in Newton's theory) not due to increased distance from the Earth. However, the gravity nevertheless is considered to be absent. In fact, Einstein's realization that a pure gravitational interaction cannot be felt, if all other forces are removed, was the key insight to leading him to the view that the gravitational "force" can in some ways be viewed as non-existent. Rather, objects tend to follow geodesic paths in curved space-time, and this is "explained" as a force, by "Newtonian" observers who assume that space-time is "flat," and thus do not have a reason for curved paths (i.e., the "falling motion" of an object near a gravitational source).
   Vehicles sent on lunar or planetary missions are generally not launched by direct injection to departure trajectory, but first put into a low Earth parking orbit; this allows the flexibility of a bigger launch window and more time for checking that the vehicle is in proper condition for the flight. A popular misconception is that escape velocity is required for flight to the Moon; it is not. Rather, the vehicle's apogee is raised high enough to take it to a point (before it reaches apogee) where it enters the Moon's gravitational sphere of influence (though the required velocity is close to that of escape.) This is defined as the distance from a satellite at which its gravitational pull on a spacecraft equals that of its central body, which is
   At a distance relatively close to Earth (less than 3000 km), gravity is only slightly reduced. As an object orbits a body such as the Earth, gravity is still attracting objects towards the Earth and the object is accelerated downward at almost 1g. Because the objects are typically moving laterally with respect to the surface at such immense speeds, the object will not lose altitude because of the curvature of the Earth. When viewed from an orbiting observer, other close objects in space appear to be floating because everything is being pulled towards Earth at the same speed, but also moving forward as the Earth's surface "falls" away below. All these objects are in free fall, not zero gravity.
   It is a common misconception that astronauts in orbit are weightless because they have flown high enough to escape the Earth's gravity. In fact, at an altitude of , equivalent to a typical orbit of the ISS, gravity is still nearly 90% as strong as at the Earth's surface. Weightlessness actually occurs because orbiting objects are in free-fall.
   The gross mass of the station changes over time. The total launch mass of the modules on orbit is about (). The mass of experiments, spare parts, personal effects, crew, foodstuff, clothing, propellants, water supplies, gas supplies, docked spacecraft, and other items add to the total mass of the station. Hydrogen gas is constantly vented overboard by the oxygen generators.
  
  Section::::Structure.
  
  The ISS is a third generation modular space station. Modular stations can allow modules to be added to or removed from the existing structure, allowing greater flexibility.
   Although it might be thought that this requires constant energy input, it can in fact be shown to be energetically favorable to lift cargo off the surface of the Moon and drop it into a lower Earth orbit, and thus it can be achieved without any significant use of propellant, since the Moon's surface is in a comparatively higher potential energy state. Also, this system could be built with a total mass of less than 28 times the mass of the payloads.
   Team 2 were very much aware that their minimal downmass provision might attract criticism: "The acceptability of this level of return (approximately 15 percent of delivered mass) represents an issue that should be addressed in the final Space Station Freedom logistics scenario." However, later ISS experience suggested that this would not have been a problem.
  
  The HL-42 had about the same cargo capacity as the later uncrewed SpaceX Dragon, and for at least five years after the retirement of the Shuttle in July 2011 the Dragon was the only craft capable of carrying significant downmass from the ISS.
   The anchor point of a space elevator is normally considered to be at the equator. However, there are several possible cases to be made for locating a lunar base at one of the Moon's poles; a base on a peak of eternal light could take advantage of near-continuous solar power, for example, or small quantities of water and other volatiles may be trapped in permanently shaded crater bottoms. A space elevator could be anchored near a lunar pole, though not directly at it. A tramway could be used to bring the cable the rest of the way to the pole, with the Moon's low gravity allowing much taller support towers and wider spans between them than would be possible on Earth.
   Lunar mascons make most low lunar orbits unstable ... As a satellite passes 50 or 60 miles overhead, the mascons pull it forward, back, left, right, or down, the exact direction and magnitude of the tugging depends on the satellite's trajectory. Absent any periodic boosts from onboard rockets to correct the orbit, most satellites released into low lunar orbits (under about 60 miles or 100 km) will eventually crash into the Moon. ... [There are] a number of 'frozen orbits' where a spacecraft can stay in a low lunar orbit indefinitely. They occur at four inclinations: 27°, 50°, 76°, and 86°"—the last one being nearly over the lunar poles. The orbit of the relatively long-lived Apollo 15 subsatellite PFS-1 had an inclination of 28°, which turned out to be close to the inclination of one of the frozen orbits—but less fortunate PFS-2 had an orbital inclination of only 11°.
   On the near side of the Moon, the strength-to-density required of the tether of a lunar space elevator exists in currently available materials. A lunar space elevator would be about long. Since the Moon does not rotate fast enough, there is no effective lunar-stationary orbit, but the Lagrangian points could be used. The near side would extend through the Earth-Moon L1 point from an anchor point near the center of the visible part of Earth's Moon.
   The pull of gravity in LEO is only slightly less than on the Earth's surface. This is because the distance to LEO from the Earth's surface is far less than the Earth's radius. However, an object in orbit is, by definition, in free fall, since there is no force holding it up. As a result objects in orbit, including people, experience a sense of weightlessness, even though they are not actually without weight.
   BULLET::::- Because the force of gravity decreases with distance, objects with non-zero size will be subjected to a tidal force, or a differential pull, between the ends of the object nearest and furthest from the Earth. (An extreme version of this effect is spaghettification.) In a spacecraft in low Earth orbit (LEO), the centrifugal force is also greater on the side of the spacecraft furthest from the Earth. At a 400 km LEO altitude, the overall differential in g-force is approximately 0.384 μ"g"/m.
   Considering the Earth–Moon system as a binary planet, its centre of gravity is within Earth, about or 72.6% of the Earth's radius from the centre of the Earth. This centre of gravity remains on the line between the centres of the Earth and Moon as the Earth completes its diurnal rotation. The path of the Earth–Moon system in its solar orbit is defined as the movement of this mutual centre of gravity around the Sun. Consequently, Earth's centre veers inside and outside the solar orbital path during each synodic month as the Moon moves in its orbit around the common centre of gravity.
   BULLET::::- MBSU was moved to the truss during Expedition 52 and the Latching End Effector was moved to ESP2 to prepare for the spacewalk on January 23, 2018. The failed MBSU was returned to earth on Space X CRS12.
  
  Section::::ESP-3.
   In typical free-fall, the acceleration of gravity acts along the direction of an object's velocity, linearly increasing its speed as it falls toward the Earth, or slowing it down if it is moving away from the Earth. In the case of an orbiting spacecraft, which has a velocity vector largely "perpendicular" to the force of gravity, gravitational acceleration does not produce a net change in the object's speed, but instead acts centripetally, to constantly "turn" the spacecraft's velocity as it moves around the Earth. Because the acceleration vector turns along with the velocity vector, they remain perpendicular to each other. Without this change in the direction of its velocity vector, the spacecraft would move in a straight line, leaving the Earth altogether.
  