Temperatures at Mercury Orbit

sorry if this is a repeat post...

How hot would a nearly ideal black body object get in Mercury orbit?

I've read that Mercury's daytime temperatures can spike to 800F, but my
calculation for average temperatures at Mercury orbit was 440K/328F.
Mike Miller, Materials Engineer

In article .com,
wrote:
How hot would a nearly ideal black body object get in Mercury orbit?

Mercury's average distance from the Sun is about 0.39 Earth's, so by the
inverse-square law, a black body gets about 6.6x as much solar energy.
However, energy radiated as heat is proportional to the fourth power of
temperature, so temperature only needs to rise to 1.6x to match this.
However however, that's *absolute* temperature, so a black body's
temperature goes from around 300K at Earth to around 480K at Mercury,
i.e. from around room temperature to around 200degC.

Caution, I oversimplify in several ways. Inverse square is not exactly
right for a source of finite size and this effect is not negligible for
Mercury; Mercury's orbit is noticeably elliptical and the semimajor axis
is not really the average distance; and most important, Mercury is not an
ideal black body in several ways, and that can make a big difference.

I've read that Mercury's daytime temperatures can spike to 800F, but my
calculation for average temperatures at Mercury orbit was 440K/328F.

See above. Your calculation's certainly in the right ballpark and is
probably correct, but it's for an oversimplified model.
--
"Think outside the box -- the box isn't our friend." | Henry Spencer
-- George Herbert |

"Henry Spencer" wrote in message
...
In article .com,
wrote:
How hot would a nearly ideal black body object get in Mercury orbit?

Mercury's average distance from the Sun is about 0.39 Earth's, so by the
inverse-square law, a black body gets about 6.6x as much solar energy.
However, energy radiated as heat is proportional to the fourth power of
temperature, so temperature only needs to rise to 1.6x to match this.
However however, that's *absolute* temperature, so a black body's
temperature goes from around 300K at Earth to around 480K at Mercury,
i.e. from around room temperature to around 200degC.

Caution, I oversimplify in several ways. Inverse square is not exactly
right for a source of finite size and this effect is not negligible for
Mercury; Mercury's orbit is noticeably elliptical and the semimajor axis
is not really the average distance; and most important, Mercury is not an
ideal black body in several ways, and that can make a big difference.

I've read that Mercury's daytime temperatures can spike to 800F, but my
calculation for average temperatures at Mercury orbit was 440K/328F.

See above. Your calculation's certainly in the right ballpark and is
probably correct, but it's for an oversimplified model.
--
"Think outside the box -- the box isn't our friend." | Henry Spencer
-- George Herbert |


What would be the temperature underground on mercury say from 20 to 100 feet
down.

Henry Spencer wrote:
Mercury is not an ideal black body in several
ways, and that can make a big difference.

Thank for the answer and explanation.

I was actually thinking of a black sunshield for a
Mercury orbiting object, but the other issues are
noted.

Two follow-up questions:

*If the sunshield is uninsulated, would the IR
radiation from the sunshield warm the objects
behind the sunshield as much as if they were
directly exposed to the sun?

*If the sunshield is "perfectly" insulated on
its back (leaving it with half the area to radiate
heat), would its absolute temperature climb by
the fourth root of 2 (1.189) to about 570K?
Mike Miller, Materials Engineer

On Tue, 25 Jan 2005 07:54:08 -0800, wrote:
I was actually thinking of a black sunshield for a Mercury orbiting
object, but the other issues are noted.

Two follow-up questions:

*If the sunshield is uninsulated, would the IR radiation from the
sunshield warm the objects behind the sunshield as much as if they were
directly exposed to the sun?

How about a sun shield with a radiator extending backward (away from
the Sun and orthogonal to the shield)? The radiator faces "cold"
space, so it should work ok. If passive cooling is not enough, active
cooling, like heat pipes, might work.

-paul-
--
Paul E. Black )

" writes:

sorry if this is a repeat post...

How hot would a nearly ideal black body object get in Mercury orbit?

I've read that Mercury's daytime temperatures can spike to 800F, but my
calculation for average temperatures at Mercury orbit was 440K/328F.
Mike Miller, Materials Engineer

Your calculations are about right for a spherical black body at Mercury's
distance from the sun.

A flat plate at the same distance, front face painted black and pointed
at the sun, back face coated with an ideal insulator, will reach 640K
or 700F. Same heat input, less surface area for radiant heat output.

As Mercury doesn't have an atmosphere or an ocean to complicate things,
we might reasonably conclude that the *average* temperature on Mercury
would be somewhere around 440K and the *maximum* temperature would be
more like 640K. On an equatorial plain of loose, dark regolith at local
noon.


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JRS: In article .com
, dated Tue, 25 Jan 2005 07:54:08, seen in news:sci.space.science,
posted :
Henry Spencer wrote:
Mercury is not an ideal black body in several
ways, and that can make a big difference.

Thank for the answer and explanation.

I was actually thinking of a black sunshield for a
Mercury orbiting object, but the other issues are
noted.

Henry assumed a spherical body.

In a non-uniform radiation field, such as that coming from the Sun, the
equilibrium temperature of a general unsymmetrical body depends on its
orientation.

A sphere of radius r intercepts pi r^2 of radiation, but radiates from 4
pi r^2; a circular plate radiates from 2 pi r^2, but can intercept from
pi r^2 down to almost zero.


Two follow-up questions:

*If the sunshield is uninsulated, would the IR
radiation from the sunshield warm the objects
behind the sunshield as much as if they were
directly exposed to the sun?

Only if it were at ground level. If it were at a reasonable height, its
back would be radiating out into half of the universe, with Mercury in
front of a bit of that; and most of Mercury's re-radiation would also
miss the shield.


*If the sunshield is "perfectly" insulated on
its back (leaving it with half the area to radiate
heat), would its absolute temperature climb by
the fourth root of 2 (1.189) to about 570K?

Yes and no, since it would not have been at 570/2^0.25 K without
insulation.


In this case, a single shield is probably sufficient. But one can put
shields in series; a second shield sees no direct sun, and blocks most
of the first from Mercury.

Much the same is done in cryostats; consider a tall vacuum-insulated
test-tube with liquid helium at the bottom, and a room-temperature cap
at the top. Put a few discs at intervals between top and bottom, and
boil-off is much reduced.

--
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