Thanks everyone. Just to clarify the reason I asked about Earth's SOI, here's the problem I encountered: I was in Low Earth Orbit and engaged the main thrusters to take the XR5 Ravenstar out to an altitude of 700,000 km (outside of Earth's SOI); I then did a retrograde burn and engaged the thrusters until the ship's radial velocity with respect to Earth was zero. Then I used Attitude MFD to point the ship's longitudinal axis toward to center of Earth. I then engaged the main thrusters and accelerated to 2 km/sec in an attempt to impact the Earth but instead I headed away from Earth rather than toward it. When I did the same thing from an altitude of 70,000 km (inside Earth's SOI) I did indeed impact the Earth. I was wondering what accounted for the difference. Why did the ship move away from the Earth when I started from outside Earth's SOI?
I believe that Urwumpe answered the question when he said that "Sphere of influence only means, being in a place, where Orbit MFD shows a green "gravity quality" indicator at the bottom and thus, in a place where maneuvers based on the theory of Kepler orbits are possible". When I was 70,000 km from Earth the Orbit MFD showed 0.82G in green characters at the bottom of the display however when I was 700,000 km from Earth Orbit MFD showed 0.05G in red characters. If I understand Urwumpe correctly that would mean that even though the gravitational field was 5% of Earth gravity at 700,000 km I was outside the sphere where a Keplerian orbital maneuver with respect to Earth was possible.
Thanks again,
Peter