Problem Set 2

Contents

Problem Set 2#

Earth data $\( R^{Equator} = 6384 km \)\( \)\( R^{Pole} = 6353 km \)\( \)\( \mu = 3.986 \times 10^5 km^3s^{-2} \)$

Question 1#

A remote sensing satellite is in a polar orbit with its line of apsides on the equator. The perigee of the orbit is at altitude of \(620\) \(km\) and the eccentricity of the orbit is \(e = 0.04\). Calculate the semi-major axis of this orbit and show that the altitude at apogee is approximately \(1200\) \(km\).

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# Your coded answers here (and create more Code cells if you wish to)

Question 2#

The satellite carries a camera with a field of view of \(26^o\). The camera has a CCD array of \(1000\) pixels. Compute the resolution per pixel of this camera at perigee and apogee.

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Question 3#

Find the altitude of the satellite as it passes over the poles. For the camera onboard the satellite, compute the image resolution over the poles.

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# Your coded answers here (and create more Code cells if you wish to)

Question 4#

Calculate the velocity of this spacecraft at perigee, and the angular velocity. Neglecting the eccentricity of the orbit and taking the Earth as a sphere, how long will it take for the spacecraft to disappear over the horizon of an observer directly below the perigee point?

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