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4.4. SPACE FLIGHT
k k
k k 114 FLIGHT PERFORMANCE
FIGURE 4 – 7. Orbital energy, orbital velocity, period of revolution, and Earth escape velocity for a space vehicle as a function of altitude for circular satellite orbits. Values are based on a spherical Earth and neglect the Earth’s oblate shape, its rotation, and atmospheric drag.
continuously brings the vehicle’s orbit closer to the Earth. However, radiation effects in the Van Allen belt on human beings and on sensitive equipment at times often necessitate the selection of Earth orbits at low altitudes.
For a satellite’s circular trajectory, the velocity must be sufficient so that its cen-trifugal force precisely balances the Earth’s gravitational attraction:
mu2s∕R = mg
For a circular orbit, the satellite velocity usis found by using Eq. 4–12, us= R0√
g0∕(R0+ h) =√
𝜇∕R (4–26)
which is smaller than the escape velocity by a factor of√
2. The period𝜏 in seconds for one revolution in a circular orbit relative to a stationary Earth is
𝜏 = 2𝜋(R0+ h)∕us = 2𝜋(R0+ h)3∕2∕(R0√
g0) (4–27)
Neglecting drag, the energy E necessary to bring a unit of mass into a circular satellite orbit consists of its kinetic and potential energy, namely,
E =1
2u2s + ∫
R R0
gdR
= 1
2R20 g0
R0+h+ ∫
R R0
g0R
2 0 R2dR = 1
2R0g0R0+2h
R0+h (4–28)
k k
TABLE4–1.CharacteristicDataforSeveralHeavenlyBodies Name MeanRadius ofOrbit (millionkm)Periodof Revolution Mean Diameter (km)RelativeMass (Earth=1.0)aSpecific Gravity
Accelerationof GravityatSurface (m/sec2)EscapeVelocity atSurface(m/sec) Sun——1,393,000332,9501.41273.4616,000 Moon0.38327.3days34750.0123.341.582380 Mercury57.8787.97days46700.065.53.674200 Venus108.1224.70days12,4000.865.38.6710,300 Earth149.6365.256days12,7421.0035.529.80611,179 Mars227.7686.98days67600.153.953.7496400 Jupiter777.811.86year143,000318.41.3326.059,700 Saturn148629.46year121,00095.20.6911.435,400 Uranus286984.0year47,10017.01.710.922,400 Neptune4475164.8year50,70017.21.811.931,000 Pluto5899248year23680.002181.440.6581229 aEarthmassis5.976×1024kg. Source:InpartfromRefs4–3and4–4.
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Escape velocity, satellite velocity, satellite period, and satellite orbital energy are all shown as functions of altitude in Fig. 4–7.
A satellite moving around the Earth at an altitude of 300 miles or 482.8 km has a velocity usof about 7375 m/sec or 24,200 ft/sec, circles a stationary Earth in𝜏 = 1.63 hr.; ideally it requires an energy of 3.35 × 107J to place 1 kg of spaceship mass into its orbit. An equatorial satellite in a circular orbit at an altitude of 6.611 Earth radii (about 26,200 miles, 42,200 km, or 22,700 nautical miles) has a period of revolu-tion of exactly 24 hr. It will, therefore, appear starevolu-tionary to an observer on Earth. This is known as a synchronous satellite in geo synchronous Earth orbit, usually abbrevi-ated as GEO. This orbit is used extensively for communications satellite and Earth observation applications. In the part of Section 4.7 on launch vehicles, we describe how the payload of any given space vehicle diminishes as the orbit’s circular altitude is increased and as the inclination (angle between orbit plane and Earth equatorial plane) is changed. See Refs. 4–3, 4–4, 4–5, 4–6 and 4–9.
Elliptical Orbits
The circular orbit described above is a special case of the more general elliptical orbit shown in Fig. 4–8; here, the Earth (or any other heavenly body around which another body is moving) is located at one of the focal points of this ellipse. The relevant equations of motion come from Kepler’s laws and elliptical orbits may be described as follows, when expressed in polar coordinates:
u = [𝜇(2
R−1 a
)]1∕2
(4–29) where u is the velocity of the body in the elliptical orbit, R is the instantaneous radius from the center of the Earth (a vector quantity, which changes direction as well as magnitude), a is the major axis of the ellipse, and𝜇 is the Earth’s gravitational con-stant, 3.986 × 1014m3/sec2. These symbols are defined in Fig. 4–8. From Eq. 4–29 it can be seen that the velocity has its maximum value upwhen the moving body comes closest to its focal point at its orbit’s perigee and the minimum value uaat its apogee.
By substituting for R in Eq. 4–29, and by defining the ellipse’s shape factor e as the eccentricity of the ellipse, e =√
a2− b2∕ a, the apogee and perigee velocities can be expressed as
ua=
√𝜇(1 − e)
a(1 + e) (4–30)
up=
√𝜇(1 + e)
a(1 − e) (4–31)
Another property of an elliptical orbit is that the product of velocity and instanta-neous radius remains constant for any location x or y on the ellipse, namely, uxRx= uyRy= uR. The exact path that a satellite takes depends on the velocity (magnitude and vector orientation) with which it is started or was injected into orbit.
k k
4.4. SPACE FLIGHT 117
√a2 – b2
FIGURE 4 – 8. Elliptical orbit; the attracting body is at one of the focal points of the ellipse.
For interplanetary transfers, an ideal mission can be achieved with minimum energy with a simple transfer ellipse, as suggested originally by Hohmann (see Ref. 4–7). Assuming that planetary orbits about the sun are circular and coplanar, Hohmann demonstrated that the path of minimum energy is an ellipse tangent to both planetary orbits as shown in Fig. 4–9. This operation requires a velocity increment (of relatively high thrust) at the initiation (planet A at time t1) and another at termination (planet B at time t2): both increments equal the velocity differences between the respective circular planetary velocities and the perigee and apogee velocities which define the transfer ellipse. Thrust levels at the beginning and end maneuvers of the Hohmann ellipse must be high enough to amount to a short operating time and an acceleration of at least 0.01 g0, but preferably more.
Note that because electrical propulsion accelerations are much lower, amounting
FIGURE 4 – 9. Schematic of interplanetary transfer paths. These same transfer maneuvers apply when going from a low-altitude Earth satellite orbit to a higher orbit.
k k 118 FLIGHT PERFORMANCE
to about 10−5g0, and operating times longer, weeks or months, the best transfer trajectories in electrical propulsion turn out to be much different from Hohmann ellipses; these are described in Chapter 17.
Departure dates or the relative positions of the launch planet and the target planet in planetary transfer missions become critical, because the spacecraft must meet with the target planet when it arrives at the target orbit. Transfer times (t2− t1) for Hohmann-ellipse flights starting on Earth are about 116 hours to go to the moon and about 259 days to Mars. If faster flight paths (shorter transfer times) are desired (see dashed lines in Fig. 4–9), they will require more energy than those with a Hohmann transfer ellipse. This means a larger vehicle with more propellant and a larger propulsion system, or a higher total impulse. There always is a time window for launching a spacecraft that will make for a successful rendezvous. For Mars missions an Earth-launched spacecraft may have a launch time window of more than two months. Hohmann transfer ellipses or faster transfer paths apply not only to planetary flight but also to Earth satellites when they go from one circular orbit to another (but within the same plane). Also, if one spacecraft goes to rendezvous with another spacecraft in a different orbit, the two have to be in the proper predetermined positions prior to any thrust application to simultaneously reach their rendezvous location.
When the launch orbit (or launch planet) is not in the same plane as the target orbit, then additional energy will be needed for applying thrust in directions normal to the launch orbit plane. More information can be found in Refs. 4–3, 4–4, 4–6, and 4–10.
Example 4–2. A satellite is launched from a circular equatorial parking orbit at an altitude of 160 km into a coplanar circular synchronous orbit by using a Hohmann transfer ellipse. Assume a homogeneous spherical Earth with a radius of 6371 km. Determine the velocity increments for entering the transfer ellipse and for achieving the synchronous orbit at 42,200 km altitude.
See Fig. 4–9 for the terminology of the orbits.
SOLUTION. The two orbits are RA= 6.531 × 106m; RB= 48.571 × 106m. The major axis ateof the transfer ellipse is
ate=1
2(RA+ RB) = 27.551 × 106m The orbit velocities of the two satellites are
uA=√
𝜇∕RA= [3.986005 × 1014∕6.571 × 106]1∕2= 7788 m∕sec uB=√
𝜇∕RB= 2864.7 m∕sec
The velocities needed to enter and exit the transfer ellipse are (ute)A=√
𝜇[(2∕RA) − (1∕a)]1∕2= 10,337 m∕sec (ute)B=√
𝜇[(2∕RB) − (1∕a)]1∕2= 1394 m∕sec
The changes in velocity going from parking orbit to ellipse ΔuAand from ellipse to final orbit ΔuBare
ΔuA=|(ute)A− uA| = 2549 m∕sec ΔuB=|uB− (ute)B= 1471 m∕sec
k k
4.4. SPACE FLIGHT 119
The total velocity change for the transfer maneuvers is
Δutotal= ΔuA+ ΔuB= 4020 m∕sec
Figure 4–10 shows the elliptical transfer trajectory of a ballistic missile or a satel-lite launch or an ascent vehicle. During the initial powered flight the trajectory angle is adjusted by signals from the guidance system and torques from the reaction con-trol system to an angle that will allow the vehicle to reach the apogee of its elliptical path at exactly the desired altitude. An orbit injection velocity increase of the space vehicle is now applied by a chemical propulsion system at this apogee, which causes the vehicle to change from an elliptical transfer flight path to a circular-orbit flight path. The horizontal arrow symbolizes this velocity increase. For an ideal satellite the simplified theory assumes that an orbit injection maneuver is essentially an instanta-neous application of the total impulse when the ballistic elliptic trajectory reaches its
FIGURE 4 – 10. Long-range ballistic missiles follow an elliptical free flight trajectory, which is nearly drag free, with the Earth’s center as one of the focal points. The surface launch is usu-ally verticusu-ally up (not shown here) but the flight path is quickly tilted during the early powered flight to enter into an elliptic trajectory. The ballistic range is the arc distance on the Earth’s surface. The same elliptical flight path can be used by launch vehicles for satellites; another powered flight period occurs (called orbit injection) just as the vehicle reaches its elliptical apogee (as indicated by the arrow), causing the vehicle to enter an orbit.
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apogee or zenith. In reality, the rocket propulsion system for orbit injection operates over a finite time, during which gravity losses and changes in altitude occur.
Deep Space
Lunar and interplanetary missions may include circumnavigation, landing, and return flights. The energy necessary to escape from the Earth may be calculated as 1
2m𝑣2e
from Eq. 4–25 as 6.26 × 107J∕kg, which is more than that required to launch an Earth satellite. The gravitational attraction of various heavenly bodies and their respective escape velocities depends on their mass and diameter; approximate values are listed in Table 4–1. An idealized diagram of an interplanetary landing mission is shown in Fig. 4–11.
Escape from the solar system requires approximately 5.03 × 108J∕kg which is eight times as much energy as is required for escape from the Earth. Technology exists today to send small, unmanned probes away from the sun into outer space, but before any mission to the nearest star can be achieved some very long-duration, novel, rocket propulsion system must be introduced. The ideal trajectory for a spacecraft to escape from the sun is either a parabola (minimum energy) or a hyperbola. See Refs. 4–6 and 4–10.
The Voyager 2 Spacecraft, developed by NASA’s Jet Propulsion Laboratory, was the first man-made object to escape from the solar system and enter interplanetary space. It was launched on August 20, 1977 for exploring the outer planets (flybys of Jupiter, Saturn, Neptune, and Uranus) and then leaving the solar system. It was not expected that Voyager 2 would continue to be operational for over 37 years.
A three-axis stabilization system with gyroscopic and celestial reference instruments
FIGURE 4 – 11. Schematic of typical powered flight maneuvers during a hypothetical two-dimensional interplanetary mission with a landing (not drawn to scale). The numbers indicate typical thrust magnitudes of the maneuvers in percent of launch takeoff thrust. Heavier lines show powered flight path segments.
k k
4.4. SPACE FLIGHT 121 is needed to provide a signal that periodically operates its rocket propulsion system which consists of a gas pressurized feed system and 16 small hydrazine monopro-pellant thrusters, 8 of which remain working to keep a 12-foot-diameter antenna pointed to Earth. Voyager 2 has been powered by three radioisotope thermoelectric generators, which collectively delivered 420 electrical watts at launch (Reference:
http://en.wikipedia.org/wiki/Voyager2).
Perturbations
This section gives a brief discussion of forces and torques that cause perturbations and/or deviations from intended space flight paths or satellite’s flight orbits. For a more detailed treatment of flight paths and their perturbations, see Refs. 4–3, 4–4, and 4–13. A system that measures the satellite’s position and its deviation from the intended flight path is required to determine the needed periodic correction maneuvers in order to apply corrective forces and/or torques. It is called an orbit maintenance system; it corrects the perturbed or altered orbit by periodically applying small rocket propulsion forces in predetermined directions. Typically, these corrections are per-formed by a set of small reaction control thrusters that provide predetermined total impulses in desired directions. These corrections are needed throughout the life of any spacecraft (for 1 to 20 years and sometimes more) to overcome the effects of distur-bances so as to maintain the intended flight regime.
Perturbations may be categorized as short term and long term. Daily or orbital period oscillating forces are called diurnal, and those with long periods are called secular.
High-altitude Earth satellites (36,000 km and higher) experience perturbing forces primarily as gravitational pulls from the sun and the moon, with these forces acting in different directions as the satellite flies around the Earth. Such third-body effects can increase or decrease the velocity magnitude and change the satellite’s direction.
In extreme cases the satellite may come close enough to the third body, such as a planet or one of its moons, to undergo what is called a hyperbolic maneuver (caused by the attraction of that heavenly body) that will radically change its trajectory. Such encounters have been used to increase or decrease the satellite’s energy and inten-tionally change the velocity and the shape of the orbit.
Medium- and low-altitude satellites (500 to 35,000 km) experience perturbations because of the Earth’s oblateness. The Earth bulges at the equator, and its cross section through the poles is not entirely circular. Depending on the inclination of the orbital plane to the Earth equator and the altitude of the satellite orbit, two per-turbations result: (1) the regression of the nodes and (2) a shifting of the apsides line (major axis). Regression of the nodes is shown in Fig. 4–12 as a rotation of the plane of the orbit in space, and it can be as high as 9∘ per day at relatively low altitudes.
Theoretically, regression does not occur in truly equatorial orbits.
Figure 4–13 shows an exaggerated shift of the apsidal line, with the center of the Earth remaining as a focus point. This perturbation may be visualized as the move-ment of the prescribed elliptical orbit in a fixed plane. Obviously, both apogee and perigee points change in position, the rate of change being a function of the satellite
k k 122 FLIGHT PERFORMANCE
FIGURE 4 – 12. The regression of nodes is shown as a rotation of the plane of the orbit.
The movement direction will be opposite to the east–west components of the Earth’s satellite motion.
FIGURE 4 – 13. Shifting of the apsidal line of an elliptic orbit from position 1 to 2 because of the oblateness of the Earth.
altitude and plane inclination angle. At an apogee altitude of 1000 nautical miles (n.m.) and a perigee of 100 n.m. in an equatorial orbit, the apsidal drift is approxi-mately 10∘ per day.
Satellites of modern design, with irregular shapes due to protruding antennas, solar arrays, or other asymmetrical appendages, experience torques and forces that tend to perturb the satellite’s position and orbit throughout its orbital life. Principal torques and forces result from the following factors:
1. Aerodynamic drag. This factor is significant at orbital altitudes below 500 km and is usually assumed to cease at 800 km above the Earth. Reference 4–8 gives
k k
4.4. SPACE FLIGHT 123 a detailed discussion of aerodynamic drag, which, in addition to affecting the attitude of unsymmetrical vehicles, causes a change in elliptical orbits known as apsidal drift, a decrease in the major axis, and a decrease in eccentricity of orbits about the Earth. See Refs. 4–6, 4–8, 4–12, and 4–13.
2. Solar radiation. This factor dominates at high altitudes (above 800 km) and is due to impingement of solar photons upon satellite surfaces. The solar radiation pressure p (N/m2) on a given surface of the satellite in the vicinity of the Earth exposed to the sun can be determined from
p = 4.5 × 10−6cos𝜃[(1 − ks)cos𝜃 + 0.67 kd] (4–32) where𝜃 is the angle (in degrees) between the incident radiation vector and the normal to the surface and ksand kd are the specular and diffuse coefficients of reflectivity. Typical values are 0.9 and 0.5, respectively, for ks and kd on the body and antenna and 0.25 and 0.01, respectively, for ksand kdwith solar array surfaces. Radiation intensity varies as the square of the distance from the sun (see Refs. 4–4 and 4–14). The torque T on the vehicle is given by T = pAl, where A is the projected area normal to the flight direction (or normal to the sun’s rays) and l is the offset distance between the spacecraft’s center of gravity and the center of solar pressure. For a nonsymmetrical satellite with a large solar panel on one side, solar radiation will cause a small torque that will rotate the vehicle.
3. Gravity gradients. Gravitational torques in spacecraft result from variations in the gravitational force on the distributed mass of a spacecraft. Determination of this torque requires knowledge of the gravitational field and the distribution of spacecraft mass. This torque decreases as a function of the orbit radius and increases with the offset distances of masses within the spacecraft (including booms and appendages); it is most significant in large spacecraft or in space stations operating in relatively low orbits (see Refs. 4–4 and 4–15).
4. Magnetic field. The Earth’s magnetic field and any magnetic moment within the satellite can interact to produce torque. The Earth’s magnetic field precesses about the Earth’s axis but is very weak (0.63 and 0.31 gauss at poles and equa-tor, respectively). This field is continually fluctuating in direction and inten-sity because of magnetic storms and other influences. Since the field strength decreases with 1/R3 with the orbital altitude, magnetic field forces are often neglected in the preliminary analysis of satellite flight paths (see Ref. 4–16).
5. Internal accelerations. Deployment of solar array panels, the shifting of liquid propellants, the movement of astronauts or other masses within the satellite, or the “unloading” of reaction wheels may produce noticeable torques and forces.
6. For precise low Earth orbits the oblateness of the Earth (diameter at equator being slightly larger than diameter between poles), high mountains, or Earth surface areas of different densities will cause perturbations of these orbits.
We can categorize satellite propulsion needs according to their function as listed in Table 4–2, which shows the total impulse “budget” applicable to a typical
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TABLE 4 – 2. Typical Propulsion Functions and Approximate Total Impulse Needs of a 2000-lbm Geosynchronous Satellite with a Seven-Year Life
Function Total Impulse (N-sec)
Acquisition of orbit 20,000
Attitude control (rotation) 4000
Station keeping, E–W 13,000
Station keeping, N–S 270,000
Repositioning (Δu, 200 ft/sec) 53,000
Control apsidal drift (third-body attraction) 445,000
Deorbit 12,700
Total 817,700
high-altitude, elliptic orbit satellite. The control system designer often distinguishes two different kinds of station-keeping orbit corrections needed to keep the satellite in a synchronous position. The east–west correction refers to a correction that moves the point at which a satellite orbit intersects the Earth’s equatorial plane in an east or west direction; it usually corrects forces caused largely by the oblateness of the Earth. The north–south correction counteracts forces usually connected with the third-body effects of the sun and the moon.
For many satellite missions any gradual changes in orbit caused by perturbation forces are of little concern. However, in certain missions it is necessary to compensate for these perturbing forces and maintain the satellite in a specific orbit at a particu-lar position in that orbit. For example, synchronous communications satellites in a Geosynchronous Earth Orbit, or GEO, need to maintain their position and their orbit so as to be able to (1) keep covering a specific area of the Earth or communicate with the same Earth stations within its line of sight and (2) not become a hazard to other satellites in this densely populated synchronous equatorial orbit. Another example is Low Earth Orbit or LEO communications satellites system with several coordinated satellites; here at least one satellite has to be in a position to receive and transmit radio-frequency (RF) signals to specific locations on the Earth. The orbits and rela-tive positions of several satellites with respect to each other also need to be controlled and maintained (see Ref. 4–3).
Orbit maintenance requires applying small correcting forces and torques peri-odically to compensate for perturbation effects; for GEO this happens every few months. Typical velocity increments for the orbit maintenance of synchronous satel-lites require a Δu between 10 and 50 m/sec per year. For a satellite mass of about 2000 kg a 50-m/sec correction for a 10-year orbit life would need a total impulse of about 100,000 N-sec, which corresponds to a chemical propellant mass of 400 to 500 kg (about a quarter of the satellite mass) when done with small monopropellant or bipropellant thrusters. It would require much less propellant if electrical propul-sion were to be used, but for some spacecraft the inert mass of the power supply and mission duration might represent a substantial increase . See Refs. 4–6, 4–13, and 4–14.
k k
4.4. SPACE FLIGHT 125
Mission Velocity
A convenient way to describe the magnitude of the energy requirement for a space mission is to use the concept of the mission velocity. It is the sum of all the flight velocity increments needed (in all the vehicle’s stages) to attain the mission objec-tive even though these increments are provided by different propulsion systems and their thrusts may be in different directions. In the sketch of a planetary landing mis-sion of Fig. 4–11, it is the sum of all the Δu velocity increments shown by the heavy lines (rocket-powered flight segments) of the trajectories. Even through some velocity increments might be achieved by retro-action (a negative propulsion force to decelerate the flight velocity), all these maneuvers require energy and their absolute magnitude is counted in the mission velocity. The initial velocity from the Earth’s rotation (464 m/sec at the equator and 408 m/sec at a launch station at 28.5∘ latitude) does not need to be provided by the vehicle’s propulsion systems. For example, the required mission velocity for launching at Cape Kennedy, bringing the space vehicle into an orbit at 110 km, staying in orbit for a while, and then entering a deorbit maneu-ver has the Δu components shown in Table 4–3.
The required mission velocity is the sum of the absolute values of all translation velocity increments that have forces going through the center of gravity of the vehicle (including turning maneuvers) during the mission flight. It is the hypothetical velocity that would be attained by the vehicle in a gravity-free vacuum, if all the propulsive energy of the momentum-adding thrust chambers in all stages were to be applied in the same direction. This theoretical value is useful for comparing one flight vehicle design with another and as an indicator of total mission energy.
The required mission velocity must equal to the “supplied” mission velocity, that is, the sum of all the velocity increments provided by the propulsion systems during each of the various vehicle stages. The total velocity increment that was “supplied” by the Shuttle’s propulsion systems for the Shuttle mission (solid rocket motor strap-on boosters, main engines and, for orbit injection, also the increment from the orbital maneuvering system—all shown in Fig. 1–14) had to equal or exceed 9347 m/sec.
When the reaction control system propellant and an uncertainty factor are added, this value would have needed to exceed 9621 m/sec. With chemical propulsion systems and a single stage, we can achieve space mission velocities of 4000 to 13,000 m/sec,
TABLE 4 – 3. Typical Estimated Space Shuttle Incremental Flight Velocity Breakdown for Flight to Low Earth Orbit and Return
Ideal satellite velocity 7790 m/sec
Δu to overcome gravity losses 1220 m/sec
Δu to turn the flight path from the vertical 360 m/sec
Δu to counteract aerodynamic drag 118 m/sec
Orbit injection 145 m/sec
Deorbit maneuver to reenter atmosphere and aerodynamic braking 60 m/sec
Correction maneuvers and velocity adjustments 62 m/sec
Initial velocity provided by the Earth’s rotation at 28.5∘ latitude −408 m/sec
Total required mission velocity 9347 m/sec
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depending on the payload, mass ratio, vehicle design, and propellant. With two stages they can be between perhaps 12,000 and 22,000 m/sec.
Rotational maneuvers (to be described later) do not change the flight velocity and some analysts do not add them to the mission velocity requirements. Also, maintain-ing a satellite in orbit against long-term perturbmaintain-ing forces (see prior section) is often not counted as part of the mission velocity. However, designers need to provide addi-tional propulsion capabilities for these purposes. These are often separate propulsion systems, called reaction control systems.
Typical vehicle velocities required for various interplanetary missions have been estimated as shown in Table 4–4. By starting interplanetary journeys from a space station, considerable savings in vehicle velocity can be achieved, namely, the velocity necessary to attain the Earth-circling satellite orbit. As space flight objectives become more ambitious, mission velocities increase. For a given single or multistage vehi-cle it is possible to increase the vehivehi-cle’s terminal velocity, but usually only at the expense of payload. Table 4–5 shows some typical ranges of payload values for a TABLE 4 – 4. Approximate Vehicle Mission Velocities for Typical Space and Interplanetary Missions
Mission
Ideal Velocity (km/sec)
Approximate Actual Velocity (km/sec) Satellite orbit around Earth (no return) 7.9–10 9.1–12.5
Escape from Earth (no return) 11.2 12.9
Escape from moon 2.3 2.6
Earth to moon (soft landing on moon, no return) 13.1 15.2
Earth to Mars (soft landing) 17.5 20
Earth to Venus (soft landing) 22 25
Earth to moon (landing on moon and return to Eartha) 15.9 17.7 Earth to Mars (landing on Mars and return to Eartha) 22.9 27
aAssumes air braking within atmospheres.
TABLE 4 – 5. Approximate Relative Payload-Mission Comparison Chart for Typical Multistage Rocket Vehicles Using Chemical Propulsion Systems
Mission Relative Payloada(%)
Earth satellite 100
Earth escape 35–45
Earth 24-hr orbit 10–25
Moon landing (hard) 35–45
Moon landing (soft) 10–20
Moon circumnavigation (single fly-by) 30–42
Moon satellite 20–30
Moon landing and return 1–4
Moon satellite and return 8–15
Mars flyby 20–30
Mars satellite 10–18
Mars landing 0.5–3
a300 nautical miles (555.6 km) Earth orbit is 100% reference.