Kepler's 3rd Law as a result of Newton's Laws

AI Thread Summary
Kepler's 3rd Law can be demonstrated for two gravitating bodies in circular orbits around their center of mass by equating gravitational and centripetal forces. The relationship between the distances r1 and r2 from each mass to the center of mass is crucial, with r1 being inversely proportional to m1 and r2 inversely proportional to m2. When both masses are equal (m1 = m2), the ratio of r1 to r2 is 1:1. If the mass of m2 is doubled, the ratio of r1 to r2 changes, indicating that r1 will be smaller compared to r2 due to the increased mass of m2. Understanding these relationships is essential for applying Newton's Laws to derive Kepler's 3rd Law.
takbq2
Messages
32
Reaction score
0
thanks in advance for any and all help!

The question is to show that Kepler's 3rd Law holds when you assume circular orbit with TWO gravitating bodies both orbiting around the center of mass. (by equating gravitational and centripetal forces and finding the constant of proportionality which includes the masses of the gravitating bodies).

my attempt at a solution:

I already have shown it when assuming just one mass. I'm having a very hard time differentiating between the two situations.

I know I need to start by using Newton's 3rd law to get a relationship between r1 and a (where a is the distance between the two masses) and eliminate r2 or vice versa (r1 is the distance from m1 to the center of mass, and r2 is the distance from m2 to the center of mass)


Please help me if you can, I appreciate it so much.
 
Astronomy news on Phys.org
please.. anyone?
 
What do you think the ratio of r1 to r2 would be as compared to the ratio of m1 to m2?
 
bigger m1 means smaller r1.. which would in turn mean smaller m2 and larger r2
 
Alright, what is the ratio of r1 to r2 if m1=m2.

What happens to the ratio of r1:r2 if you now double the mass of m2?
 

Thread 'Does it make sense to build new radio telescopes?'

TL;DR Summary: In 3 years, the Square Kilometre Array (SKA) telescope (or rather, a system of telescopes) should be put into operation. In case of failure to detect alien signals, it will further expand the radius of the so-called silence (or rather, radio silence) of the Universe. Is there any sense in this or is blissful ignorance better? In 3 years, the Square Kilometre Array (SKA) telescope (or rather, a system of telescopes) should be put into operation. In case of failure to detect...
View full post »
Thread 'Could gamma-ray bursts have an intragalactic origin?'

Thread 'Could gamma-ray bursts have an intragalactic origin?'

This is indirectly evidenced by a map of the distribution of gamma-ray bursts in the night sky, made in the form of an elongated globe. And also the weakening of gamma radiation by the disk and the center of the Milky Way, which leads to anisotropy in the possibilities of observing gamma-ray bursts. My line of reasoning is as follows: 1. Gamma radiation should be absorbed to some extent by dust and other components of the interstellar medium. As a result, with an extragalactic origin, fewer...
View full post »

Thread 'Can the signal WOW be explained by the maser effect?'

This hypothesis of scientists about the origin of the mysterious signal WOW seems plausible only on a superficial examination. In fact, such a strong coherent radiation requires a powerful initiating factor, and the hydrogen atoms in the cloud themselves must be in an overexcited state in order to respond instantly. If the density of the initiating radiation is insufficient, then the atoms of the cloud will not receive it at once, some will receive it earlier, and some later. But then there...
View full post »

Similar threads

I Newton's 3rd law and ether in space
Replies
3
Views
1K
I Estimating Mass of Central Object Using S2's Orbit Motion and Kepler's 3rd Law
Replies
3
Views
2K
I Separating Masses in Kepler's Third Law
Replies
1
Views
2K
B Re-evaluating Dark Matter and Kepler's Law in Spiral Galaxies
Replies
3
Views
3K
Kepler's 3rd Law: Solving Questions & Math
Replies
3
Views
3K
I How Can We Measure Properties of Distant Planets and Stars?
Replies
12
Views
2K
B Kepler's 3rd Law, geometric relationship?
Replies
6
Views
5K
I Spring balance analysis from a system point of view
Replies
24
Views
2K
Kepler's Laws: Definition & Equations
Replies
1
Views
2K
A N-Body inputs from Keplerian Orbits
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top