Orbit
During freefall the trajectory is part of an elliptic orbit as given by the orbit equation. The perigee distance is less than the radius of the Earth R including atmosphere, hence the ellipse intersects the Earth, and hence the spacecraft will fail to complete an orbit. The major axis is vertical, the semi-major axis a is more than R/2. The specific orbital energy is given by:
where is the standard gravitational parameter.
Almost always a < R, corresponding to a lower than the minimum for a full orbit, which is
Thus the net extra specific energy needed compared to just raising the spacecraft into space is between 0 and .
Read more about this topic: Sub-orbital Spaceflight
Famous quotes containing the word orbit:
“Words can have no single fixed meaning. Like wayward electrons, they can spin away from their initial orbit and enter a wider magnetic field. No one owns them or has a proprietary right to dictate how they will be used.”
—David Lehman (b. 1948)
“The Fitchburg Railroad touches the pond about a hundred rods south of where I dwell. I usually go to the village along its causeway, and am, as it were, related to society by this link. The men on the freight trains, who go over the whole length of the road, bow to me as to an old acquaintance, they pass me so often, and apparently they take me for an employee; and so I am. I too would fain be a track-repairer somewhere in the orbit of the earth.”
—Henry David Thoreau (1817–1862)
“The human spirit is itself the most wonderful fairy tale that can possibly be. What a magnificent world lies enclosed within our bosoms! No solar orbit hems it in, the inexhaustible wealth of the total visible creation is outweighed by its riches!”
—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)