Question

A satellite orbits the earth with an elliptical orbit modeled by x squared over 43 million eight hundred twenty four thousand four hundred plus y squared over forty seven million one hundred ninety six thousand nine hundred equals 1 comma where the distances are measured in km. The earth shares the same center as the orbit. If the radius of the earth is 6,370 km, what is the maximum distance between the satellite and the earth?.

Answer 1

According to the given information, the maximum distance between the satellite and the earth is 510 km.

The function that represents the elliptical route of the satellite is presented as follows;

$\frac{x^2}{47,334,400} + \frac{y^2}{43,956,900}$

The compass of the Earth, R = ,370 km.

The equation of an cirque is presented as follows;

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}$

a = The major axis( the longer axis), which gives the maximum distance

between the satellite and Earth.

b = The minor axis( the shorter axis)

By comparison, we get;

a² = 47,334,400 km²

Therefore;

a = √(47,334,400 km²) = 6,880 km.

The distance between the satellite and the face of the Earth, d, is given as follows;

d = a - R

Which gives;

d = 6,880 km - 6,370 km = 510 km

Distance between the satellite and the face of the Earth, d = 510 km.

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