= Solution
Measure angles from <periapsis> in the direction of motion. The <true anomaly> $f$ is the angle at the stellar focus between the pericentre ray and the star-particle radius vector. Draw the auxiliary circle of radius $a$ around the <ellipse>'s center; the point on that circle with the same projected major-axis coordinate as the particle defines the <eccentric anomaly> $E$ at the center.
The <mean anomaly> $M=n(t-\tau)$ is a uniformly advancing time phase, with $M=0$ at pericentre passage $t=\tau$. It is the angle swept by a fictitious uniformly moving circular phase marker, not generally the actual position angle. The <mean motion> is the <angular frequency>
$$
\boxed{n=\sqrt{GM_\star/a^3}=\frac{2\pi}{T},\qquad M=E-e\sin E.}
$$
The second formula is <Kepler's equation>, which converts the uniform time phase into geometric position.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/iii/paper-316-orbital-anomalies.png]
{title=<True anomaly>, <eccentric anomaly>, and <mean anomaly>}
{description=The <ellipse>, its auxiliary circle, the stellar focus, the particle, and the uniform mean-phase marker. E is measured at the center and f at the focus; M is a time phase.}
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