Kepler's 3rd law to determine mass of jupiter

In summary, the problem at hand is creating a graph of log10(a) vs log10(P) and calculating the mass of Jupiter from the graph. The graph has been created with a trend line of 3/2, but the issue is determining how to calculate the mass from the graph. The equation used is m1+m2= (4*P^2*a^3)/(G*P^2), but there may be a typo or misprint as P^2 appears in both the numerator and denominator. Seeking help and clarification on the equation, the problem should be posted in the Homework Questions section of PF for assistance.
  • #1
bemc
3
0
my problem involves creating a graph of log10(a) vs log10(P) and to calculate the mass of Jupiter from the graph.

I have created the graph and it seems to be right since the of the trend line is 3/2. My problem is that I am unsure how to go about calculating the mass from the graph.

I used the orbital period and length of the semi-major axis of the Galilean satellites and 3 others to get the equation y = 1.5012x - 8.1973

I have tried using m1+m2= (4*P^2*a^3)/(G*P^2), though that produced a rather large value and doesn't utilize the graph at all.

Any help or nudges in the right direction would be greatly appreciated, Thanks!
 
Astronomy news on Phys.org
  • #2
You might try posting this same question in the Homework Questions section of PF
https://www.physicsforums.com/forumdisplay.php?f=153

They are good at giving nudges without actually doing the problem for you.

It looks to me as if you have a typo or misprint in your equation. You wrote a P instead of a Pi (the number 3.14...)
at one point.

m1+m2= (4*P^2*a^3)/(G*P^2)

Better check in your textbook or your notes from class. A plain letter P would stand for the period.
On the other hand Pi^2 is a number roughly about equal to 10. So 4*Pi^2 is roughly about 40.
Once you check to make sure you don't have any major misprints like that, then if you need help
you could see what you can learn at the PF Homework forum.
 
Last edited:
  • #3
thanks for the input - it is actually P, being the period, in my equation, not Pi. I hadn't realized that I had posted in the wrong area.
 
  • #4
Seriously, you need to check your equation in the textbook or the class notes.
In the way you have written it, you have P^2 both in the numerator and in the denominator.
In one case that is correct, it is supposed to be the period squared.
In another case it is not correct---where you have written P^2 you should have written Pi^2.

The Kepler law equation, as usually written, has a pi^2 in it, and what you have written does not. So it looks to me like you have screwed up the equation. Better check.
 

1. How does Kepler's 3rd law help determine the mass of Jupiter?

Kepler's 3rd law, also known as the law of harmonies, states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. By measuring the orbital period and semi-major axis of Jupiter's moons, we can use this law to calculate Jupiter's mass.

2. What is the formula for using Kepler's 3rd law to determine Jupiter's mass?

The formula is M = 4π²a³/GT², where M is the mass of Jupiter, a is the semi-major axis of its moons' orbits, G is the gravitational constant, and T is the orbital period of the moons.

3. How accurate is Kepler's 3rd law in determining Jupiter's mass?

Kepler's 3rd law is a very accurate method for determining Jupiter's mass. It has been used by scientists for centuries and has been confirmed by modern space missions such as Voyager and Juno. However, it may not account for small perturbations caused by other planets or objects in the solar system.

4. Can Kepler's 3rd law be used to determine the mass of other planets?

Yes, Kepler's 3rd law can be used to determine the mass of any planet, as long as we know the orbital period and semi-major axis of its moons or satellites. It has been used to calculate the masses of many planets in our solar system and beyond.

5. Are there any other methods for determining Jupiter's mass besides Kepler's 3rd law?

Yes, there are other methods for determining Jupiter's mass, such as analyzing its gravitational effect on other objects in the solar system or using data from spacecraft missions. However, Kepler's 3rd law remains one of the most reliable and widely used methods for calculating the mass of Jupiter.

Similar threads

  • Astronomy and Astrophysics
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
398
  • Astronomy and Astrophysics
Replies
4
Views
2K
  • Astronomy and Astrophysics
Replies
1
Views
2K
  • Classical Physics
Replies
2
Views
768
  • Advanced Physics Homework Help
Replies
2
Views
4K
  • Astronomy and Astrophysics
Replies
2
Views
1K
  • Astronomy and Astrophysics
Replies
17
Views
3K
  • Classical Physics
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
940
Back
Top