inner solar system - terrestrial planets

Inner Solar System - Terrestrial Planets

Exterior/Atmosphere: 3 Ways to Gain

Exterior/Atmosphere: 5 Ways to Lose

Atmospheric Heating:

Exosphere

ThermosphereIonosphere

Stratosphere

Troposphere

X-ray UV visible

Ground

infrared

The Sun-Planet Connection: Radiation• Light (bulk of energy)• Most photons make it out

Not stopped (absorbed),Not reflectedNot altered (change frequency)Do not decay

• Total luminosity of Sun is uniformly spread over surface area of sphere at each radius.

sfrequencieofproportionSamed

LI

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π=

d

The amount of solar radiation energy per unit area received by a planet is inversely proportional to the square of its distance from the sun.

When we discussed the black-body spectrum of light that a heated object gives off, we mentioned the Stefan-Boltzmann law.

This law states that the amount of energy radiated by an opaque object (a “black body”) is proportional to its temperature, T, raised to the fourth power. That is, it is proportional to T×T×T×T = T 4

This radiated energy does not count any radiation that is shining on the object and is simply reflected by it.

These considerations together imply that a planet’s surface will heat up until its temperature T is so high that its “black body” radiation into space just balances the radiant heat energy it receives (and does not simply reflect) from the sun.

2Rπ

Area of disk

R

Disk

Sun

Planet

202

4 dLRπ

π

Area of disk

IncomingRadiantIntensity

R

DiskDistance d to the Sun

Planet

Pad

LR =− )1(4 2

02

ππ

Area of disk

IncomingRadiantIntensity Reflection Power

R

Disk

Planet

22

02 4)1(4

Rad

LR ππ

π −

Area of disk Area onSphere

IncomingRadiantIntensity Reflection

R R

Disk Sphere

Planet

R R

Disk Sphere

T

422

02 4)1(4

TRad

LR σππ

π =−



OutgoingRadiantIntensity perUnit Area

Reflection

422

02 4)1(4

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OutgoingRadiantIntensity perUnit Area

Reflection

R R

Disk Sphere

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aT −T

•T=Eff. Temp. where rad. escapes

This balance of radiant energy received from the sunand reradiated as a “black body” into space determines the temperature of a planet’s surface.

But we have to be careful here.

The “surface” of the planet in this case is the place where the planet’s thermal radiation can escape into space.

This might not be the surface that you would walk on.

If the planet has an atmosphere, this surface where the heat radiation escapes into space could be very high in the atmosphere.

(In this same sense the sun has a surface, although the sun is gas all the way to the core, and there is no part of it that is solid.)

The surface where heat radiation escapes from a planet will be high in the atmosphere if the atmosphere is opaque to that thermal radiation.

The radiation striking a planet from the sun is pretty close to the black body spectrum for an object of temperature 5800 °K.

Thus sunlight is concentrated mostly in the part of the electro-magnetic spectrum that our eyes respond to (that we see).

But the temperature for a planet’s surface that would give enough black body radiation into space to balance this incident sunlight is very much smaller than the sun’s 5800 °K.

For Mars, Venus, and Earth, this balancing surface temperature ranges between 200 and 270 °K.

Black body radiation from objects at these temperatures is concentrated in the infrared portion of the electromagnetic spectrum, a part of the spectrum our eyes cannot see.

The atmosphere of the planet Venus strongly absorbs such infrared radiation, and does not let it pass through. Therefore it can be radiated into space only from near the top of the atmosphere, where there is hardly any absorbing gas.

The atmosphere of Venus therefore acts like a greenhouse by trapping warmth from the sun inside.

About 70% of the sunlight striking Venus is reflected back into space.

Most of the remaining 30% of the light passes through the atmosphere without being reflected or absorbed.

This sunlight is absorbed by the surface of the planet, and its energy is converted into heat.

The heated surface of the planet warms the atmosphere in contact with it by thermal conduction.

The infrared thermal radiation from the surface is absorbed in the lower atmosphere, which is warmed by it.

This heated gas near the surface rises, and cools as it expands on its ascent into lower pressure and lower density regions.

Throwing on the Blankets

Greenhouse effect in TroposphereGround

infrared

T

T-dT

T-2*dT

T-3*dT

T-4*dT

net

Rad.Escapes

Mars Earth Venus

Rad.Escapes

T TT

Atmospheric temperature

profiles

The atmosphere above the surface therefore gets steadily cooler with height.

It also gets steadily more rarefied with height.Eventually, at some height above the surface, the gas density is

so low that this gas can no longer absorb the infrared thermal radiation coming from the denser gas below.

Here, high in the atmosphere, the thermal radiation of the planet finally escapes into space.

The temperature at this level must be high enough so that the thermal radiation associated with that temperature will balance the heat energy absorbed from sunlight by the planet.

This is the temperature the surface of the planet would have if there were no atmosphere. But this temperature develops high in the atmosphere, and it is much hotter at the bottom of the atmosphere (on the solid surface).

An aside: It is worthwhile to contrast the above arguments about the greenhouse effect for a planet like Venus with the earlier discussion about cooling of such a planet’s interior.

The surface (solid surface, that is) of Venus is raised in temperature by the greenhouse effect that its atmosphere produces. Thus this surface temperature is about 700° K rather than the 270° K or so that it would be, on average, without the atmosphere.

This greenhouse effect therefore can reduce the cooling of the interior. Clearly, without an atmosphere, the interior of Venus would ultimately cool to about 270° K, while with the atmosphere it will not cool below about 700° K.

This difference is a factor of about 2, which may seem big, but compared to the original temperature of the Venutian interior, which was thousands of degrees, far above the melting point of rock, both of the above surface temperatures are small.

Our earlier remarks about cooling of a terrestrial planet by a combination of convection and conduction ignored any surface heating from the sun.

The reason we ignored this is that this is a very small effect near the beginning, when the surface temperature is thousands of degrees, the whole planet is molten, and much more heat reaches the surface from the interior than from the exterior (in the form of sunlight).

Very late in the cooling process, when the interior begins to approach the temperature to which sunlight is able to heat up the surface, solar heating will begin to matter.

A greenhouse effect can make the solar heating of the surface more efficient by trapping more of the sun’s radiant energy, but this will not make any appreciable difference until quite late in the cooling process.

The atmosphere affects how much solar heat is captured at the solid surface of the terrestrial planet, but it has almost no effect upon how much interior heat is escaping from this surface until the interior cools down so far that its temperature becomes comparable to the surface temperature.

It is tempting to make an analogy of the cooling of a planet like Venus to the cooling of a house in a Minnesota winter. Roughly speaking, we can say that the temperature of the planet’s deep interior corresponds to the temperature of the house, as determined by the thermostat setting at the house’s center.

The house will cool partly by conduction to the outside air, with which its outer walls and windows are in contact, and also partly by radiating infrared black body radiation into the air. If there is any appreciable wind, the thin layer of outside air that is heated by contact with the house will be quickly blown away, so that the outside air temperature will not rise.

For Venus, the “air” temperature that is in contact with the solid surface of the planet is always near 740° K, a value that is constantly maintained by solar heating together with motion of the atmosphere from the illuminated to the dark side of the planet.

Like the walls of the house, the surface of Venus can cool by heating the atmosphere by contact through conduction and also by emitting energy in the form of black body radiation. But now we encounter a significant difference. The air outside the house will let the radiation travel quite far, especially in winter, when little water is in the atmosphere. In contrast, infrared radiation from the surface of Venus does not get far in the thick atmosphere mostly composed of CO2.

Thus it does not matter for Venus whether radiation or conduction is the more important process of heat loss for the surface, the “ambient” temperature that the surface sees at present is the 740° K or so established by solar heating.

We all know that a house will cool only when the outside is cooler than the inside, and it will cool faster when this temperature difference is larger.

To cool at all, the interior of Venus must heat the surface above the temperature that the sun’s radiation could maintain with no help from heat escaping from the interior.

Early on, the surface of Venus must have been very hot indeed, even molten. It must have radiated more black body energy into space than it received from the sun in this early era.

The cooling rate for the planet’s interior can only have been influenced appreciably by the solar heating (and the greenhouse effect) when the surface temperature had cooled to close to the value that solar heating can maintain. The flow of heat outward from the deep interior would then be somewhat less than would occur if the surface temperature could have cooled to 270° rather than 740° K.

The cooling rate for the planet’s interior can only have been influenced appreciably by the solar heating (and the greenhouse effect) when the surface temperature had cooled to close to the value that solar heating can maintain. The flow of heat outward from the deep interior would then be somewhat less than would occur if the surface temperature could have cooled to 270° rather than 740° K.

Here the analogy with the house is helpful. With an atmosphere and a greenhouse effect, the ambient temperature of the “outside air” for Venus is about 740° K rather than 270° K. This will make a big difference to the rate at which heat is lost from the interior of Venus only when the temperature difference between the center and surface of Venus begins to approach a few hundred degrees K, which would then be comparable to the difference between the 740 and 270 °K. We think that this has not yet happened.

The atmosphere thus affects the heat received from the sun but not the heat escaping from the interior to any appreciable degree, so long as the interior is much hotter than the surface.

Cooling from the hot interior can also be nonuniform. It can be concentrated in regions of volcanic activity or in upwelling material where new planetary surface is being created.

For Venus, its interior cooling to the present time is thought to have been determined largely by its size, and only to a minor degree from the amount of solar heating it receives, even accounting for its atmospheric greenhouse effect.

How an actual greenhouse works:Sunlight passes through the panes of glass in the roof of a

greenhouse without being reflected or absorbed.The sunlight is absorbed by the plants and the floor of the

greenhouse, and its energy is converted into heat.The heated plants and floor in the greenhouse make the air in the

greenhouse warm by thermal conduction.If this heated air were not confined in the greenhouse, it would

rise, and cooler air would descend to replace it.The greenhouse roof keeps the heated air in, so the greenhouse

stays warm.This mechanism for trapping solar heat is actually different from

the “greenhouse effect” in the atmosphere of a planet.

No-Atmosphere Surface Temp

050

100150200250300350400450

0 0.5 1 1.5 2

Orbital Radius [AU]

Surf

ace

Tem

pera

ture

[K]

(albedo = 0.5)

Mercury Venus Earth Moon Mars

42

)1(~d

aT −

Surface T Corrected for Albedo

050

100150200250300350400450500

0 0.5 1 1.5 2

Orbital Radius [AU]

Surf

ace

Tem

pera

ture

[K]

Mercury0.11

Venus0.72

Earth Moon0.36 0.07

Mars0.25

42

)1(~d

aT −

Observed Surface Temperatures

0100200300400500600700800

0 0.5 1 1.5 2

Orbital Radius [AU]

Surf

ace

Tem

pera

ture

[K]


Surface Temperature Ranges

0100200300400500600700800

0 0.5 1 1.5 2

Orbital Radius [AU]

Surf

ace

Tem

pera

ture

[K]


Mercury & Moon:•Little Atmosphere•Slow Rotation


0100200300400500600700800

0 0.5 1 1.5 2

Orbital Radius [AU]

Surf

ace

Tem

pera

ture

[K]


Venus:•Thick atmosphere•Slow rotation•Slow winds


0100200300400500600700800

0 0.5 1 1.5 2

Orbital Radius [AU]

Surf

ace

Tem

pera

ture

[K]


Earth & Mars:•Thin to medium Atmosphere•Rotation•Strong winds

inner solar system - terrestrial planets

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