# Calculate The Surface Temperature of Mercury

## Homework Statement

Estimate the surface temperature of Mercury (the planet). Mercury is distant 0.38 ORE from the Sun, where the Earth-Sun distance, ORE is 1.49.108m. The radii of the Sun, Earth and Mercury are 696.103, 6.38.103 and 2.42.103 km respectively.

## Homework Equations

Heat (IR Radiation) follows inverse square Law

## The Attempt at a Solution

See I am confused with why the Sun Earth and Mercury's radius are on here. I know that Infra Red radiation follows the inverse square law, so I would ave thought you would have used this to find the temperature on Mars, however, the radius are given, so I am slightly confused...is there more to this question???

TFM

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TFM,

It's asking you to find the surface temperature. When it references Mercury-Sun distance it's probably referencing the distance between their COMs.

Okay so the Distance from the Earth to the Sun is

$$1.49*10^8$$ m

So we take out the sun/Earth radius, giving:

$$1.483*10^8$$ m

the distance from Sun to the Mercury is 0.38x this, so:

$$5.635*10^7$$m

The Surface Temperature of Earth is 14 degrees C

So now Do we have to use ratios to find the temperature of Mercury using:

$$T \propto \frac{1}{d^2}$$

ie

$$\frac{T_{Earth}}{T_{Mercury}} \propto \frac{\frac{1}{d_{Earth}^2}}{\frac{1}{d_{Mercury}^2}}$$

???

Okay, I have tried out my ratio methiod, and it gives me a average surface temperature of 97 Degrees Celsius. Does this sound right?

Looking on the web, I have found a maximum Daytime temp of about 400, minimum of -200, which gives an average of 100 degrees C, so does seem to agree there...

Does this look okay???

TFM

Does the above look okay???

I've been wondering lately how to calculate Mercury's surface temperature, so I'm glad you asked this.

Your logic sounds good. However, when taking the ratios of the temperatures, they need to be in degrees Kelvin, which is Celsius plus 273 degrees, the absolute zero point in Celsius. If you do this and apply the inverse square law, you'll get an average temperature of 1650 deg Celsius, which is too high.

This approach would probably work better for gases rather than rock. Also, Mercury has no atmosphere to speak of, so most of whatever heat it receives during its day is radiated away at night, more so than it would be on the earth.