Trig question in Astronomy

Question

When Jupiter is at a distance of 630 million kilometers from Earth (4.2 astronomical units), it has an apparent angular diameter of 46 arcseconds (46/3600 of a degree). Calculate Jupiter’s diameter in kilometers, and state how many times larger this is than the diameter of Earth.

Answer 1

Draw the line segment from Jupiter's center J to Earth's point of observation E; draw right from center of Jupiter to point of tangency T and ASSUME that this makes right triangle  TJE...approximation! 

 

Then tan (23/3600 degrees) = radius TJ / (6.3X10⁸ km).  Solve for TJ, the radius.

 

For radius of Earth, use 3959 miles (convert to km).