Calculating the visibility of a satellite

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Calculating satellite visibility involves using orbital elements to determine the satellite's position and velocity over time. Software applications utilize these calculations to assess when a satellite will be visible from a specific location on Earth, factoring in the satellite's altitude above the horizon and the time of day. Visibility is limited to nighttime conditions when the satellite is sufficiently elevated. The inclination of certain orbits, such as that of the International Space Station, affects visibility opportunities based on geographic location. Understanding these dynamics is essential for accurate satellite tracking and observation.
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Hi,

I'm familiar with the use of orbital elements to describe the motion of a satellite, and using those to calculate the state vector (position and velocity as a function of time) of the satellite.

I am wondering how it is possible to use this information to calculate when a satellite will be visible in the night sky. I know various pieces of software are available to do this, but are there standard equations that the software uses?

Many thanks,

F
 
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You can find apps to do this on the internet and even on iPhones. In the case of the iPhone app, you can aim the iPhone at the intended satellite.

What they do is determine the satellites poisition relative to a specific point on the Earth and specific time. The window of visiblity will require the satellite be sufficiently above the horizon from that specific point on the earth, and for the time when it's sufficiently above the horizon to be at night.

In some cases, like the space station, the orbit is not on the same plane as the equator, so the "north / south" position of the satellite relative to the extended equator plane varies with time. This reduces the number of oppurtunities for the space station to be visible at some specific point on the earth.
 
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