Kepler's Third Law: Proportional Orbit Period to Distance^1.5

AI Thread Summary
Kepler's Third Law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. In the case of two gravitationally bound stars of equal mass, their orbital period (tau) can be shown to be proportional to the distance (d) raised to the power of 1.5, or d^(3/2). The radius of each star's orbit is directly related to the distance between them, which is crucial for deriving the relationship. Understanding these principles allows for the calculation of orbital periods based on their separation. This discussion emphasizes the mathematical relationship between orbital period and distance in a binary star system.
eku_girl83
Messages
89
Reaction score
0
Two gravitionally bound stars with equal masses m, separated by a distance d, revolve about their center of mass in circular orbits. Show that the period tau is proportional to d^1.5

Could someone get me started on this? I have no idea where to begin!

Thanks!
 
Physics news on Phys.org
First of all, state Keppler's Third Law.

Also, realize that d^1.5 is the same as d^(3/2)

And then notice how the radius of the orbits is directly proportional to the distance between them.
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »
Thread 'Voltmeter readings for this circuit with switches'

Thread 'Voltmeter readings for this circuit with switches'

TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
View full post »
Thread 'Trying to understand the logic behind adding vectors with an angle between them'

Thread 'Trying to understand the logic behind adding vectors with an angle between them'

My initial calculation was to subtract V1 from V2 to show that from the perspective of the second aircraft the first one is -300km/h. So i checked with ChatGPT and it said I cant just subtract them because I have an angle between them. So I dont understand the reasoning of it. Like why should a velocity be dependent on an angle? I was thinking about how it would look like if the planes where parallel to each other, and then how it look like if one is turning away and I dont see it. Since...
View full post »

Similar threads

Kepler's Third Law vs Conservation of angular momentum
Replies
8
Views
2K
Kepler's third law implies force proportional to mass
Replies
10
Views
2K
Kepler's Law of planetary motion
Replies
10
Views
3K
Kepler's Third Law and Motion of Two Point Masses
Replies
8
Views
2K
Double star mutual orbit calculations
Replies
13
Views
2K
Asteroid Orbits: Finding r with Kepler's Laws
Replies
3
Views
2K
How Does Force Scale with Radius in Orbital Motion?
Replies
12
Views
1K
I Kepler orbits for planets of similar masses
Replies
2
Views
1K
Can a change in units cancel out G/4π2 in Kepler's third law?
Replies
5
Views
2K
Law of universal gravitation and Kepler's law
Replies
29
Views
3K

Hot Threads

Recent Insights

Back
Top