Determining angle to which satellite is visible

[unscientific]

Homework Statement

An Earth satellite is moving in the plane of the Earth's equator. Satellite is 1680km above Earth's surface, with a period of 2 hours. Determine the angle through which satellite is visible to an observer at an equator, measured about the centre of the Earth.

Homework Equations

the first part involved finding the height above the satellite, which I have found to be 1680km. This is the second part. I know a geometrical approach is required, but can't seem to draw it out.

The Attempt at a Solution

Tried drawing a sphere and satellite but can't seem to work it out.. Appreciate help! (Already tried but failed to understand the provided answers)Original souce: question 2b(iii) of http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_Paper2_2006_QP.pdf

Answer: http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_Paper2_2006_MS.pdf

 

[Spinnor]

I think drawing an accurate picture helps. Does this drawing help? You have two lengths of a triangle, problem started?

 

[unscientific]

so I assume the guy is at the top, and since the line is a tangent to his line of sight, any where lower than the tangent, the line produced will cut through the Earth's surface, resulting in the satellite being blocked.

Is that analogy correct?

 

[Spinnor]

Give or take a little I think the sketch is the geometry you are looking for.

 

[rwisz]

I understand the difficulty in visualizing a problem and finding a solution. In this case, we can use basic geometric principles to determine the angle through which the satellite is visible to an observer at the equator.

First, we know that the satellite is orbiting in the plane of the Earth's equator, which means it is also moving in a circular path around the Earth's center. This circular path can be represented as a circle on a 2D plane.

Next, we can draw a line from the center of the Earth to the satellite. This line represents the radius of the circle and also the distance between the center of the Earth and the satellite. In this case, the distance is given as 1680km.

Now, we can draw a tangent line from the observer's position on the equator to the circle. This tangent line represents the line of sight between the observer and the satellite.

The angle between the radius and the tangent line is the angle through which the satellite is visible to the observer. This angle can be calculated using the tangent function, where the tangent of the angle is equal to the opposite side (radius) divided by the adjacent side (distance between the center of the Earth and the observer). In this case, the angle is approximately 5.3 degrees.

Therefore, the satellite is visible to the observer at the equator through an angle of approximately 5.3 degrees, measured about the center of the Earth.