Suppose you discovered an object in the Solar System ?

Suppose you discovered an object in the Solar System that you determined was 0.348 arc seconds in angular diameter. After observing it for a few weeks, you determine its orbit (using Kepler's Laws) and find out it is 7.71 billion kilometers away from Earth. What is the diameter of the object you discovered?Suppose you discovered an object in the Solar System ?
Basic trigonometry:





It's diameter is given by:





sin(a) * d





Where a is the angular diameter %26amp; d is the distance. Plug those numbers in and you get:





sin(0.348/3600) * 7,710,000,000 km = 13,008 km





Note that I divided the angular diameter by 3600 to convert it to degrees: 0.348 arc-seconds = 0.348/60 arc-minutes = (0.348/60)/60 degrees.





Also note that often people approximate sin(x) as x for very very small x (this certainly qualifies) but to do that you'd need to convert it to radians first. Using that approximation you'd get the same number. The difference is in the ninth or tenth digit:





Using sin(x): 13,007.93896


Using x: 13,007.93891