Interstellar TV: Calculating Detection Range

[Urvabara]

I am just "trying" to watch interstellar TV...

The detection range in lightyears is
$$R = \sqrt{\frac{\text{EIRP}\cdot A_{e}_{r}\cdot\text{twc}}{4\pi\cdot\text{SNR}\cdot B_{r}\cdot k_{B}\cdot T_{sys}}}\cdot\frac{1\,\text{ly}}{9454254955488000\,\text{m}}$$, where
$$\text{EIRP} = P_{t}G_{t},$$
$$\text{twc} = \sqrt{B_{r}t} = 1\,\text{for modulated signals,}$$
$$\text{SNR}$$ is signal-to-noise ratio,
$$A_{e}_{r}$$ is receiver's radio telescope's effective area,
$$B_{r}$$ is receiver's bandwidth which is larger or equal to transmitters bandwidth,
$$k_{B}$$ is Boltzmann's constant and
$$T_{sys}$$ is system's temperature in Kelvins.

I put these numbers in:
$$\text{EIRP} = 15000\,\text{W}$$,
$$A_{e}_{r} = 15707963\,\text{m}^{2}$$,
$$\text{twc} = 1$$,
$$\text{SNR} = 22$$,
$$B_{r} = 8\cdot 10^{6}\,\text{Hz}$$,
$$k_{b} = 1.3806504\cdot 10^{-23}\,\text{J/K}$$, and
$$T_{sys} = 10\,\text{K}$$.
I get: $$R = 0.000093\,\text{ly}.$$

Questions:
1. Is the equation correct?
2. Is my answer about correct?
3. How to reduce the SNR?
4. How to reduce the system temperature?
5. Can I really rise the detection range just only reducing the system temperature? So technically I can watch interstellar TV shows with a very, very small disc, if I can go to very near the absolute zero?

 

[Urvabara]

Guys? Anyone?

PS.
$$P_{t}$$ is transmitter's power.
$$G_{t}$$ is transmitter's antenna gain.

 

[oswaler]

1. The equation appears to be correct, but it is always important to double check and make sure all units are consistent.
2. Your answer appears to be correct based on the numbers you provided.
3. To reduce the SNR, you could try using a higher gain antenna or increasing the transmitter power, which would increase the EIRP.
4. To reduce the system temperature, you could try using better insulation or cooling techniques for the receiver.
5. Yes, reducing the system temperature can increase the detection range, but it is not the only factor. Other factors such as transmitter power and antenna gain also play a role. And while technically you could watch interstellar TV with a very low system temperature, it is not practical or feasible to reach absolute zero in real-world scenarios.