The Comet Borrelly has an elliptical orbit with an eccentricity of $e \approx 0.624$ .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun?
A) $\frac { 1.780 } { 1 - 1.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.
B) $\frac { 1.780 } { 1 + \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.
C) $\frac { 0.624 } { 1 + 1.780 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.
D) $\frac { 1.780 } { 1 + 0.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.
E) $\frac {1.780}{ 1 - 1.624 \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.

Question

The Comet Borrelly has an elliptical orbit with an eccentricity of ​ $e \approx 0.624$ .The length of the major axis of the orbit is approximately 5.83 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun? ​
A) $\frac { 1.780 } { 1 - 1.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.
B) $\frac { 1.780 } { 1 + \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.
C) $\frac { 0.624 } { 1 + 1.780 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.
D) $\frac { 1.780 } { 1 + 0.624 \sin \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.
E) $\frac {1.780}{ 1 - 1.624 \cos \theta }$ Closest point to the sun is $\approx$ 1.096 astronomical unit.

Quizplus · Accepted Answer

The polar equation for an elliptical orbit is given by $\frac{a(1-e^2)}{1+e\cos\theta}$, where $a$ is the semi-major axis. Here, $a = \frac{5.83}{2} = 2.915$ and $e = 0.624$. The correct equation is $\frac{1.780}{1 + 0.624 \cos \theta}$. The closest point to the sun (perihelion) is $a(1-e) = 2.915(1-0.624) \approx 1.096$ astronomical units.

The Comet Borrelly Has an Elliptical Orbit with an Eccentricity e≈0.624e \approx 0.624e≈0.624

The Comet Borrelly Has an Elliptical Orbit with an Eccentricity $e \approx 0.624$