Measurements indicate that the orbital eccentricity of Mars is $0.0935$ and its semimajor axis is $1.517323951$ astronomical units.
(a) Write a Cartesian equation for the orbit of Mars.
(b) Do $x$ and $y$ have the same meaning as in Exercise 53?
(c) Give a polar coordinate equation for the orbit of Mars, assuming that the sun is the focus of the elliptical orbit.

Question

Accepted Answer

Part (a) The cartesian equation is $\frac{x^{2}}{2.230227197} + \frac{y^{2}}{2.28214493} = 1 .$

Part (b) The coordinates $x, y$ have the same meaning as given for the earth's orbit.

Part (c) The polar equation is $r = \frac{1.517323951}{1 + 0.0935 \cos θ}$ .

Short Answer