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Thread moved from the technical forums, so no Homework Template is shown

A space vehicle enters the sensible atmosphere of the earth (300,000 ft) with a velocity of 25,000 ft/sec at a flight-path angle of -60 degrees. What is its velocity and flight-path angle at an altitude of 100 nautical miles during descent?

(Assuming no drag or perturbations, two body orbital mechanics)

My answers I am getting are V = 25,370.7 ft/s at a flight-path angle of -60.029 degrees.

The correct answers the book states are: V = 24,618 ft/s at a flight-path angle of 59 degrees and 58 minutes.

There is a clear correlation between my answers and the correct answers, because it seems that my answers are numerically mirrored over the 25,000 ft/s and the 60 degrees.

If someone could work this out mathematically so I can see what I am doing wrong, or just explain if I'm making a simple conceptual mistake, that would be appreciated.

Thank you in advance,

Adrian

(Assuming no drag or perturbations, two body orbital mechanics)

My answers I am getting are V = 25,370.7 ft/s at a flight-path angle of -60.029 degrees.

The correct answers the book states are: V = 24,618 ft/s at a flight-path angle of 59 degrees and 58 minutes.

There is a clear correlation between my answers and the correct answers, because it seems that my answers are numerically mirrored over the 25,000 ft/s and the 60 degrees.

If someone could work this out mathematically so I can see what I am doing wrong, or just explain if I'm making a simple conceptual mistake, that would be appreciated.

Thank you in advance,

Adrian