1
ENAE 404 SPACE FLIGHT DYNAMICS
COMPREHENSIVE PRACTICE EXAMINATION
FULL PACKAGE QUESTIONS ANSWERS AND
RATIONALES 2026-27 LATEST VERSION
Instructions: Select the single best answer for each question. This
examination covers the fundamental principles and applications of
space flight dynamics as tested in the ENAE 404 curriculum at the
University of Maryland.
Section 1: Two-Body Problem & Fundamental Concepts (Questions
1–15)
1. The two-body problem in orbital mechanics assumes which of
the following?
A) Both bodies are extended, non-spherical objects
B) Both bodies are point masses, and the only force acting is the
mutual gravitational attraction between them
C) The gravitational influence of third bodies is considered
D) Atmospheric drag and solar radiation pressure are included
Explanation: The two-body problem assumes both bodies are point
masses with spherically symmetric mass distributions, and the only
force is the mutual gravitational attraction. It neglects third-body
perturbations, drag, and other non-gravitational forces.
2. In the relative two-body problem, the motion of one body with
respect to the other is governed by:
A) Newton's First Law only
B) The relative equation of motion: r̈ = -μ(r/r³)
,2
C) Kepler's third law only
D) The vis-viva equation
Explanation: The relative equation of motion for the two-body
problem is r̈ = -μ(r/r³), where μ = G(m₁ + m₂) is the gravitational
parameter. This equation leads to conic-section trajectories.
3. The specific mechanical energy (ε) of a two-body orbit is:
A) Always positive for bound orbits
B) Constant for a given orbit and determines the type of conic
trajectory
C) Equal to the kinetic energy only
D) Dependent on the position along the orbit
Explanation: Specific mechanical energy ε = v²/2 - μ/r is a constant of
motion in the two-body problem. Its sign determines the orbit type:
negative for ellipses, zero for parabolas, and positive for hyperbolas.
4. The specific angular momentum vector (h) in the two-body
problem is:
A) A constant vector that defines the orientation of the orbital
plane
B) Always parallel to the position vector
C) Zero for elliptical orbits
D) Dependent on the eccentricity only
Explanation: h = r × v is a constant vector in the two-body problem. Its
direction is perpendicular to the orbital plane, thus defining the
plane's orientation. Its magnitude h = |r × v| is also constant.
5. The vis-viva equation relates the speed of a satellite in a two-
body orbit to:
A) The satellite's mass only
B) The radial distance from the central body and the semi-major
,3
axis
C) The eccentricity only
D) The orbital period only
Explanation: The vis-viva equation is v² = μ(2/r - 1/a). It gives the
speed v at any point in the orbit as a function of the radial distance r
and the semi-major axis a.
6. The trajectory equation for the two-body problem is:
A) r = a(1 - e²)/(1 + e cos θ)
B) r = p/(1 + e cos θ), where p = h²/μ is the semi-latus rectum
C) r = a(1 - e²)
D) r = h²/(μ(1 + e cos θ))
Explanation: The conic trajectory equation is r = p/(1 + e cos θ),
where p = h²/μ is the semi-latus rectum, e is the eccentricity, and θ is
the true anomaly.
7. Which of the following is NOT conserved in the two-body
problem?
A) Specific mechanical energy
B) Specific angular momentum
C) The velocity vector
D) The orbital plane orientation
Explanation: While energy and angular momentum (magnitude and
direction) are conserved, the velocity vector changes continuously as
the satellite moves along its orbit. Only the energy and angular
momentum are constants of motion.
8. The "n-body problem" differs from the two-body problem
primarily because:
A) It considers only two bodies
B) It accounts for the gravitational perturbations from multiple
, 4
bodies simultaneously
C) It ignores gravitational forces altogether
D) It only applies to artificial satellites
Explanation: The n-body problem considers the gravitational
interactions among n bodies, making it analytically unsolvable in
closed form for n ≥ 3. The two-body problem is a simplification that is
analytically solvable.
9. A satellite is in a circular orbit around Earth. If the satellite's
altitude is doubled, the orbital speed will:
A) Double
B) Decrease by a factor of √(R/(R+h))
C) Remain the same
D) Increase by a factor of √2
Explanation: For a circular orbit, v = √(μ/r). If the radius increases
(altitude doubles), the speed decreases as 1/√r. Doubling the altitude
does not exactly halve the speed, but the speed decreases.
10. The standard gravitational parameter (μ) of a central body is:
A) The product of the universal gravitational constant G and the
mass of the central body
B) The mass of the satellite only
C) The radius of the central body
D) The orbital period of the satellite
Explanation: μ = GM, where G is the universal gravitational constant
and M is the mass of the central body. For Earth, μ ≈ 398,600 km³/s².
11. In the two-body problem, the trajectory of a satellite with zero
total mechanical energy is:
A) An ellipse
B) A parabola
ENAE 404 SPACE FLIGHT DYNAMICS
COMPREHENSIVE PRACTICE EXAMINATION
FULL PACKAGE QUESTIONS ANSWERS AND
RATIONALES 2026-27 LATEST VERSION
Instructions: Select the single best answer for each question. This
examination covers the fundamental principles and applications of
space flight dynamics as tested in the ENAE 404 curriculum at the
University of Maryland.
Section 1: Two-Body Problem & Fundamental Concepts (Questions
1–15)
1. The two-body problem in orbital mechanics assumes which of
the following?
A) Both bodies are extended, non-spherical objects
B) Both bodies are point masses, and the only force acting is the
mutual gravitational attraction between them
C) The gravitational influence of third bodies is considered
D) Atmospheric drag and solar radiation pressure are included
Explanation: The two-body problem assumes both bodies are point
masses with spherically symmetric mass distributions, and the only
force is the mutual gravitational attraction. It neglects third-body
perturbations, drag, and other non-gravitational forces.
2. In the relative two-body problem, the motion of one body with
respect to the other is governed by:
A) Newton's First Law only
B) The relative equation of motion: r̈ = -μ(r/r³)
,2
C) Kepler's third law only
D) The vis-viva equation
Explanation: The relative equation of motion for the two-body
problem is r̈ = -μ(r/r³), where μ = G(m₁ + m₂) is the gravitational
parameter. This equation leads to conic-section trajectories.
3. The specific mechanical energy (ε) of a two-body orbit is:
A) Always positive for bound orbits
B) Constant for a given orbit and determines the type of conic
trajectory
C) Equal to the kinetic energy only
D) Dependent on the position along the orbit
Explanation: Specific mechanical energy ε = v²/2 - μ/r is a constant of
motion in the two-body problem. Its sign determines the orbit type:
negative for ellipses, zero for parabolas, and positive for hyperbolas.
4. The specific angular momentum vector (h) in the two-body
problem is:
A) A constant vector that defines the orientation of the orbital
plane
B) Always parallel to the position vector
C) Zero for elliptical orbits
D) Dependent on the eccentricity only
Explanation: h = r × v is a constant vector in the two-body problem. Its
direction is perpendicular to the orbital plane, thus defining the
plane's orientation. Its magnitude h = |r × v| is also constant.
5. The vis-viva equation relates the speed of a satellite in a two-
body orbit to:
A) The satellite's mass only
B) The radial distance from the central body and the semi-major
,3
axis
C) The eccentricity only
D) The orbital period only
Explanation: The vis-viva equation is v² = μ(2/r - 1/a). It gives the
speed v at any point in the orbit as a function of the radial distance r
and the semi-major axis a.
6. The trajectory equation for the two-body problem is:
A) r = a(1 - e²)/(1 + e cos θ)
B) r = p/(1 + e cos θ), where p = h²/μ is the semi-latus rectum
C) r = a(1 - e²)
D) r = h²/(μ(1 + e cos θ))
Explanation: The conic trajectory equation is r = p/(1 + e cos θ),
where p = h²/μ is the semi-latus rectum, e is the eccentricity, and θ is
the true anomaly.
7. Which of the following is NOT conserved in the two-body
problem?
A) Specific mechanical energy
B) Specific angular momentum
C) The velocity vector
D) The orbital plane orientation
Explanation: While energy and angular momentum (magnitude and
direction) are conserved, the velocity vector changes continuously as
the satellite moves along its orbit. Only the energy and angular
momentum are constants of motion.
8. The "n-body problem" differs from the two-body problem
primarily because:
A) It considers only two bodies
B) It accounts for the gravitational perturbations from multiple
, 4
bodies simultaneously
C) It ignores gravitational forces altogether
D) It only applies to artificial satellites
Explanation: The n-body problem considers the gravitational
interactions among n bodies, making it analytically unsolvable in
closed form for n ≥ 3. The two-body problem is a simplification that is
analytically solvable.
9. A satellite is in a circular orbit around Earth. If the satellite's
altitude is doubled, the orbital speed will:
A) Double
B) Decrease by a factor of √(R/(R+h))
C) Remain the same
D) Increase by a factor of √2
Explanation: For a circular orbit, v = √(μ/r). If the radius increases
(altitude doubles), the speed decreases as 1/√r. Doubling the altitude
does not exactly halve the speed, but the speed decreases.
10. The standard gravitational parameter (μ) of a central body is:
A) The product of the universal gravitational constant G and the
mass of the central body
B) The mass of the satellite only
C) The radius of the central body
D) The orbital period of the satellite
Explanation: μ = GM, where G is the universal gravitational constant
and M is the mass of the central body. For Earth, μ ≈ 398,600 km³/s².
11. In the two-body problem, the trajectory of a satellite with zero
total mechanical energy is:
A) An ellipse
B) A parabola
