5 ms·
If its mass is 10 times Earth but it has similar density, its diameter would be 10^1/3 times Earth's, or 2.75 x 10^7 m. 1000 AU is 1.50 x 10^14 m. Their ratio
by dietrichepp 11y ago
If its mass is 10 times Earth but it has similar density, its diameter would be 10^1/3 times Earth's, or 2.75 x 10^7 m. 1000 AU is 1.50 x 10^14 m. Their ratio is equal to the angular size in radians, since atan(x) = x to within our desired precision, giving 2.75e7/1.5e14/2pi36060*60 = 0.0378 arcseconds.
The Keck observatory has angular resolution of 0.04 arcseconds at best, according to Wikipedia. So, by this back of the envelope calculation, the answer is "theoretically, but probably not".
- tomr_stargazer 11y agoIn your above calculation, you're assuming that an object needs to be resolved to be visible. To the contrary, telescopes are able to see un-resolved objects (objects whose angular size is below the angular resolution of the telescope) all the time -- they are called "stars". The relevant parameter here isn't angular size, but flux[0] (brightness). [0] https://en.wikipedia.org/wiki/Radiative_flux https://en.wikipedia.org/wiki/Radiative_flux
- dietrichepp 11y agoYou're absolutely right, I realized that right after I posted that.