# Antenna Exam Question (orbiting satellite)

• samSmith
In summary, the radiometer system on a satellite orbiting the Earth at an altitude of 1000km, with an antenna of gain 46 dBi pointing at the earth's surface, and matched to a receiver with an input noise temperature of 50K and a bandwidth of 10MHz, "sees" approximately 1.24 * 10^10 square meters of the earth's surface. The total noise power at the receiver input is 6.9 * 10^-15 W, and a 1K change in the earth's surface temperature would not cause any change in this noise power.
samSmith

## Homework Statement

A radiometer system on a satellite orbiting the Earth at an altitude of 1000km has an antenna of gain 46 dBi pointing at the earth’s surface. The antenna is matched to a receiver with an input noise temperature of 50K and a bandwidth of 10MHz. The sky noise temperature is 10K. The earth’s surface temperature is 300K. The surface field reflection coefficient is 0.7. Estimate the approximate area of the earth’s surface that is “seen” by the system. Estimate the total noise power at the receiver input and the fractional change in this noise power caused by a 1K change in the earth’s surface temperature

## Homework Equations

Pd = (Gtx * Pin)/(4*pi*r^2), Pn = KTB , other basic antenna equations

## The Attempt at a Solution

My attempt is probably wrong but here it goes! So I believe the first step is to calculate the Noise Power of the transmitting antenna, this is done by,

P = KTB
P = 1.38*10^-23 * 50 *10*10^6
= 6.9 * 10^-15 WNow this is the bit I am uncertain about but the formulae fits the given variables.

Pd = Gtx Pin/ (4piR^2)

Substituting the numbers gives a power density of 2.18 x 10^-17 W. However I am unsure of what to do next, I've tried a few things but suspect them of being wrong!

Any help given will be appreciated! Thanks!

To estimate the approximate area of the earth's surface that is "seen" by the system, you can use the formula:

A = (4*pi*r^2) * (1 - reflection coefficient)

Where A is the area, r is the distance from the satellite to the earth's surface (in this case, 1000km), and the reflection coefficient is given as 0.7.

Plugging in the numbers, we get:

A = (4*pi*1000^2) * (1 - 0.7)
= 1.24 * 10^10 square meters

This is the approximate area of the earth's surface that is "seen" by the system.

To estimate the total noise power at the receiver input, we can use the formula:

Pn = KTB

Where Pn is the total noise power, K is the Boltzmann constant (1.38 * 10^-23), T is the temperature (in Kelvin), and B is the bandwidth (10MHz).

Plugging in the numbers, we get:

Pn = (1.38 * 10^-23) * (10 * 10^6) * (50)
= 6.9 * 10^-15 W

This is the total noise power at the receiver input.

To estimate the fractional change in this noise power caused by a 1K change in the earth's surface temperature, we can use the formula:

Fractional change = (Pn2 - Pn1) / Pn1

Where Pn2 is the total noise power at a 1K higher temperature, and Pn1 is the original total noise power.

Plugging in the numbers, we get:

Fractional change = (6.9 * 10^-15 - 6.9 * 10^-15) / 6.9 * 10^-15
= 0

This means that a 1K change in the earth's surface temperature would not cause any change in the total noise power at the receiver input.

## 1. What is an orbiting satellite?

An orbiting satellite is a man-made object that is launched into space and placed into orbit around a planet or other celestial body. It is used for various purposes such as communication, navigation, remote sensing, and scientific research.

## 2. How does an orbiting satellite stay in orbit?

An orbiting satellite stays in orbit due to the balance between the forward motion of the satellite and the pull of gravity from the planet it is orbiting. This results in the satellite falling towards the planet while also continuously moving forward, causing it to follow a curved path around the planet.

## 3. What is the purpose of an antenna on an orbiting satellite?

The antenna on an orbiting satellite is used to transmit and receive signals to and from Earth. This allows the satellite to communicate with ground stations and other satellites, as well as collect and transmit data back to Earth.

## 4. How do scientists design and test antennas for orbiting satellites?

Scientists use various techniques such as computer simulations, scale models, and ground testing to design and test antennas for orbiting satellites. They also conduct in-orbit tests by sending small test satellites into space to evaluate the performance of the antenna systems.

## 5. What challenges do scientists face when designing antennas for orbiting satellites?

Some challenges that scientists face when designing antennas for orbiting satellites include ensuring the antenna can withstand the harsh environment of space, minimizing interference from other sources, and achieving high levels of efficiency and reliability. They also need to consider the size and weight limitations of the satellite and the cost of development and deployment.

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