Question

Satellites can be put into elliptical orbits if they need only sometimes to be in high- or low-earth orbit, thus avoiding the need for propulsion and navigation in low-earth orbit and the expense of launching into high-earth orbit. Suppose a satellite is in an elliptical orbit, with $a=4420$ and $b=4416$, and with the center of the Earth being at one of the foci of the ellipse. Assuming the Earth has a radius of about $3960$ miles, find the lowest and highest altitudes of the satellite above the Earth.

• A. The minimum altitude is $272$miles above the Earth.
• B. The minimum altitude is $292$miles above the Earth.
• C. The maximum altitude is $548$miles above the Earth.
• D. The maximum altitude is $648$miles above the Earth.

Answer 1

Answer: (A), (D)

The correct options are
A The minimum altitude is $272$miles above the Earth.
D The maximum altitude is $648$miles above the Earth.

Let e be the eccentricity of the elipse

The minimum altitude$=a-(ae+r)$

The maximum altitude$=(a+ae)-r$

We know $ae=\sqrt{a^2-b^2}$ in ellipse

$ae=\sqrt{{4420}^2-{4416}^2}=188$

So minimum altitude$=4420-(188+3960)=272miles$

Maximum altitude$=4420+188-3960=648miles$