Understanding Kepler's Laws and Parallax in Astronomy

[Wellsi]

I have been reading into Kepler's laws lately because I am absolutely intrigued by space and the cosmos, but the second one about equal time and equal areas doesn't quite make sense on wikipedia or the physics textbook (Giancoli 3rd Edition i believe)...
and can someone help me understand parallax a little better? its a little confusing

 

[Kurdt]

Parallax can be understood by a simple trick I was told when I was first learning about it. If you hold your finger out at arms length upright and alternately open and close each eye you can see your finger appears to move against the background. If you move your finger closer to your eyes and try it again you will notice it appears to move a greater distance on the background. We can measure the distance to the few hundred nearest stars by a similar principle. As the Earth orbits about the sun the star you are measuring appears to move wrt the background stars that are further away. If you observe for a year you can see how far it moves wrt the background stars and thus how far away it is from the Earth.

With regards to Kepler's 2nd law all it implies is that the planet moves quicker when closest to the star and slower when its further away. This is because the orbit is elliptical and the force between the planet and the star is stronger when the two are closer and weaker when the two are farther away. I'm not sure how much more I could add to that.

 

[Wellsi]

ok thanks for the kepler thing that helps a lot :)
But parallax? i get the bit about how the star moves in relation to the background, so how do they calculate how far it is?

 

[russ_watters]

Draw a triangle and calculate the distance based on the angles you just measured and the distance to the known object.

 

[Wellsi]

so the base of the triangle is 1AU, that's ok, the right angle is at the sun's corner? we have the angle to the star - so its all trigonometry now?

 

[SpaceTiger]

I have been reading into Kepler's laws lately because I am absolutely intrigued by space and the cosmos, but the second one about equal time and equal areas doesn't quite make sense on wikipedia or the physics textbook (Giancoli 3rd Edition i believe)...

Kepler's second law is basically a statement of conservation of angular momentum. In general, this will be:

$$\vec{L}=m\vec{r}\times \vec{v}$$

As the planet gets closer to the sun, its speed increases and its radius decreases. The area swept out per unit length is smaller when closer to the star, but the fact that it's moving faster compensates, keeping the area swept per unit time constant.

That's a very crude explanation, but should give the general picture.

 

[russ_watters]

so the base of the triangle is 1AU, that's ok, the right angle is at the sun's corner? we have the angle to the star - so its all trigonometry now?

Yep, you got it...