Spaceflight Mechanics - Position & Velocity as a Function of Time Quiz(MCQ)

A)
Johannes Kepler
B)
Ptolemy
C)
Tycho Brahe
D)
Nicolas Copernicus

Correct Answer :   Johannes Kepler


Explanation : Time of flight which is the transit time between two positions in an orbit was found out by Johannes Kepler. He found out the relation between the orbital position and time of flight which came to be known as Kepler’s equation.

A)
h
B)
h/2
C)
h/3
D)
2h

Correct Answer :   h/2


Explanation : According to the figure below, the rate of area swept by the radius vector is always a constant. This is h/2. Where A1 is the area swept by the planet by moving from periapsis to point P. The relation is given by:
dA/dt = h/2

A)
Eccentricity
B)
True anomaly
C)
Mean anomaly
D)
Eccentric anomaly

Correct Answer :   Eccentric anomaly


Explanation : Eccentric anomaly is the angle that is formed by drawing an auxiliary circle of an ellipse with center O and focus F. A perpendicular line is drawn to the semimajor axis intersecting at A. The angle E thus formed is the eccentric anomaly. It is used to obtain the position of the body in the orbit.

A)
Eccentricity
B)
True anomaly
C)
Mean anomaly
D)
Eccentric anomaly

Correct Answer :   Mean anomaly


Explanation : The mean anomaly is an angle an imaginary satellite would have if it were in a circular orbit around the center point O with a time period T equal to the true satellite orbit.

A)
Barker’s equation
B)
Euler’s equation
C)
Kepler’s equation
D)
Madelung equation

Correct Answer :   Barker’s equation


Explanation : Barker’s equation is used to determine the time of flight from periapsis to a position on the parabolic trajectory at a true anomaly of θ.