Astronomy Homework Questions! Help!

[Joshua Simons]

Okay, I received 30 astronomy problems to solve for my homework. This is an advanced course, but I originally wanted to attend an introductory course at my local high school (I virtually have no background in astronomy). I solved all of them except these 5 challenge problems. Can someone walk me through them? I have been trying to answer these for a week now. I need to finish these by tomorrow afternoon for my third period class! Thanks!

 

The Crab Nebula subtends an angle of 5.5 arcminutes in the sky. If it is 6300 LY away, what is its linear diameter in light years?

 

What focal length of eyepiece should be used with a 20 cm diameter objective that has a 100 cm focal length to obtain a magnification of 50X?

2cm, right?

The energy emitted by the sun each second is greatest at a wavelength of 500nm. What would be the wavelength of light from a star with three times the sun's temperature? (1,500 nm right?)

 

An asteroid orbits the sun in a nearly circular orbit twice the radius of Earth's orbit. What is its sidereal period? What is its synodic period?

 

Jupiter has a mass of approximately 1.9*1027 kg, and an equatorial diameter of about 1.43*105km. What velocity must an object have to escape its gravitational field from this location?

[AidanThomas]

The Siderial Period - This is the time required for a celestial body within the solar system to complete one revolution with respect to the fixed stars.
The synodic period - This is a rotation of a planet so that it appears to be in the same place in the night sky.

 

Taking into consideration that this object could be smaller than earth but has twice the orbital radius. All you need to figure out is the Siderial and Synodic Periods of earth. From there you can figure out but doubling.