The Mars Polar Lander spacecraft was launched on January 3, 1999. On December 3, 1999, the day Mars Polar Lander touched down on the Martian surface, the positions of the earth and Mars were given by these coordinates: 

In these coordinates, the sun is at the origin and the plane of the earth€™s orbit is the xy-plane. The earth passes through the +x-axis once a year on the autumnal equinox, the first day of autumn in the northern hemisphere (on or about September 22). One AU, or astronomical unit, is equal 1.496 x 10⁸ to km, the average distance from the earth to the sun.

(a) In a diagram, show the positions of the sun, the earth, and Mars on December 3, 1999.

(b) Find the following distances in AU on December 3, 1999:

(i) From the sun to the earth;

(ii) From the sun to Mars;

(iii) From the earth to Mars. 

(c) As seen from the earth, what was the angle between the direction to the sun and the direction to Mars on December 3, 1999?

(d) Explain whether Mars was visible from your location at midnight on December 3, 1999. (When it is midnight at your location, the sun is on the opposite side of the earth from you.)

Transcribed Image Text:

х 0.3182 AU 1.3087 AU 0.9329 AU Earth Mars 0.0000 AU -0.0414 AU -0.4423AU