# Equilibrium Temperature of a Spherical Black Body Satellite

• CaptainJames
In summary, the conversation discusses the process of finding the equilibrium temperature of a simplified satellite model with a spherical black body and 3900 watts of generated electronics. The equation used is T=oT^4 and the correct answer is found by dividing the total power by the surface area and equating it to the right side of the equation.
CaptainJames
b) Real satellites are complicated objects (see photo above). To simplify the problem, suppose the satellite is a spherical black body with a 0.3 m radius. Suppose the satellite's electronics generated 3900 Watts. What would be the equilibrium temperature, Teq, of the satellite?

Okeedoke, so I started with the equation T=oT^4. So...

3900 J=(5.67x10^-8 W/m^2K^4)T^4

T=(3900 J/(5.67x10^-8 W/m^2 K^4))^(1/4)

Which gives me an incorrect answer... any hints in the right direction?

CaptainJames said:
b) Real satellites are complicated objects (see photo above). To simplify the problem, suppose the satellite is a spherical black body with a 0.3 m radius. Suppose the satellite's electronics generated 3900 Watts. What would be the equilibrium temperature, Teq, of the satellite?

Okeedoke, so I started with the equation T=oT^4. So...

3900 J=(5.67x10^-8 W/m^2K^4)T^4

T=(3900 J/(5.67x10^-8 W/m^2 K^4))^(1/4)

Which gives me an incorrect answer... any hints in the right direction?
You are given the total power but you need the power/unit area. On the Left side, divide the power by the surface area and equate that to the right side.

AM

Ah! Thanks a bunch, I got it.

## 1. What is the Equilibrium Temperature of a Spherical Black Body Satellite?

The Equilibrium Temperature of a Spherical Black Body Satellite is the temperature at which the satellite's rate of heat absorption from sunlight is equal to its rate of heat emission, resulting in a stable temperature.

## 2. How is the Equilibrium Temperature of a Spherical Black Body Satellite calculated?

The Equilibrium Temperature of a Spherical Black Body Satellite is calculated using the Stefan-Boltzmann Law, which takes into account the satellite's size, distance from the sun, and surface properties.

## 3. Why is the Equilibrium Temperature of a Spherical Black Body Satellite important?

The Equilibrium Temperature of a Spherical Black Body Satellite is important because it affects the satellite's overall performance and functionality. If the temperature is too high, it can damage the satellite's components, while a temperature that is too low can affect its ability to function properly.

## 4. How does the Equilibrium Temperature of a Spherical Black Body Satellite differ from other types of satellites?

The Equilibrium Temperature of a Spherical Black Body Satellite is specific to a spherical shape and black body properties, while other types of satellites may have different equilibrium temperatures due to their different shapes and surface properties.

## 5. Can the Equilibrium Temperature of a Spherical Black Body Satellite be controlled?

Yes, the Equilibrium Temperature of a Spherical Black Body Satellite can be controlled through various methods such as thermal coatings, insulation, and thermal control systems. These methods help regulate the amount of heat absorbed and emitted by the satellite, thus controlling its equilibrium temperature.

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