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Chapter 11: Problem 47

(a) Suppose you have a telescope with an angular resolution of 1 arcsec. What is the size (in kilometers) of the smallest feature you could have seen on the Martian surface during the opposition of 2005 , when Mars was \(0.464\) AU from Earth? (b) Suppose you had access to the Hubble Space Telescope, which has an angular resolution of \(0.1\) arcsec. What is the size (in kilometers) of the smallest feature you could have seen on Mars with the HST during the 2005 opnosition?

Short Answer

Expert verified
The smallest feature seen through the telescope is approximately \(334.07\) kilometers and \(33.407\) kilometers when utilizing the Hubble Space Telescope.

Step by step solution

01

Convert Angular Resolution to Radian

First, convert the angular resolution given in arcseconds to radians by the multiplier \(4.8481368 * 10^{-6}\) rad/arcsec.
02

Convert Distance from AU to Kilometers

Next convert the distance from Earth to Mars from astronomical units (AU) to kilometers. Knowing that 1 AU equals approximately 149.6 million km.
03

Calculate Telescope Feature Size

For the (a) scenario, using small angle approximation \(θ = s/d\), where θ is the angle in radians, s is the feature size and d is the distance. Solve for the smallest feature size s: \(s = θ*d\).
04

Calculate Hubble Feature Size

For the (b) scenario, repeat step 3, with the Hubble's angular resolution. Significantly, the smaller resolution leads to a smaller feature size, meaning a more detailed view of Mars.

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