The distance between the Earth and Mars when the two planets are at opposition varies greatly because of the large eccentricity of Mars's orbit. The perihelion distance of a planet is given by r_{min} = a(1 - e) and the aphelion distance by r_{max} = a(1 + e) where a is the semimajor axis and e the orbital eccentricity. Find the smallest and largest opposition distances assuming that the Earth's orbit is a circle.

2

At an average opposition, the Earth and Mars are separated by 0.52 AU. Suppose an astronomer observes Mars at opposition and that seeing blurs the images to a resolution of 1.0 seconds of arc. What is the smallest surface feature the astronomer would be able to resolve on Mars? How does this size compare with the diameter of Mars? (You will need the small angle equation, Equation 3.1, to do this problem.)

3

An astronomer observed Mars at opposition using a telescope that has a lens 50 cm (20 inches) in diameter. The astronomer observes in visible light at a wavelength of 500 nanometers. What is the smallest feature the astronomer could resolve on Mars if the image were not affected by seeing? How does this compare to the diameter of Mars? To the diameter of Olympus Mons? (Use the equation for angular resolution, Equation 6.6.)

4

How long, deep, and wide would a terrestrial chasm have to be to have the same proportions relative to the Earth that Valles Marineris has to Mars?

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