The Insolation at Pluto E. VAN H E M E L R I J C K

ICARUS 52, 560--564 (1982)

The Insolation at Pluto E. VAN H E M E L R I J C K

Belgian Institute for Space Aeronomy, 3, Avenue Circulaire, B-1180, Brussels, Belgium R e c e i v e d M a y 11, 1982; revised A u g u s t 6, 1982

Calculations o f the daily solar radiation incident at the top o f P l u t o ' s a t m o s p h e r e a n d its variabil- ity with latitude and s e a s o n and o f the latitudinal variation o f the m e a n a n n u a l daily insolation are p r e s e n t e d . T h e large eccentricity o f Pluto p r o d u c e s significant n o r t h - s o u t h s e a s o n a l a s y m m e t r i e s in the daily insolation. A s for U r a n u s , having a similarly large obliquity, the e q u a t o r receives less annual average energy t h a n the poles.

1. I N T R O D U C T I O N

The upper-boundary insolation of the at- mospheres of the outer planets, excluding Pluto, has been computed by, e.g., Voro- b'yev and Monin (1975) and Levine et al.

(1977). To the best of our knowledge, simi- lar calculations for Pluto have never been published, mainly due to the fact that the angle between the planet's spin axis and its orbit normal (G) is very poorly determined (Davies et al., 1980).

In spite of the fact that the obliquity (G) of Pluto is so questionable, we calculated the solar radiation incident on the planet for three fixed values of G ranging from 60 ° (An- dersson and Fix, 1973) over 75 ° (Golitsyn, 1979) to 90 ° ( H a n d b o o k o f the British A s - tronomical Association, 1981). The results illustrate the sensitivity of the daily and of the annual average insolation to changes in the obliquity.

First, we briefly discuss the calculation of the planetocentric longitude of Pluto's perihelion (hp). Then, the daily insolation and the mean annual daily insolation are considered.

For the methods of calculation we refer to Ward (1974), Vorob'yev and Monin (1975), Levine et al. (1977), Van Hemelri- jck and Vercheval (1981), and Van He-

melrijck (1982a, b).

0019-1035/82/120560-05 $02.00/0 Copyright © 1982 by Academic Press. Inc.

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2. P L A N E T O C E N T R I C L O N G I T U D E O F P L U T O ' S P E R I H E L I O N

The position of perihelion (hp) for the planets in the solar system, except for Pluto, is given by Melbourne et al. (1968), Vorob'yev and Monin (1975), and Levine et al. (1977). It may be written in terms of the heliocentric longitude of the planet's peri- helion (~r0) and the heliocentric longitude of the ascending node (fl0) as

)kp = 71" 0 -- ~'~0 + A, (1) where A is the planetocentric longitude of the ascending node altered by 180 °. A de- tailed description of the procedure to calcu- late A is beyond the scope of the present work. However, A can be obtained from standard spherical trigonometric relation- ships (Vorob'yev and Monin, 1975). It is dependent upon several orbital and plane- tary data and can be expressed in the gen- eral form

A = f ( i , l)0, 7r0, G, G0, ct0, 80), (2) where i, G0, or0, and 80 are, respectively, the inclination to the ecliptic, the obliquity of the Earth's equator (G0 = 23.°45), and the right ascension and declination of Pluto's north pole. For the direction of the north pole, we adopted the recommended values published by the IAU Working Group on

56O

INSOLATION AT PLUTO TABLE I

ADOPTED PLANETARY DATA FOR PLUTO

561

i a [1o ° ~ro a ao b ~o b aC e a T ° To e

(o) (o) (o) (o) (o) (AU) (Earth days) (Earth days)

17.14 109.51 222.50 305 5 39.72 0.2523 6.3867 90583

a Data drawn from Seidelmann et al. (1980).

b Data drawn from Davies et al. (1980).

Data drawn from Golitsyn (1979).

cartographic c o o r d i n a t e s and rotational ele- m e n t s of the planets and satellites (Davies e t al., 1980).

T h e a d o p t e d p l a n e t a r y data are given in Table I, w h e r e a o , e, T, and To signify, re- spectively, the s e m i m a j o r axis, the eccen- tricity, the sidereal d a y , and the tropical year. T h e results o f the calculations are r e p r e s e n t e d in Table II, w h e r e o n e c a n also find the length o f the s e a s o n s (Ts and Tw) for the three obliquities u n d e r consider- ation. It c a n be seen that hp is only w e a k l y d e p e n d e n t on •.

3. D I S C U S S I O N O F C A L C U L A T I O N 3 . 1 . D a i l y I n s o l a t i o n

F o r the daily insolation, we followed the m e t h o d a d o p t e d b y V o r o b ' y e v and Monin (1975) and L e v i n e et al. (1977) in presenting o u r results in the f o r m o f a c o n t o u r m a p giving the seasonal distribution in t e r m s o f the planetocentric longitude o f the Sun t a k e n to be 0 ° at the n o r t h e r n h e m i s p h e r e vernal equinox. In addition, we included t w o figures showing the latitudinal variation of the daily insolation at the e q u a t o r and the poles as a function of solar longitude. T h e isopleth for • = 75 ° is illustrated in Fig. 1 and the equatorial and polar distributions are plotted in Figs. 2 and 3.

F r o m the c o n t o u r m a p and particularly f r o m Figs. 2 and 3 it follows that the maxi- m u m solar radiation is incident at the poles with values o f a b o u t I I to 13 cal c m -2 (plan- etary day) -1 (north pole) and 13.5 to 15.5 cal c m -2 (planetary day) -~ (south pole). T h e m a x i m u m difference b e t w e e n the p e a k in- solations attains a p p r o x i m a t e l y 20%; the

n o r t h - s o u t h seasonal a s y m m e t r i e s are pro- duced b y the large eccentricity o f P l u t o ' s orbit. M o r e o v e r , it is found that o v e r prac- tically the entire Pluto y e a r the polar insola- tion is greater than that at the equator.

T h e c o n t o u r m a p and especially Fig. 3 reveal that the position o f m a x i m u m solar radiation is shifted, b y a b o u t 20 ° , f r o m the position o f s u m m e r solstices. This is due to the fact that the perihelion position (hp

190 ° ) is located a p p r o x i m a t e l y 80 ° f r o m the south s u m m e r solstice. F r o m Fig. 3 it can be seen that the m a x i m u m insolations o c c u r n e a r 1 l0 and 250 °.

It is e a s y to show that, at s u m m e r sol- stice, the polar daily insolation e x c e e d s that o f the e q u a t o r for • > 17.°7 (all planets ex- cept Jupiter). F o r Pluto, the ratio o f b o t h insolations a m o u n t s to a b o u t 5.4, 11.7, and infinity (in this case the Sun d o e s not rise at s u m m e r solstice), r e s p e c t i v e l y , for obliqui- ties equal to 60, 75, and 90 ° .

T h e global latitudinal redistribution caused mainly b y the change in the obli- quity is also illustrated in Figs. 2 and 3. It can be seen that the polar insolation in- creases with increasing obliquity, this gain being a c c o m p a n i e d b y a c o r r e s p o n d i n g de- crease of the equatorial solar radiation.

T A B L E II

COMPUTED PLANETARY DATA FOR PLUTO

~,p Ts Tw

(o) (o) (Earth days) (Earth days)

60 192.17 48,455 42,128

75 191.12 48,187 42,396

90 190.81 48,108 42,475

"• ^2¢

C 8

-20

- ~ 0

- 6 0

- 8 0

0 40 80 120 160 2 0 0 240 2 8 0 320 3 6 0

S O L A R LONGITUDE ( d e g r e e s , )

FIG. 1. Seasonal and latitudinal variation of the daily insolation at the top of the atmosphere of Pluto for an obliquity e = 75 °. Solar declination is represented by the dashed line. The areas o f p e r m a n e n t darkness are shaded. Values o f the daily insolation, in cal c m -2 (planetary day) 1, are given on each curve.

7 [ I I I I I I i I [ I 1 l I I I 1

5 ,o '7 E

v 4

8

_z

c~ 2

t / t //

/// t . . E = e 0 . , /j

= 9 0

E Q U A T O R

\

0 40 80 120 160 2 0 0 240 2 8 0 320 3 6 0

S O L A R L O N G I T U D E ( d e g r e e . s )

Fro. 2. Seasonal variation of the daily insolation at the equator of Pluto for various values of the obliquity.

562

INSOLATION AT PLUTO 563

16

1/4

12 C

'uE 10 u

~8

_z

>, 6

N O R T H POLE

E=90

,

t I

/ I

:=90

:'% t ' "\

SOUTH POLE

0 40 80 120 160 200 240 280 320 360

SOLAR LONGITUDE (degrees)

FIG. 3. Seasonal variation of the daily insolation at the poles of Pluto for various values of the obliquity.

Comparison of Fig. 1 with the isopleths for ~ = 60 and 90 ° (not represented in this paper) reveals that the general pattern of those three contour maps is only slightly different. In the solar longitude interval (~r/

2-3xr/2) and especially at equatorial and midlatitudes the isocontours closely paral- lel the seasonal march of the Sun. In the region where the Sun does not set, the shape of the lines of constant daily insola- tion is roughly similar, although shifted with respect to the summer solstices, to the curve limiting the area of permanent sun- light. Furthermore, the isopleths illustrate that for nearly half the Pluto year some parts of the planet are in darkness. It is evi- dent that the zone where the Sun does not rise increases with increasing obliquity.

Uranus and Pluto rotate lying practically on their sides in the orbital planes. In the polar regions the day and the night are ap-

proximately half a year long and the Sun is close to the zenith midway through the sun- lit half of the year. Summer and winter are, roughly speaking, repeated twice a year in the equatorial region, the two seasons being substantially more temperate than in the polar regions. This phenomenon is demon- strated in Fig. 2 (contrast this diagram with Fig. 3).

3.2. Mean Annual Daily Insolation

The latitudinal variation of the mean daily insolation taken over a year is given in Fig. 4.

For the outer planets, there exists a criti-

cal obliquity (e ~ 54 °) (Ward, 1974; Voro-

b'yev and Monin, 1975; Toon et al., 1980)

past which the equator receives less annum

average energy than the poles. This situa-

tion is not only realized by Uranus but also

by Pluto when assuming that ~ is equal to or

564 E. VAN HEMELRIJCK

80

60

40

~ 2O

0

,~ -20 ._1

-40

-60

-80

T

/ /,

E = 90 75 60 f f

MEAN ANNUAL DALLY INSOLATION [ c o l cm-2(doy) -1 ]

FIG. 4. Latitudinal variation of the mean annual daily insolation at the top of the atmosphere of Pluto for various values of the obliquity.

larger than 60 ° . This phenomenon is evident from Fig. 4. The ratio of both insolations amounts to about 0.9 (~ = 60°), 0.7 (~ = 75°), and 0.6 (~ = 90°).

From Fig. 3 it follows that the daily inso- lation at the south pole during summer sol- stice is appreciably higher than that of the north pole at its summer solstice. On the other hand, Fig. 4 indicates that the hemi- spheric seasonal a s y m m e t r y in the solar ra- diation disappears when averaging the in- coming solar energy over the year. This is explained by observing that the length of the northern summer (Ts) (Table II) is longer than the length of the southern sum- mer (Tw).

In conclusion, we believe the calcula- tions presented in this work could help in studies of the radiation and energy budget of Pluto.

ACKNOWLEDGMENTS

We particularly thank Dr. V. K. Abalakin and Dr.

M. E. Davies for bringing the Report of the IAU

Working Group on cartographic coordinates and rota- tional elements of the planets and satellites to our at- tention. We are grateful to Dr. J. Vercheval and Dr.

M. Scherer for clarifying discussions and to the anony- mous referees for their helpful comments and con- structive criticisms. The careful drawings of J. Sch- mitz are also very much appreciated.

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