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Astronomical Observations and Technology: Homework 7


    Figure 10 taken from Chemin et al., arXiv 0909.3846 (2009)

  1. M31 is a distance of approximately 800 kpc from the Earth. Use the rotation curve above to estimate the its mass.
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  3. Consider a terrestrial planet like the Earth. An ordinary photo of the planet from space shows large land masses and oceans.


    Image courtesy of NASA

    We can still recognize -- sort of -- these rough features if the photo is degraded to a lower resolution, like this:

    Suppose that we wished to take pictures of a similar planet around some OTHER star -- pictures as detailed as this, from which we might learn at least a bit about the nature of the planet's surface.

    1. Estimate the linear resolution (in km) of the degraded image above. Treat this as the minimum linear resolution required to see continental features.
    2. Consider the TRAPPIST-1 system, which is known to contain a number of Earth-ish-sized planets. What is the distance to this star, according to Gaia DR3?
    3. What is the angular resolution required to reach the linear resolution from part "a" at the distance of TRAPPIST-1? Express your answer in both radians and arcseconds.
    4. Suppose we build an optical interferometer in order to achieve this angular resolution, one that operates at a wavelength of λ = 500 nm. How far apart must be place the elements in order to achieve this resolution?
  4. Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.