- #1

glorfindel1000

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- Homework Statement
- Satellite is orbiting earth and is heated by sun to 323 K. To what temperature satellite cools down during its 45 min cycle in shadow? Satellite is 1 m radius and 2 mm thick copper. Emissivity is 0,75. Space temperature is assumed to be 0 K.(hint. Write a formula to heat change in function of time, you have to integrate)

- Relevant Equations
- \begin{align*}

\frac{dQ}{dt} &= e \sigma A T^4 \text{ or } \frac{dQ}{dt} = e * \sigma * A * T^4 \\

\text{(maybe)}E &= cm \Delta T \\

A &= 4 * \pi * r^2 \\

\sigma &= 5,67 \times 10^{-8}{\rm W/(m^2 * K^4)} \\

e &= 0,75

\end{align*}

Mass of a satellite is 750g(##m = \rho V = 8,96 \frac{g}{cm^3}\cdot (\frac{4\pi(100cm)^3}{3} -\frac{4\pi(99,9cm)^3}{3}) = \approx 750g =0,75kg##)

I am not sure what to integrate. I solved T there but it seems far stretched

$$T =\sqrt[4]{\frac{dQ}{dt}\frac{1}{e\sigma A}} $$

How to get the function to integrate is basically my problem. I changed that dt to other side

##dQ = e\sigma AT^4dt##

and integrated it from 0 to 2700.

##Q = \bigg/_{\!\!\! 0}^{\,2700}e\sigma AT^4t##

Not really sure if that helps. What to do with Q then?

I am not sure what to integrate. I solved T there but it seems far stretched

$$T =\sqrt[4]{\frac{dQ}{dt}\frac{1}{e\sigma A}} $$

How to get the function to integrate is basically my problem. I changed that dt to other side

##dQ = e\sigma AT^4dt##

and integrated it from 0 to 2700.

##Q = \bigg/_{\!\!\! 0}^{\,2700}e\sigma AT^4t##

Not really sure if that helps. What to do with Q then?

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