Units for Kepler's 3rd Law

  • Thread starter Calpalned
  • Start date
  • #1
297
6

Homework Statement


Kepler's 3rd law can be written as ##p^2=a^3##
If p, the period, is given in years, what are the units for a?

Homework Equations


n/a

The Attempt at a Solution


The answer is AU. Is there a proof for this or is this merely a definition? Thank you.
 

Answers and Replies

  • #2
63
10
Let's consider the Earth.

If we choose the "year" for period, then the value of ## a ## also have to be ## 1 ## with some unit and the only thing is ## 1 \text{AU}. ## You may think that this is the definition for ## \text{AU}. ##

BTW, be careful about dimensions of each side. ## (\text{Year})^2 \neq (\text{AU})^3, ## and so usually we write the law as ## p^2 \propto a^3. ##
 
  • #3
S.G. Janssens
Science Advisor
Education Advisor
980
755
Please pardon my ignorance, but I would feel that, strictly speaking, we cannot know the units of ##a## as long as we do not know the units of the proportionality constant ##C## in the relation ## \frac{a^3}{p^2} = C##? And vice versa, of course.
 
  • #4
63
10
Please pardon my ignorance, but I would feel that, strictly speaking, we cannot know the units of ##a## as long as we do not know the units of the proportionality constant ##C## in the relation ## \frac{a^3}{p^2} = C##? And vice versa, of course.
Otherwise, you may fix first the units of ## a## and ## p##, then you can get the constant ## C ## with some unit.
 
  • Like
Likes S.G. Janssens

Related Threads on Units for Kepler's 3rd Law

  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
5
Views
1K
Replies
8
Views
3K
  • Last Post
Replies
11
Views
1K
  • Last Post
Replies
5
Views
1K
Replies
7
Views
9K
D
  • Last Post
Replies
2
Views
798
Top