Orbital Dynamics

Which statements regarding the gravitational n-body problem are true?: The system is described by 6n first-order scalar differential equations.

True

Which statements regarding the gravitational n-body problem are true?: The system can yield chaotic solutions

True

Which statements regarding the gravitational n-body problem are true?: The 10 first integrals correspond to conservation of mass and energy

False

Which statements regarding the gravitational n-body problem are true?: The barycenter must be at rest for the momentum to be conserved.

False

Which statements regarding the gravitational n-body problem are true?: The system is described by deterministic equations.

True

Which statements regarding the gravitational n-body problem are true?: Total energy, linear, and angular momentum are conserved quantities.

True

Which statements regarding the gravitational n-body problem are true?: The barycenter is an inertial frame of reference

True

Which statements on a Kepler orbit are generally true?: The angular momentum is constant indicating a fixed shape of the orbit

False

Which statements on a Kepler orbit are generally true?: For closed orbits the potential energy is larger than the kinetic energy

True

Which statements on a Kepler orbit are generally true?: The angular velocity is constant since the angular momentum is constant.

False

Which statements on a Kepler orbit are generally true?: The eccentricity vector is constant and normal to the orbital plane.

False

Which statements on elliptic Kepler orbits are generally true?: The angular momentum is negative for all elliptic orbits.

False

Which statements on elliptic Kepler orbits are generally true?: The kinetic energy is largest at periapsis and smallest at apoapsis.

True

Which statements on elliptic Kepler orbits are generally true?: The areal velocity is constant since the angular momentum is constant.

True

Which statements on elliptic Kepler orbits are generally true?: The eccentricity vector is constant indicating a fixed size of the orbit.

False

Which statements on the orbital elements of a Kepler orbit are generally true?:The set {rp, ra, a, i, Ω, ω} fully describes the movement of the satellite.

False

Which statements on the orbital elements of a Kepler orbit are generally true?: i = 0 means the satellite is in a prograde orbit in the reference plane.

True

Which statements on the orbital elements of a Kepler orbit are generally true?: t − t0 < 0 and e > 1 means the satellite has already passed the periapsis.

False

Which statements on the orbital elements of a Kepler orbit are generally true?: E lags ϑ, i.e. E < ϑ, if e ∈ (0, 1) and ϑ ∈ (0, π).

True

Which statements on the orbital elements of a Kepler orbit are generally true?: The initial conditions ˙r0 and r0 give a full set of orbital parameters.

True

Which statements on the orbital elements of a Kepler orbit are generally true?: e < 0 means the satellite is in a retrograde orbit.

False

Which statements on the orbital elements of a Kepler orbit are generally true?: t − t0 > 0 and e > 1 means the satellite is about to pass the apoapsis.

False

Which statements on the orbital elements of a Kepler orbit are generally true?: E lags ϑ, i.e. E < ϑ, if e ∈ (0, 1) and ϑ ∈ (π, 2π).

False

What is generally true for a circular restricted three-body system? The collinear Lagrange points are stable for moderate perturbations.

False

What is generally true for a circular restricted three-body system? All orbits of the tertiary body are confined to a plane.

False

What is generally true for a circular restricted three-body system? The Jacobi integral is a measure of the total mechanical energy.

True

What is generally true for a circular restricted three-body system? Sun, Jupiter, and Saturn constitute a circular restricted 3-body system

False

Which statements on the perturbation by aerodynamic drag are true? The semi-major axis and the eccentricity of the orbit decrease.

True

Which statements on the perturbation by aerodynamic drag are true? The potential energy of the orbiting object decreases over time.

True

Which statements on the perturbation by aerodynamic drag are true? The drag force acts perpendicular to the direction of the flight.

False

Which statements on the perturbation by aerodynamic drag are true? The drag coefficient depends on the shape of the orbiting object.

True

Which statements on the perturbation by Earth’s geopotential are true? The geopotential is a conservative force.

True

Which statements on the perturbation by Earth’s geopotential are true? The effect of Earth’s oblateness is the largest geopotential perturbation.

True

Which statements on the perturbation by Earth’s geopotential are true? Earth’s oblateness induces secular perturbations in a, e and i.

False

Which statements on the perturbation by Earth’s geopotential are true? Satellites in Molniya orbits do not experience apsidal precession.

True

Which statements regarding the gravitational n-body system are true? The system is fully described by 6n first-order differential equations.

False

Which statements regarding the gravitational n-body system are true? The system cannot yield closed form solutions.

False

Which statements regarding the gravitational n-body system are true? The 10 first integrals correspond to conserved physical quantities.

True

Which statements regarding the gravitational n-body system are true? The barycenter is an inertial frame of reference.

True

Which statements on a hyperbolic Kepler orbit are generally true? The angular velocity increases as ϑ → ϑ∞.

False

Which statements on a hyperbolic Kepler orbit are generally true? The kinetic energy is larger than the potential energy for all ϑ.

True

Which statements on a hyperbolic Kepler orbit are generally true? Kinetic energy decreases and potential energy goes to zero as ϑ → ϑ∞.

True

Which statements on a hyperbolic Kepler orbit are generally true? e × h = 0 and e · rp = 0

False

What is generally true for the orbital elements of a Kepler orbit? The initial conditions ˙r0 and r0 give a full set of orbital parameters.

True

What is generally true for the orbital elements of a Kepler orbit? i = −π/3 means the satellite is in a prograde orbit.

False

What is generally true for the orbital elements of a Kepler orbit? The parameters ϑ, E, M, and t are interchangeable.

True

What is generally true for the orbital elements of a Kepler orbit? E lags ϑ, i.e. E < ϑ, if e ∈ (0, 1) and ϑ ∈ (π, 2π).

False