- Email: [email protected]
Connecting atmospheric science and atmospheric models for aerocapture at Titan and the outer planets
ARTICLE IN PRESS
Planetary and Space Science 53 (2005) 601–605 www.elsevier.com/locate/pss
Connecting atmospheric science and atmospheric models for aerocapture at Titan and the outer planets C.G. Justusa, Aleta Duvalla,, Vernon W. Kellerb, Thomas R. Spilkerc, Mary Kae Lockwoodd a
Morgan Research Corporation, EV13/Morgan, Marshall Space Flight Center, Huntsville, AL 35812, USA b NASA Marshall Space Flight Center, EV13, Marshall Space Flight Center, AL 35812, USA c Jet Propulsion Laboratory, Pasadena, CA 91109, USA d NASA Langley Research Center, Vehicle Analysis Branch, Hampton, VA 23681, USA Available online 12 February 2005
Abstract Many atmospheric measurement systems, such as the sounding instruments on Voyager, gather atmospheric information in the form of temperature versus pressure level. In these terms, there is considerable consistency among the mean atmospheric profiles of the outer planets Jupiter through Neptune, including Titan. On a given planet or on Titan, the range of variability of temperature versus pressure level due to seasonal, latitudinal, and diurnal variations is also not large. However, many engineering needs for atmospheric models relate not to temperature versus pressure level but atmospheric density versus geometric altitude. This need is especially true for design and analysis of aerocapture systems. Drag force available for aerocapture is directly proportional to atmospheric density. Available aerocapture ‘‘corridor width’’ (allowable range of atmospheric entry angle) also depends on height rate of change of atmospheric density, as characterized by density scale height. Characteristics of hydrostatics and the gas law equation mean that relatively small systematic differences in temperature versus pressure profiles can integrate at high altitudes to very large differences in density versus altitude profiles. Thus, a given periapsis density required to accomplish successful aerocapture can occur at substantially different altitudes ( 150–300 km) on the various outer planets, and significantly different density scale heights ( 20–50 km) can occur at these periapsis altitudes. This paper will illustrate these effects and discuss implications for improvements in atmospheric measurements to yield significant impact on design of aerocapture systems for future missions to Titan and the outer planets. Relatively small-scale atmospheric perturbations, such as gravity waves, tides, and other atmospheric variations can also have significant effect on design details for aerocapture guidance and control systems. This paper will discuss benefits that would result from improved understanding of Titan and outer planetary atmospheric perturbation characteristics. Details of recent engineering-level atmospheric models for Titan and Neptune will be presented, and effects of present and future levels of atmospheric uncertainty and variability characteristics will be examined. r 2005 Elsevier Ltd. All rights reserved. Keywords: Aerocapture; Global reference atmospheric model; Titan atmosphere; Titan-GRAM; Neptune atmosphere; Neptune-GRAM
1. Consistency of temperature–pressure profiles The outer planets, including the gas giants Jupiter, Saturn, Uranus, and Neptune, represent by far the leaststudied portion of the Solar System. The first satellites Corresponding author. Tel.: +1 256 544 6030; fax: +1 256 544 5754. E-mail address: [email protected] (A. Duvall).
0032-0633/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2004.12.002
to visit the outer Solar System, Pioneer 10 and 11, were designed to test the navigability of the asteroid belt and measure the strength of the magnetic and radiation environments around Jupiter. Voyager 1 and 2 made a collective sweep of the four gas giants during the period 1979–1989. Among many other findings, the twin Voyagers observed Jupiter and Neptune’s weather patterns and characterized the atmospheric composition of Saturn’s moon, Titan, through the use of on-board
ARTICLE IN PRESS C.G. Justus et al. / Planetary and Space Science 53 (2005) 601–605
infrared interferometer spectrometry (IRIS), ultraviolet spectrometry (UVS), and radio science (RS) instrumentation. Many atmospheric measurement systems, such as the sounding instruments on Voyager, still gather atmospheric information in the form of temperature versus pressure level. In these terms, there is considerable consistency among the mean atmospheric profiles of the outer planets Jupiter through Neptune, including Titan. In the present discussion, a simplified naming scheme is applied to the layers of a planet’s atmosphere, according to the behavior of temperature gradients. If the temperature gradients are steeper than the adiabatic gradient and temperature decreases with height above the 1-bar pressure level (or above the surface, for Titan), then this region is named the troposphere. The generally Outer Planets Temperature vs Pressure
Pressure, N/m2
Titan Uranus
102
Neptune
103 104 Jupiter 105 0
50
100 150 Temperature, K
200
250
Fig. 1. Measured profiles of temperature versus pressure on the outer planets and Titan.
Normalized Temperature versus Pressure
Pressure, N/m2
Saturn
Neptune
Jupiter Uranus
102 103
800
+/- factor of 1.19
+/- factor of 1.24 600 Minimum
Maximum
+/- factor of 1.20
400
+/- factor of 1.13
200
0 60
80
100
120 140 160 Temperature, K
180
200
220
Saturn
101
101
Range due to Latitude, Season, Time-of-Day, & Measurment Uncertainty
Fig. 3. Titan profiles of maximum and minimum expected temperature due to variations in latitude, season, time of day, and measurement uncertainty.
10-1 100
Titan Minimum and Maximum Temperature Profiles
Height, km
602
Titan
104
105 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Temperature Ratio [T(p)/T(1 bar) or T(p)/T(surface)] Fig. 2. Measured temperature profiles normalized by temperature at 1-bar level (or at surface for Titan).
isothermal region overlying the troposphere is named the mesosphere. The name mesopause is assigned to the region of increasing temperature with height which represents the interface between the mesosphere and the thermosphere. Fig. 1 shows consistency of temperature profiles in the mesopauses (100–0.1 N=m2 pressure levels) of the outer planets and Titan. To remove the steady trend toward lower temperatures as distance from the Sun increases, temperature can normalized by temperature at the surface for Titan, or at the 1-bar pressure level for the gas giants. After such normalization, Fig. 2 indicates considerable consistency of temperature profiles in the tropospheres and mesospheres (surface/1-bar level to 1000 N=m2 ) of the outer planets and Titan. On a given planet or on Titan, the range of variability of temperature versus pressure level (or temperature versus altitude) due to seasonal, latitudinal, and diurnal variations is also not large. For example, Fig. 3 illustrates that the range of temperature variation expected on Titan, due to effects of latitude, season, and time of day (plus measurement uncertainty) is at most about a factor of 1.24 above or below the mean temperature. The model atmospheres in Fig. 3 were developed for engineering purposes as conservative bounds on temperature variation; Yelle et al. (1997) provide a detailed discussion of the uncertainties incorporated in these models.
2. Engineering needs for atmospheric density Many engineering needs for atmospheric models relate not only to temperature versus pressure level but
ARTICLE IN PRESS C.G. Justus et al. / Planetary and Space Science 53 (2005) 601–605
3. Range of density and density scale height values at aerocapture For qualitative discussion of aerocapture design parameters, therefore, it is instructive to treat the Titan Minimum and Maximum Density Profiles Range due to Latitude, Season, Time-of-Day, & Measurment Uncertainty
+/- factor of 12.66
800
+/- factor of 6.16
Height, km
600
+/- factor of 2.73 400
Gas Giants Atmospheric Density 800 700 600 Height, km
also to atmospheric density versus geometric altitude (in the present discussion, ‘‘density’’ refers everywhere to mass density rather than number density). This need is especially true for design and analysis of aerocapture systems. Aerocapture differs from aerobraking in that it relies on a single pass, rather than multiple passes, through a planetary atmosphere to remove enough energy from the satellite’s trajectory to change it from hyperbolic to elliptical with respect to the planet. Some of the key assumptions inherent in classical aerobraking theory fail when applied to aerocapture; a case in point is the well-known ‘‘square root of scale height’’ law. This relation states that the integral of density with respect to time over an aerobraking pass is proportional to the square root of the scale height and inversely proportional to the square root of the eccentricity (Tolson, 2001). Derivation of the ‘‘square root of scale height’’ law is based on the inherent assumption that scale height remains constant over the duration of the pass. For aerocapture this assumption is invalid; an aerocapture pass may span multiple scale heights in order to remove the energy associated with typically high atmospheric entry velocity. In a recent Titan aerocapture systems analysis study, for example, Lockwood (2003) utilized reference values of 6.5 km/s for entry velocity, 36 for nominal entry flight path angle, and 200–400 km for aerocapture altitude range.
603
500
Saturn Aerocapture Density
Neptune
400 Jupiter 300 200
Uranus
100 0 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 Density, kg/m3 Fig. 5. Profiles of mean density versus height for the gas giant planets. Vertical dashed line shows typical aerocapture periapsis density.
concepts of density and density scale height separately. Drag force available for aerocapture is directly proportional to atmospheric density. Characteristics of hydrostatics and the gas law equation mean that relatively small systematic differences in temperature versus pressure profiles, such as those illustrated in Fig. 3, can integrate at high altitudes to very large differences in density versus altitude profiles. This fact is shown in Fig. 4, which shows the range of expected density variability and uncertainty for Titan’s atmosphere increasing exponentially from a factor of 1.67 at 200 km altitude to a factor of 12.66 at 800 km altitude. The corresponding range of variability in atmospheric drag on an aerocapture vehicle is an important design consideration for on-board guidance systems. In a similar fashion, despite the consistency among the outer planets for temperature versus pressure (shown in Figs. 1 and 2), there is a wide range of variability among the planets in their mean profiles of density versus altitude, as shown by Fig. 5. Fig. 5 indicates that a given periapsis density required to accomplish successful aerocapture can occur at substantially different altitudes ( 150–300 km) on the various outer planets. For a stratified atmosphere, density scale height H as a function of altitude z is defined as HðzÞ ¼ ðrðzÞÞ=ðdrðzÞ=dzÞ,
200
+/- factor of 1.67
0 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 Density, kg/m3 Fig. 4. Titan profiles of maximum and minimum expected atmospheric density due to variations in latitude, season, time of day, and measurement uncertainty.
(1)
where rðzÞ is density at height z: Density scale height represents the height rate of change of atmospheric density. Fig. 6 shows that density scale height at aerocapture altitudes varies from about H ¼ 20 –50 km for the outer planets and Titan. Available aerocapture ‘‘corridor width’’ (allowable range of atmospheric entry angle) depends on density scale height. Thus, significant differences in available aerocapture corridor width are expected for these destinations.
ARTICLE IN PRESS C.G. Justus et al. / Planetary and Space Science 53 (2005) 601–605
604
Variablity We Can Model (season, latitude, etc.) Measurement Uncertainty (Big improvement for Titan after Huygens/Cassini) Residual Uncertainty (Monte-Carlo-modeled waves, turbulence, etc.)
Density Scale Height Comparison 400 350
Neptune A
Height, km
300
Titan
Jupiter
250
A Titan
200
Mars
A 150
A Neptune
100
Earth Titan 0 A = Aerocapture Altitude
10
20 30 40 50 Variation, % of Mean
60
70
50 Saturn 0 0
10
20
30 40 50 60 70 80 Density Scale Height, km
90
100
Fig. 6. Profiles of mean density scale height versus altitude for the gas giant planets. Typical altitudes and density scale heights for aerocapture are shown by letter A.
Sample Neptune-GRAM monte-Carlo Density Output 300
Height, km
250
Fminmax = -1
Fminmax = 0
Fminmax = 1
200
Fig. 8. Approximate variability and uncertainty in density at aerocapture altitude for Neptune, Titan, Mars, and Earth. Titan variability and uncertainty are shown for current conditions and postCassini/Huygens.
Fig. 7 provides example simulations of these high frequency perturbations from the Neptune Global Reference Atmospheric Model (Neptune-GRAM). Neptune-GRAM is one of series of atmospheric models entitled the GRAM series, developed by NASA Marshall Space Flight Center (Justus et al., 2002, 2003a–c; Justus et al., 2004a,b; Justus and Johnson, 1999, 2001).
150
4. Summary of atmospheric density variability and uncertainty
100 50 0 -100
-50 0 50 100 150 200 250 Perturbed Density (% from Neptune Average)
Fig. 7. Simulated ‘‘high-frequency’’ perturbations about Neptune minimum ðF minmax ¼ 1Þ; average ðF minmax ¼ 0Þ; and maximum ðF minmax ¼ 1Þ density profiles (perturbations expressed as percent deviation from average density).
Relatively small-scale, ‘‘high-frequency’’ atmospheric perturbations, such as gravity waves, tides, and other atmospheric variations, can also have significant effect on design details for aerocapture guidance and control systems. Ability to successfully aerocapture into highly eccentric orbits can depend significantly on details of such high-frequency perturbations. For highly eccentric orbits there may be only a small margin for error between successful aerocapture and ‘‘skip-out’’ conditions in which no aerocapture is achieved. Ability to aerocapture into highly eccentric orbits can be an important aspect for designing missions such as a Neptune orbiter that can visit Triton, or a Jupiter orbiter that can visit the Galilean satellites.
Fig. 8 compares estimates of variability and uncertainty in atmospheric density at aerocapture altitude for Earth, Mars, Titan, and Neptune. Variability includes effects that can be modeled, such as latitude, seasonal, and diurnal variations. Uncertainties include measurement uncertainty and residual uncertainty due to effects such as waves and turbulence which cannot be modeled in other than a statistical, or Monte Carlo, sense. For Titan, Fig. 8 shows measurement uncertainty both presently and as estimated after successful observations by Huygens entry probe and Cassini atmospheric soundings. Much of this reduction in uncertainty for Titan is expected to come from the in-situ measurements provided by the Huygens entry probe. Fig. 8 shows that combined variability-plus-uncertainty for Titan should be reduced to a level not much larger than combined variability-plus-uncertainty for Earth’s atmosphere.
5. Potential for future science missions to reduce atmospheric density uncertainty Scientific measurements of temperature–pressure profiles for Titan and the outer planets have a fairly small range of residual measurement uncertainty and they
ARTICLE IN PRESS C.G. Justus et al. / Planetary and Space Science 53 (2005) 601–605
have characterized fairly well the level of expected temperature variability due to effects such as latitude, season, and time-of-day. Nevertheless, small degrees of variability and uncertainty in temperature profiles can integrate to large levels of density variability and uncertainty, especially at high altitudes where aerocapture will occur. There is therefore considerable potential for science measurements of temperature, made on future missions to the outer planets, for significant improvement in the level of uncertainty in atmospheric density. These improvements can make for significant improvement in confidence levels and margin estimates for design of future missions that rely on aerocapture at these destinations.
6. Conclusions Atmospheric density and density scale height are important parameters for engineering applications such as aerocapture. Although variability and uncertainty of temperature versus pressure is fairly small for the outer planets and Titan, variability and uncertainty of atmospheric density is fairly large and increases exponentially with altitude. Relatively modest improvements in science measurements of temperature versus pressure made by future missions to the outer planets can produce significant reductions in atmospheric density uncertainty for these destinations.
Acknowledgements The authors gratefully acknowledge support from the NASA/Marshall Space Flight Center (MSFC) In-Space Propulsion Program. Particular thanks go to Bonnie James (MSFC), Manager of the Aerocapture Technol-
605
ogy Development Project, to Michelle M. Munk (LaRC/MSFC), Lead Systems Engineer for Aerocapture, and to Melody Herrmann (MSFC), team lead for the Titan/Neptune Systems Analysis study.
References Justus, C.G., Johnson, D.L., 1999. The NASA/MSFC global reference atmospheric model—1999 version (GRAM-99). NASA/TM-1999209630. Justus, C.G., Johnson, D.L., 2001. Mars global reference atmospheric model 2001 version (Mars-GRAM 2001) Users Guide. NASA/TM2001-210961. Justus, C.G., Duvall, A.L., Johnson, D.L., 2002. Mars-GRAM validation with mars global surveyor data. 34th COSPAR Scientific Assembly, Houston, Texas, Paper C3.3-0029-02. Justus, C.G., Duvall, A.L., Johnson, D.L., 2003a. Mars global reference atmospheric model (Mars-GRAM) and database for mission design. International Workshop on Mars Atmosphere Modeling and Observations, Granada, Spain. Justus, C.G., Duvall, A.L., Johnson, D.L., 2003b. Engineering-level model atmospheres for Titan and Neptune. AIAA 2003-4803, 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference. Justus, C.G., Duvall, A.L., Keller, V.W., 2003c. Engineering-level model atmospheres for Titan and Mars. International Workshop on Planetary Probe Atmospheric Entry and Descent Trajectory Analysis and Science, Lisbon, Portugal. Justus, C.G., Duvall, A.L., Johnson, D.L., 2004a. Earth global reference atmospheric model (GRAM-99) and trace constituents. Adv. Space Res. 34 (2004) 1731–1735. Justus, C.G., Duvall, A.L., Johnson, D.L., 2004b. Mars-GRAM validation with Mars Global Surveyor data. Adv. Space Res. 34 (2004) 1673–1676. Lockwood, M.K., 2003. Titan aerocapture systems analysis. AIAA 2003-4799, 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference. Tolson, R., 2001. Aerobraking in a constant density scale height atmosphere. Personal communication. Yelle, R.V., Strobel, D.F., Lellouch, E., Gautier, D., 1997. Engineering models for Titan’s atmosphere. In: Wilson, A. (Ed.), Huygens Science, Payload and Mission, SP-1177. European Space Agency.
Planetary and Space Science 53 (2005) 601–605 www.elsevier.com/locate/pss
Connecting atmospheric science and atmospheric models for aerocapture at Titan and the outer planets C.G. Justusa, Aleta Duvalla,, Vernon W. Kellerb, Thomas R. Spilkerc, Mary Kae Lockwoodd a
Morgan Research Corporation, EV13/Morgan, Marshall Space Flight Center, Huntsville, AL 35812, USA b NASA Marshall Space Flight Center, EV13, Marshall Space Flight Center, AL 35812, USA c Jet Propulsion Laboratory, Pasadena, CA 91109, USA d NASA Langley Research Center, Vehicle Analysis Branch, Hampton, VA 23681, USA Available online 12 February 2005
Abstract Many atmospheric measurement systems, such as the sounding instruments on Voyager, gather atmospheric information in the form of temperature versus pressure level. In these terms, there is considerable consistency among the mean atmospheric profiles of the outer planets Jupiter through Neptune, including Titan. On a given planet or on Titan, the range of variability of temperature versus pressure level due to seasonal, latitudinal, and diurnal variations is also not large. However, many engineering needs for atmospheric models relate not to temperature versus pressure level but atmospheric density versus geometric altitude. This need is especially true for design and analysis of aerocapture systems. Drag force available for aerocapture is directly proportional to atmospheric density. Available aerocapture ‘‘corridor width’’ (allowable range of atmospheric entry angle) also depends on height rate of change of atmospheric density, as characterized by density scale height. Characteristics of hydrostatics and the gas law equation mean that relatively small systematic differences in temperature versus pressure profiles can integrate at high altitudes to very large differences in density versus altitude profiles. Thus, a given periapsis density required to accomplish successful aerocapture can occur at substantially different altitudes ( 150–300 km) on the various outer planets, and significantly different density scale heights ( 20–50 km) can occur at these periapsis altitudes. This paper will illustrate these effects and discuss implications for improvements in atmospheric measurements to yield significant impact on design of aerocapture systems for future missions to Titan and the outer planets. Relatively small-scale atmospheric perturbations, such as gravity waves, tides, and other atmospheric variations can also have significant effect on design details for aerocapture guidance and control systems. This paper will discuss benefits that would result from improved understanding of Titan and outer planetary atmospheric perturbation characteristics. Details of recent engineering-level atmospheric models for Titan and Neptune will be presented, and effects of present and future levels of atmospheric uncertainty and variability characteristics will be examined. r 2005 Elsevier Ltd. All rights reserved. Keywords: Aerocapture; Global reference atmospheric model; Titan atmosphere; Titan-GRAM; Neptune atmosphere; Neptune-GRAM
1. Consistency of temperature–pressure profiles The outer planets, including the gas giants Jupiter, Saturn, Uranus, and Neptune, represent by far the leaststudied portion of the Solar System. The first satellites Corresponding author. Tel.: +1 256 544 6030; fax: +1 256 544 5754. E-mail address: [email protected] (A. Duvall).
0032-0633/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2004.12.002
to visit the outer Solar System, Pioneer 10 and 11, were designed to test the navigability of the asteroid belt and measure the strength of the magnetic and radiation environments around Jupiter. Voyager 1 and 2 made a collective sweep of the four gas giants during the period 1979–1989. Among many other findings, the twin Voyagers observed Jupiter and Neptune’s weather patterns and characterized the atmospheric composition of Saturn’s moon, Titan, through the use of on-board
ARTICLE IN PRESS C.G. Justus et al. / Planetary and Space Science 53 (2005) 601–605
infrared interferometer spectrometry (IRIS), ultraviolet spectrometry (UVS), and radio science (RS) instrumentation. Many atmospheric measurement systems, such as the sounding instruments on Voyager, still gather atmospheric information in the form of temperature versus pressure level. In these terms, there is considerable consistency among the mean atmospheric profiles of the outer planets Jupiter through Neptune, including Titan. In the present discussion, a simplified naming scheme is applied to the layers of a planet’s atmosphere, according to the behavior of temperature gradients. If the temperature gradients are steeper than the adiabatic gradient and temperature decreases with height above the 1-bar pressure level (or above the surface, for Titan), then this region is named the troposphere. The generally Outer Planets Temperature vs Pressure
Pressure, N/m2
Titan Uranus
102
Neptune
103 104 Jupiter 105 0
50
100 150 Temperature, K
200
250
Fig. 1. Measured profiles of temperature versus pressure on the outer planets and Titan.
Normalized Temperature versus Pressure
Pressure, N/m2
Saturn
Neptune
Jupiter Uranus
102 103
800
+/- factor of 1.19
+/- factor of 1.24 600 Minimum
Maximum
+/- factor of 1.20
400
+/- factor of 1.13
200
0 60
80
100
120 140 160 Temperature, K
180
200
220
Saturn
101
101
Range due to Latitude, Season, Time-of-Day, & Measurment Uncertainty
Fig. 3. Titan profiles of maximum and minimum expected temperature due to variations in latitude, season, time of day, and measurement uncertainty.
10-1 100
Titan Minimum and Maximum Temperature Profiles
Height, km
602
Titan
104
105 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Temperature Ratio [T(p)/T(1 bar) or T(p)/T(surface)] Fig. 2. Measured temperature profiles normalized by temperature at 1-bar level (or at surface for Titan).
isothermal region overlying the troposphere is named the mesosphere. The name mesopause is assigned to the region of increasing temperature with height which represents the interface between the mesosphere and the thermosphere. Fig. 1 shows consistency of temperature profiles in the mesopauses (100–0.1 N=m2 pressure levels) of the outer planets and Titan. To remove the steady trend toward lower temperatures as distance from the Sun increases, temperature can normalized by temperature at the surface for Titan, or at the 1-bar pressure level for the gas giants. After such normalization, Fig. 2 indicates considerable consistency of temperature profiles in the tropospheres and mesospheres (surface/1-bar level to 1000 N=m2 ) of the outer planets and Titan. On a given planet or on Titan, the range of variability of temperature versus pressure level (or temperature versus altitude) due to seasonal, latitudinal, and diurnal variations is also not large. For example, Fig. 3 illustrates that the range of temperature variation expected on Titan, due to effects of latitude, season, and time of day (plus measurement uncertainty) is at most about a factor of 1.24 above or below the mean temperature. The model atmospheres in Fig. 3 were developed for engineering purposes as conservative bounds on temperature variation; Yelle et al. (1997) provide a detailed discussion of the uncertainties incorporated in these models.
2. Engineering needs for atmospheric density Many engineering needs for atmospheric models relate not only to temperature versus pressure level but
ARTICLE IN PRESS C.G. Justus et al. / Planetary and Space Science 53 (2005) 601–605
3. Range of density and density scale height values at aerocapture For qualitative discussion of aerocapture design parameters, therefore, it is instructive to treat the Titan Minimum and Maximum Density Profiles Range due to Latitude, Season, Time-of-Day, & Measurment Uncertainty
+/- factor of 12.66
800
+/- factor of 6.16
Height, km
600
+/- factor of 2.73 400
Gas Giants Atmospheric Density 800 700 600 Height, km
also to atmospheric density versus geometric altitude (in the present discussion, ‘‘density’’ refers everywhere to mass density rather than number density). This need is especially true for design and analysis of aerocapture systems. Aerocapture differs from aerobraking in that it relies on a single pass, rather than multiple passes, through a planetary atmosphere to remove enough energy from the satellite’s trajectory to change it from hyperbolic to elliptical with respect to the planet. Some of the key assumptions inherent in classical aerobraking theory fail when applied to aerocapture; a case in point is the well-known ‘‘square root of scale height’’ law. This relation states that the integral of density with respect to time over an aerobraking pass is proportional to the square root of the scale height and inversely proportional to the square root of the eccentricity (Tolson, 2001). Derivation of the ‘‘square root of scale height’’ law is based on the inherent assumption that scale height remains constant over the duration of the pass. For aerocapture this assumption is invalid; an aerocapture pass may span multiple scale heights in order to remove the energy associated with typically high atmospheric entry velocity. In a recent Titan aerocapture systems analysis study, for example, Lockwood (2003) utilized reference values of 6.5 km/s for entry velocity, 36 for nominal entry flight path angle, and 200–400 km for aerocapture altitude range.
603
500
Saturn Aerocapture Density
Neptune
400 Jupiter 300 200
Uranus
100 0 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 Density, kg/m3 Fig. 5. Profiles of mean density versus height for the gas giant planets. Vertical dashed line shows typical aerocapture periapsis density.
concepts of density and density scale height separately. Drag force available for aerocapture is directly proportional to atmospheric density. Characteristics of hydrostatics and the gas law equation mean that relatively small systematic differences in temperature versus pressure profiles, such as those illustrated in Fig. 3, can integrate at high altitudes to very large differences in density versus altitude profiles. This fact is shown in Fig. 4, which shows the range of expected density variability and uncertainty for Titan’s atmosphere increasing exponentially from a factor of 1.67 at 200 km altitude to a factor of 12.66 at 800 km altitude. The corresponding range of variability in atmospheric drag on an aerocapture vehicle is an important design consideration for on-board guidance systems. In a similar fashion, despite the consistency among the outer planets for temperature versus pressure (shown in Figs. 1 and 2), there is a wide range of variability among the planets in their mean profiles of density versus altitude, as shown by Fig. 5. Fig. 5 indicates that a given periapsis density required to accomplish successful aerocapture can occur at substantially different altitudes ( 150–300 km) on the various outer planets. For a stratified atmosphere, density scale height H as a function of altitude z is defined as HðzÞ ¼ ðrðzÞÞ=ðdrðzÞ=dzÞ,
200
+/- factor of 1.67
0 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 Density, kg/m3 Fig. 4. Titan profiles of maximum and minimum expected atmospheric density due to variations in latitude, season, time of day, and measurement uncertainty.
(1)
where rðzÞ is density at height z: Density scale height represents the height rate of change of atmospheric density. Fig. 6 shows that density scale height at aerocapture altitudes varies from about H ¼ 20 –50 km for the outer planets and Titan. Available aerocapture ‘‘corridor width’’ (allowable range of atmospheric entry angle) depends on density scale height. Thus, significant differences in available aerocapture corridor width are expected for these destinations.
ARTICLE IN PRESS C.G. Justus et al. / Planetary and Space Science 53 (2005) 601–605
604
Variablity We Can Model (season, latitude, etc.) Measurement Uncertainty (Big improvement for Titan after Huygens/Cassini) Residual Uncertainty (Monte-Carlo-modeled waves, turbulence, etc.)
Density Scale Height Comparison 400 350
Neptune A
Height, km
300
Titan
Jupiter
250
A Titan
200
Mars
A 150
A Neptune
100
Earth Titan 0 A = Aerocapture Altitude
10
20 30 40 50 Variation, % of Mean
60
70
50 Saturn 0 0
10
20
30 40 50 60 70 80 Density Scale Height, km
90
100
Fig. 6. Profiles of mean density scale height versus altitude for the gas giant planets. Typical altitudes and density scale heights for aerocapture are shown by letter A.
Sample Neptune-GRAM monte-Carlo Density Output 300
Height, km
250
Fminmax = -1
Fminmax = 0
Fminmax = 1
200
Fig. 8. Approximate variability and uncertainty in density at aerocapture altitude for Neptune, Titan, Mars, and Earth. Titan variability and uncertainty are shown for current conditions and postCassini/Huygens.
Fig. 7 provides example simulations of these high frequency perturbations from the Neptune Global Reference Atmospheric Model (Neptune-GRAM). Neptune-GRAM is one of series of atmospheric models entitled the GRAM series, developed by NASA Marshall Space Flight Center (Justus et al., 2002, 2003a–c; Justus et al., 2004a,b; Justus and Johnson, 1999, 2001).
150
4. Summary of atmospheric density variability and uncertainty
100 50 0 -100
-50 0 50 100 150 200 250 Perturbed Density (% from Neptune Average)
Fig. 7. Simulated ‘‘high-frequency’’ perturbations about Neptune minimum ðF minmax ¼ 1Þ; average ðF minmax ¼ 0Þ; and maximum ðF minmax ¼ 1Þ density profiles (perturbations expressed as percent deviation from average density).
Relatively small-scale, ‘‘high-frequency’’ atmospheric perturbations, such as gravity waves, tides, and other atmospheric variations, can also have significant effect on design details for aerocapture guidance and control systems. Ability to successfully aerocapture into highly eccentric orbits can depend significantly on details of such high-frequency perturbations. For highly eccentric orbits there may be only a small margin for error between successful aerocapture and ‘‘skip-out’’ conditions in which no aerocapture is achieved. Ability to aerocapture into highly eccentric orbits can be an important aspect for designing missions such as a Neptune orbiter that can visit Triton, or a Jupiter orbiter that can visit the Galilean satellites.
Fig. 8 compares estimates of variability and uncertainty in atmospheric density at aerocapture altitude for Earth, Mars, Titan, and Neptune. Variability includes effects that can be modeled, such as latitude, seasonal, and diurnal variations. Uncertainties include measurement uncertainty and residual uncertainty due to effects such as waves and turbulence which cannot be modeled in other than a statistical, or Monte Carlo, sense. For Titan, Fig. 8 shows measurement uncertainty both presently and as estimated after successful observations by Huygens entry probe and Cassini atmospheric soundings. Much of this reduction in uncertainty for Titan is expected to come from the in-situ measurements provided by the Huygens entry probe. Fig. 8 shows that combined variability-plus-uncertainty for Titan should be reduced to a level not much larger than combined variability-plus-uncertainty for Earth’s atmosphere.
5. Potential for future science missions to reduce atmospheric density uncertainty Scientific measurements of temperature–pressure profiles for Titan and the outer planets have a fairly small range of residual measurement uncertainty and they
ARTICLE IN PRESS C.G. Justus et al. / Planetary and Space Science 53 (2005) 601–605
have characterized fairly well the level of expected temperature variability due to effects such as latitude, season, and time-of-day. Nevertheless, small degrees of variability and uncertainty in temperature profiles can integrate to large levels of density variability and uncertainty, especially at high altitudes where aerocapture will occur. There is therefore considerable potential for science measurements of temperature, made on future missions to the outer planets, for significant improvement in the level of uncertainty in atmospheric density. These improvements can make for significant improvement in confidence levels and margin estimates for design of future missions that rely on aerocapture at these destinations.
6. Conclusions Atmospheric density and density scale height are important parameters for engineering applications such as aerocapture. Although variability and uncertainty of temperature versus pressure is fairly small for the outer planets and Titan, variability and uncertainty of atmospheric density is fairly large and increases exponentially with altitude. Relatively modest improvements in science measurements of temperature versus pressure made by future missions to the outer planets can produce significant reductions in atmospheric density uncertainty for these destinations.
Acknowledgements The authors gratefully acknowledge support from the NASA/Marshall Space Flight Center (MSFC) In-Space Propulsion Program. Particular thanks go to Bonnie James (MSFC), Manager of the Aerocapture Technol-
605
ogy Development Project, to Michelle M. Munk (LaRC/MSFC), Lead Systems Engineer for Aerocapture, and to Melody Herrmann (MSFC), team lead for the Titan/Neptune Systems Analysis study.
References Justus, C.G., Johnson, D.L., 1999. The NASA/MSFC global reference atmospheric model—1999 version (GRAM-99). NASA/TM-1999209630. Justus, C.G., Johnson, D.L., 2001. Mars global reference atmospheric model 2001 version (Mars-GRAM 2001) Users Guide. NASA/TM2001-210961. Justus, C.G., Duvall, A.L., Johnson, D.L., 2002. Mars-GRAM validation with mars global surveyor data. 34th COSPAR Scientific Assembly, Houston, Texas, Paper C3.3-0029-02. Justus, C.G., Duvall, A.L., Johnson, D.L., 2003a. Mars global reference atmospheric model (Mars-GRAM) and database for mission design. International Workshop on Mars Atmosphere Modeling and Observations, Granada, Spain. Justus, C.G., Duvall, A.L., Johnson, D.L., 2003b. Engineering-level model atmospheres for Titan and Neptune. AIAA 2003-4803, 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference. Justus, C.G., Duvall, A.L., Keller, V.W., 2003c. Engineering-level model atmospheres for Titan and Mars. International Workshop on Planetary Probe Atmospheric Entry and Descent Trajectory Analysis and Science, Lisbon, Portugal. Justus, C.G., Duvall, A.L., Johnson, D.L., 2004a. Earth global reference atmospheric model (GRAM-99) and trace constituents. Adv. Space Res. 34 (2004) 1731–1735. Justus, C.G., Duvall, A.L., Johnson, D.L., 2004b. Mars-GRAM validation with Mars Global Surveyor data. Adv. Space Res. 34 (2004) 1673–1676. Lockwood, M.K., 2003. Titan aerocapture systems analysis. AIAA 2003-4799, 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference. Tolson, R., 2001. Aerobraking in a constant density scale height atmosphere. Personal communication. Yelle, R.V., Strobel, D.F., Lellouch, E., Gautier, D., 1997. Engineering models for Titan’s atmosphere. In: Wilson, A. (Ed.), Huygens Science, Payload and Mission, SP-1177. European Space Agency.