Main Topic 7: Escape Velocity and Gravity Assist Maneuvers

Escape velocity

• orbit.

• gravitational field

______________________________________________

• burn

• equal

__________________ is the speed at which a spacecraft’s energy is sufficient that it never achieves ______

In other words, it is how fast a spacecraft need to travel such that it continues into space and never returns to Earth under the effects of its ____________

_______________________________________________

• Consider a spacecraft of mass ms in orbit around the Earth,

  • The rocket with initial energy Ei performs a _____ to impart additional energy.

  • Conservation of energy requires that the final energy, Ef, is ______ to the initial energy

• Rf → ∞

• Vf = 0..

Derivation of escape velocity

• To escape the Earth’s gravity, the spacecraft must fly so far away that ________.

• Also, suppose that no excess kinetic energy is assumed at this distance ,_________

gravity assist,( gravitational slingshot,)

• heliocentric velocity

• flyby maneuver.

_______________________________________________

• heliocentric (inertial frame)

  • velocity

• planet-centric (non-inertial frame)

_______________________________________________________

planet-centric frame

• stationary

• equal

A __________ or __________ is a maneuver in which a spacecraft gains or loses _________ by passing close to a moving planetary body, i.e., a _____________

___________________________________________________

The analysis of such maneuver involves two reference frames:

• _________________(__________) frame

  • From this frame, there will be a change in _____ since they are on opposite direction.

• _____________ (__________) frame

________________________________________________________

In the _____________, the planet is ___________, and the spacecraft approaches with velocity Vin and exits with velocity Vout such that the magnitudes are ____ because of conservation of energy, i.e.,

________________________________________________________

• Voyager 1 and 2

  • Jupiter and Saturn

Gravity assist in space missions

• The ________ and _______ spacecraft used a series of gravity assists from ________ to ______ to accelerate out of the solar system.

deflection angle

• turned

• hyperbolic

• eccentricity approaches 1

  • θ increases

• eccentricity approaches infinity ∞

  • θ approaches zero

  • straight line.

_______________________

• The _____________ in a hyperbola is the angle by which a trajectory is “_____” as it passes around a central body when following a hyperbolic path

• The spacecraft’s trajectory is _____ relative to the planet, with the angle between Vin and Vout denoted by θ, known

  • As the ____________ approaches 1,

    • the value of the deflection angle θ ________.

  • However, as it approaches _______,

    • the deflection angle θ approaches ________ or almost _______