# 6.7: Communication with Satellites

- Page ID
- 1855

- Satellites may be used to transmit information over large distances.

Global wireless communication relies on satellites. Here, ground stations transmit to orbiting satellites that amplify the signal and retransmit it back to earth. Satellites will move across the sky unless they are in **geosynchronous orbits**, where the time for one revolution about the equator exactly matches the earth's rotation time of one day. TV satellites would require the homeowner to continually adjust his or her antenna if the satellite weren't in geosynchronous orbit. Newton's equations applied to orbiting bodies predict that the time **T** for one orbit is related to distance from the earth's center **R **as

\[R=\sqrt[3]{\frac{GMT^{2}}{4\pi ^{2}}} \nonumber \]

where **G **is the gravitational constant and **M **the earth's mass. Calculations yield **R = 42200 km**, which corresponds to an altitude of **35700 km**. This altitude greatly exceeds that of the ionosphere, requiring satellite transmitters to use frequencies that pass through it. Of great importance in satellite communications is the transmission delay. The time for electromagnetic fields to propagate to a geosynchronous satellite and return is 0.24 s, a significant delay.

In addition to delay, the propagation attenuation encountered in satellite communication far exceeds what occurs in ionospheric-mirror based communication. Calculate the attenuation incurred by radiation going to the satellite (one-way loss) with that encountered by Marconi (total going up and down). Note that the attenuation calculation in the ionospheric case, assuming the ionosphere acts like a perfect mirror, is not a straightforward application of the propagation loss formula.

**Solution**

Transmission to the satellite, known as the uplink, encounters inverse-square law power losses. Reflecting off the ionosphere not only encounters the same loss, but twice. Reflection is the same as transmitting exactly what arrives, which means that the total loss is the **product **of the uplink and downlink losses. The geosynchronous orbit lies at an altitude of **35700 km. **The ionosphere begins at an altitude of about 50 km. The amplitude loss in the satellite case is proportional to **2.8****×10 ^{-8};** for Marconi, it was proportional to

**4.4**

**×10**Marconi was

^{-10}.**very**lucky.