Measuring the distance to a superior planet

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Measuring the distance to a superior planet
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The stars are so far away that, wherever Earth is
in its orbit, we have to look in the same
direction to see the vernal equinox or any other
reference point on the sky.
D
C
S
A
Eastward
B
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Heliocentric longitude is the angular
displacement of a planet measured eastward from
the vernal equinox as seen from the Sun.
D
C
S
A
B
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The geocentric longitude of a planet is the angle
between the direction of the vernal equinox and
the direction from Earth to the planet.
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Using Triangulation to Measure the Position of
Mars on Two Dates Separated by One Sidereal Period
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Example The period of revolution of a planet is
456 days. On 22 December 1995, its geocentric
longitude was 135o. On 22 March 1997, its
geocentric longitude was 90o. Since they are
separated by 456 days, the planet was at the same
position (heliocentric ecliptic longitude,
heliocentric ecliptic latitude) on both dates.
How far from the Sun, in AUs, was it?
V
S
V