Satellites can be put into elliptical orbits if they need only sometimes to be i

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 -4425 and b 4417 (a and b in the standard formula for an ellipse), 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 altitude of the satellite above the Earth when it's on the major axis of the elliptical orbit. lowest altitude above the earth 4421.00 miles above the surface of the earth (Please round to two decimal places at least) Answer: 199.04

Explanation / Answer

let the altitude of satellite be x

distance from center of the earth to the satellite is the distance from focus to the vertex of ellipse

a=4425, b =4417

eccentricity,e=[1- (b2/a2)]

e=[1- (44172/44252)]

e=(70736/44252)

e =0.06010449793402681087675220664989

distance from center of the earth to the satellite = 3960+x

distance from focus to the vertex =a- ae= a(1-e) = 4425*(1-0.06010449793402681087675220664989)

3960+x =4425*(1-0.06010449793402681087675220664989)

=>3960+x =4159.0375966419313618703714855742

=>x=4159.0375966419313618703714855742 -3960

=>x=199.03759664193136187037148557424

=>x=199.04

therefore altitude of satellite is 199.04 miles

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