"may accelerate at a maximum of perhaps 1/10,000 m/s² (0.1 mm/s²) which is 10""g"". The velocity change would be at the rate of 3,000 m/s per year of thrusting by the photon rocket. If a photon rocket begins its journey in low earth orbit, then one year of thrusting may be required to achieve an earth escape velocity of 11.2 km/s if the vehicle is already in orbit at a velocity of 9,100 m/s. Upon escaping the Earth's gravitational field the rocket will have a heliocentric velocity of 30 km/s in interplanetary space. Eighty years of steady photonic thrusting would"
"higher orbits than lower ones. The speed needed to maintain an orbit near the Earth's surface corresponds to a sideways speed of about 7.8 km/s (17,400 mph), an energy of about 30MJ/kg. This is several times the energy per kg of practical rocket propellant mixes. Gaining the kinetic energy is awkward as the airdrag tends to slow the spacecraft, so rocket-powered spacecraft generally fly a compromise trajectory that leaves the thickest part of the atmosphere very early on, and then fly on for example, a Hohmann transfer orbit to reach the particular orbit that is required. This minimises the airdrag"
"a spacecraft must first leave the gravity well of the Earth. The only practical way of accomplishing this currently is with a rocket. Unlike other airborne vehicles such as balloons or jets, a rocket is the only known form of propulsion which can continue to increase its speed at high altitudes in the vacuum outside the Earth's atmosphere. Upon approach of the target moon, a spacecraft will be drawn ever closer to its surface at increasing speeds due to gravity. In order to land intact it must decelerate to less than about and be ruggedized to withstand a ""hard landing"""
"of the rocket exhaust. This is known as the Tsiolkovsky rocket equation: For historical reasons, as discussed above, formula_6 is sometimes written as where formula_1 is the specific impulse of the rocket, measured in seconds, and formula_11 is the gravitational acceleration at sea level. For a high delta-v mission, the majority of the spacecraft's mass needs to be reaction mass. Because a rocket must carry all of its reaction mass, most of the initially-expended reaction mass goes towards accelerating reaction mass rather than payload. If the rocket has a payload of mass ""P"", the spacecraft needs to change its velocity"
"atmospheric drag (approximately 300 m/s with the ballistic coefficient of a 20 m long dense fueled vehicle), gravity losses (depending on burn time and details of the trajectory and launch vehicle), and gaining altitude. The main proven technique involves launching nearly vertically for a few kilometers while performing a gravity turn, and then progressively flattening the trajectory out at an altitude of 170+ km and accelerating on a horizontal trajectory (with the rocket angled upwards to fight gravity and maintain altitude) for a 5-8 minute burn until orbital velocity is achieved. Currently, 2-4 stages are needed to achieve the required"
"direction in which the escaping body travels. For example, as the Earth's rotational velocity is 465 m/s at the equator, a rocket launched tangentially from the Earth's equator to the east requires an initial velocity of about 10.735 km/s ""relative to Earth"" to escape whereas a rocket launched tangentially from the Earth's equator to the west requires an initial velocity of about 11.665 km/s ""relative to Earth"". The surface velocity decreases with the cosine of the geographic latitude, so space launch facilities are often located as close to the equator as feasible, e.g. the American Cape Canaveral (latitude 28°28' N)"
"this in mind, and the thrust is used to help positively separate the two vehicles. A multistage rocket is required to reach the escape velocity of from Earth's gravity. Single-stage-to-orbit designs are sought, but have not yet been demonstrated. The reason multi-stage rockets are required is the limitation the laws of physics place on the maximum velocity achievable by a rocket of given fueled-to-dry mass ratio. This relation is given by the classical rocket equation: where: The delta v required to reach low Earth orbit (or the required velocity of a sufficiently heavy suborbital payload) requires a wet to dry"
"potential well depends on the vehicle's position, and the energy depends on the vehicle's speed. If the kinetic energy exceeds the potential energy then escape occurs. At the Earth's surface this occurs at a speed of 11.2 km/s (25,000 mph), but in practice a much higher speed is needed due to airdrag. Rocket launch is the only current way to reach space. In some cases an airbreathing (jet engine) first stage has been used as well. Non-rocket space launch is a launch into space where some or all of the needed speed and altitude are provided by something other than"
"kg or 1,000 kg; what differs is the amount of energy required. For an object of mass formula_9 the energy required to escape the Earth's gravitational field is ""GMm / r"", a function of the object's mass (where ""r"" is the radius of the Earth, ""G"" is the gravitational constant, and ""M"" is the mass of the Earth, ). A related quantity is the specific orbital energy which is essentially the sum of the kinetic and potential energy divided by the mass. An object has reached escape velocity when the specific orbital energy is greater or equal to zero. An"
"space, a propulsion method that produces tiny accelerations but runs for a long time can produce the same impulse as a propulsion method that produces large accelerations for a short time. When launching from a planet, tiny accelerations cannot overcome the planet's gravitational pull and so cannot be used. Earth's surface is situated fairly deep in a gravity well. The escape velocity required to get out of it is 11.2 kilometers/second. As human beings evolved in a gravitational field of 1g (9.8 m/s²), an ideal propulsion system would be one that provides a continuous acceleration of 1g (though human bodies"
"above the atmosphere (which causes frictional drag), and then slowly pitch over and finish firing the rocket engine parallel to the atmosphere to achieve orbit speed. Once in orbit, their speed keeps them in orbit above the atmosphere. If e.g., an elliptical orbit dips into dense air, the object will lose speed and re-enter (i.e. fall). Occasionally a space craft will intentionally intercept the atmosphere, in an act commonly referred to as an aerobraking maneuver In most situations relativistic effects can be neglected, and Newton's laws give a sufficiently accurate description of motion. The acceleration of a body is equal"
"Rocket A rocket (from Italian ""rocchetto"" ""bobbin"") is a missile, spacecraft, aircraft or other vehicle that obtains thrust from a rocket engine. Rocket engine exhaust is formed entirely from propellant carried within the rocket before use. Rocket engines work by action and reaction and push rockets forward simply by expelling their exhaust in the opposite direction at high speed, and can therefore work in the vacuum of space. In fact, rockets work more efficiently in space than in an atmosphere. Multistage rockets are capable of attaining escape velocity from Earth and therefore can achieve unlimited maximum altitude. Compared with airbreathing"
"or beneath them to push against), because there is a reduction in air pressure on the outside of the engine, and because it is possible to fit a longer nozzle without suffering from flow separation, in addition to the lack of air drag. The maximum velocity that a rocket can attain in the absence of any external forces is primarily a function of its mass ratio and its ""exhaust velocity"". The relationship is described by the ""rocket equation"": formula_1, where formula_2 is the final velocity, formula_3 is the exhaust velocity relative to the rocket, formula_4 is the initial total mass,"
"velocity of 7.29×10 rad/s. The Earth has a moment of inertia, I = 8.04×10 kg·m. Therefore, it has a rotational kinetic energy of 2.138×10 J. Another example of actually using earth's rotational energy is the locating of opportune spaceports. The European spaceport in French Guiana (Guiana Space Centre) is within about 5 degrees of the equator, so space rocket launches (for primarily geo-stationary satellites) from here to the east obtain nearly all of the full rotational speed of the earth at the equator (about 1,000 mph, sort of a ""sling-shot benefit). Rocket launches easterly from Kennedy (USA) on the other"
"reach transonic velocity while maintaining a maximum altitude of less than 13,000 feet. ""Goddard Level"" : The most advanced level, named after the American engineer and rocket scientist Robert H. Goddard, challenges students to create a rocket from scratch that can reach an altitude of 100,000 feet, which is considered to fall within the near space region of Earth’s atmosphere. Rockets for this level are often several hundred pounds and can reach velocities of Mach 3 or even Mach 4. Launches for this level are hosted by the US Army at the White Sands Missile Range, New Mexico. The SystemsGo"
"on the order of 100 atmospheres. As a side effect, these pressures on the rocket also act on the exhaust in the opposite direction and accelerate this exhaust to very high speeds (according to Newton's Third Law). From the principle of conservation of momentum the speed of the exhaust of a rocket determines how much momentum increase is created for a given amount of propellant. This is called the rocket's ""specific impulse"". Because a rocket, propellant and exhaust in flight, without any external perturbations, may be considered as a closed system, the total momentum is always constant. Therefore, the faster"
"a body that falls under the force of gravitational attraction of mass ""M"", from infinity, starting with zero velocity, will strike the massive object with a velocity equal to its escape velocity given by the same formula. When given an initial speed formula_2 greater than the escape speed formula_3 the object will asymptotically approach the ""hyperbolic excess speed"" formula_4 satisfying the equation: In these equations atmospheric friction (air drag) is not taken into account. A rocket moving out of a gravity well does not actually need to attain escape velocity to escape, but could achieve the same result (escape) at"
"than Earth, a planetoid (or ""dwarf planet""), an asteroid, or a moon where the required thrust is lower due to lower gravity fields. Currently then, for a solid core nuclear thermal rocket to be more useful than chemical rockets as a first or second stage Earth launch engine, the system would either have to be made much lighter, or provide even higher specific impulse. Until that day, it can be said that the true strength of nuclear rockets currently lies in solar system exploration, outside Earth's gravity well. One way to increase the temperature, and thus the specific impulse, is"
"a 1""mg"" upward component, completely canceled by gravity, and a horizontal component of mg×formula_1 = 2.8""mg"" (by Pythagoras' theorem), achieving a 2.8""g"" horizontal acceleration. As orbital speeds are approached, vertical thrust can be reduced as centrifugal force (in the rotating frame of reference around the center of the Earth) counteracts a large proportion of the gravitation force on the rocket, and more of the thrust can be used to accelerate. It's important to note that minimising gravity losses is not the only objective of a launching spacecraft. Rather, the objective is achieve the position/velocity combination for the desired orbit. For"
"the effect of gravity on the vehicle over the duration of the maneuver. For low-thrust, long duration propulsion, such as electric propulsion, more complicated analysis based on the propagation of the spacecraft's state vector and the integration of thrust are used to predict orbital motion. Assume an exhaust velocity of and a formula_39 of (Earth to LEO, including formula_39 to overcome gravity and aerodynamic drag). In the case of sequentially thrusting rocket stages, the equation applies for each stage, where for each stage the initial mass in the equation is the total mass of the rocket after discarding the previous"
"planet. The delta-""v"" needed is only 3.6 km/s, only about 0.4 km/s more than needed to escape Earth, even though this results in the spacecraft going 2.9 km/s faster than the Earth as it heads off for Mars (see table below). At the other end, the spacecraft will need a certain velocity to orbit Mars, which will actually be less than the velocity needed to continue orbiting the Sun in the transfer orbit, let alone attempting to orbit the Sun in a Mars-like orbit. Therefore, the spacecraft will have to decelerate in order for the gravity of Mars to capture"
"to lift it into orbit in the first place. In astrodynamics, this energy expenditure is defined by the net change in the spacecraft's velocity, or delta-v. The energy needed to reach Jupiter from an Earth orbit requires a delta-v of about 9 km/s, compared to the 9.0–9.5 km/s to reach a low Earth orbit from the ground. Gravity assists through planetary flybys (such as by Earth or Venus) can be used to reduce the energetic requirement (i.e. the fuel) at launch, at the cost of a significantly longer flight duration to reach a target such as Jupiter when compared to"
"altitude at which an object in a circular orbit can complete at least one full revolution without propulsion is approximately . The expression ""orbital spaceflight"" is mostly used to distinguish from sub-orbital spaceflights, which are flights where the apogee of a spacecraft reaches space, but the perigee is too low. Orbital spaceflight from Earth has only been achieved by launch vehicles that use rocket engines for propulsion. To reach orbit, the rocket must impart to the payload a delta-v of about 9.3–10 km/s. This figure is mainly (~7.8 km/s) for horizontal acceleration needed to reach orbital speed, but allows for"
"now taking. This means the timing of the acceleration is critical if the intention is to escape in a particular direction. When escaping a compound system, such as a moon orbiting a planet or a planet orbiting a sun, a rocket that leaves at escape velocity (formula_26) for the first (orbiting) body, (e.g. Earth) will not travel to an infinite distance because it needs an even higher speed to escape gravity of the second body (e.g. the Sun). Near the Earth, the rocket's trajectory will appear parabolic, but it will still be gravitationally bound to the second body and will"
"world speed record of Mach 8.5 (6,416 mph / 10,325 km/h) was achieved by a four-stage rocket sled at Holloman Air Force Base on April 30, 2003, the highest speed ever attained by a land vehicle. Murphy's law first received public attention during a press conference about rocket sled testing. Rocket sled A rocket sled is a test platform that slides along a set of rails, propelled by rockets. As its name implies, a rocket sled does not use wheels. Instead, it has sliding pads, called ""slippers"", which are curved around the head of the rails to prevent the sled"
"significant technical challenges, because it orbits so much closer to the Sun than Earth. A Mercury-bound spacecraft launched from Earth must travel over into the Sun's gravitational potential well. Mercury has an orbital speed of , whereas Earth's orbital speed is . Therefore, the spacecraft must make a large change in velocity (delta-v) to enter a Hohmann transfer orbit that passes near Mercury, as compared to the delta-v required for other planetary missions. The potential energy liberated by moving down the Sun's potential well becomes kinetic energy; requiring another large delta-v change to do anything other than rapidly pass by"
"instance, the way to maximize acceleration is to thrust straight downward; however, thrusting downward is clearly not a viable course of action for a rocket intending to reach orbit. On a planet with an atmosphere, the objective is further complicated by the need to achieve the necessary altitude to escape the atmosphere, and to minimize the losses due to atmospheric drag during the launch itself. These facts sometimes inspire ideas to launch orbital rockets from high flying airplanes, to minimize atmospheric drag, and in a nearly horizontal direction, to minimize gravity losses. Gravity drag In astrodynamics and rocketry, gravity drag"
"formula_3 is propulsive efficiency (typically 0.8), formula_4 is the engine's shaft horsepower, and formula_5is true airspeed in feet per second. The thrust-to-weight ratio of a rocket, or rocket-propelled vehicle, is an indicator of its acceleration expressed in multiples of gravitational acceleration g. Rockets and rocket-propelled vehicles operate in a wide range of gravitational environments, including the ""weightless"" environment. The thrust-to-weight ratio is usually calculated from initial gross weight at sea-level on earth and is sometimes called ""Thrust-to-Earth-weight ratio"". The thrust-to-Earth-weight ratio of a rocket or rocket-propelled vehicle is an indicator of its acceleration expressed in multiples of earth’s gravitational acceleration,"
"Earth's standard acceleration formula_1). It is a dimensionless parameter characteristic of rockets and other jet engines and of vehicles propelled by such engines (typically space launch vehicles and jet aircraft). If the thrust-to-weight ratio is greater than the local gravity strength (expressed in ""g""s), then flight can occur without any forward motion or any aerodynamic lift being required. If the thrust-to-weight ratio times the lift-to-drag ratio is greater than local gravity then takeoff using aerodynamic lift is possible. Flight dynamics is the science of air and space vehicle orientation and control in three dimensions. The three critical flight dynamics parameters"
"5500 km away, and according to the above formula this requires an initial speed of 6.1 km/s. Increasing the speed to 7.9 km/s to attain any point on Earth requires a considerably larger missile because the amount of fuel needed goes up exponentially with delta-v (see Rocket equation). The initial direction of a minimum-delta-v trajectory points halfway between straight up and straight toward the destination point (which is below the horizon). Again, this is the case if we ignore the earth's rotation. It is not exactly true for a rotating planet unless the launch takes place at a pole. In"
"conventional thrusters, thus, if successfully developed, can expand human space endeavors beyond earth orbits. The speed an ideal photon rocket will reach, in the absence of external forces, depends on the ratio of its initial and final mass: where formula_2 is the initial mass and formula_3 is the final mass. The gamma factor corresponding to this speed has the simple expression: We denote the four-momentum of the rocket at rest as formula_5, the rocket after it has burned its fuel as formula_6, and the four-momentum of the emitted photons as formula_7. Conservation of four-momentum implies: squaring both sides (i.e. taking"
"launch delta-v. Isaac Newton avoided this objection in his thought experiment by positing an impossibly tall mountain from which his cannon was fired. If in a stable orbit, the projectile would circle the planet and return to the altitude of launch after one orbit (see Newton's cannonball). A space gun with a ""gun barrel"" of length (formula_1), and the needed velocity (formula_2), the acceleration (formula_3) is provided by the following formula: For instance, with a space gun with a vertical ""gun barrel"" through both the Earth's crust and the troposphere, totalling ~60 km of length (formula_1), and a velocity (formula_2)"
"orbit around Earth. During the burn the rocket engine applies its delta-""v"", but the kinetic energy increases as a square law, until it is sufficient to escape the planet's gravitational potential, and then burns more so as to gain enough energy to get into the Hohmann transfer orbit (around the Sun). Because the rocket engine is able to make use of the initial kinetic energy of the propellant, far less delta-""v"" is required over and above that needed to reach escape velocity, and the optimum situation is when the transfer burn is made at minimum altitude (low periapsis) above the"