# Calculate The Surface Temperature of Mercury

• TFM
In summary, the conversation discusses estimating the surface temperature of Mercury using the inverse square law and the given distances from the Sun. The final calculated average temperature is about 97 degrees Celsius, which is in agreement with online sources. However, it is noted that this method may not be accurate for calculating the temperature of a rocky planet without an atmosphere.
TFM

## 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

Last edited:
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.

## 1. What is the surface temperature of Mercury?

The surface temperature of Mercury varies greatly due to its close proximity to the sun. On the side facing the sun, temperatures can reach up to 800 degrees Fahrenheit (427 degrees Celsius), while on the side facing away from the sun, temperatures can drop to -290 degrees Fahrenheit (-179 degrees Celsius).

## 2. How is the surface temperature of Mercury calculated?

The surface temperature of Mercury can be calculated using the Stefan-Boltzmann law, which states that the energy emitted by a body is directly proportional to its absolute temperature. By measuring the amount of energy that Mercury reflects and absorbs from the sun, scientists can calculate its surface temperature.

## 3. Why does Mercury have such extreme temperature differences on its surface?

Mercury's lack of atmosphere is one of the main reasons for its extreme temperature differences. Without an atmosphere to trap or distribute heat, the side facing the sun is exposed to intense radiation and heat, while the side facing away is exposed to the extreme cold of space.

## 4. How does the tilt of Mercury's axis affect its surface temperature?

Unlike Earth, Mercury's axis has virtually no tilt, which means that its poles do not experience any seasonal variation in sunlight. This results in the polar regions having a more consistent temperature compared to the rest of the planet's surface.

## 5. Can the surface temperature of Mercury change over time?

Yes, the surface temperature of Mercury can change over time, but it is a gradual process. Due to its slow rotation and lack of atmosphere, Mercury's surface temperature changes very slowly over millions of years. However, volcanic activity and impacts from asteroids can also cause temporary fluctuations in the surface temperature.

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