How does Kepler's 3rd law relate to binary stars?

Question

I have to give a powerpoint presentation on binary stars but I don't really understand Kepler's 3rd law so I won't know how to explain it during the presentation. Can someone tell me a way to explain it in a way that I will also understand it? Thanks!!

Answer 1

Kepler's third law states that the square of a planet's orbital period is proportional to the cube of its average orbital radius. This doesn't apply directly to systems of only two bodies.

However, the underlying principle behind this law is the inverse square law of gravitation. This is important in binary systems because if we can measure the distance and period of the motion, we can calculate the masses of the stars involved - see the second link.

Answer 2

This is a hard one... Kepler's 3rd law mostly has to do with planets & their central star. It states that, the square of a planet's year is proportional to the cube of it's distance from the sun.

Now, if the binary system we're talking about is Sirius a & b, then the small companion star can be regarded as a planet; it's orbit about Sirius a can be calculated using Kepler's 3rd law. Sirius b is a small white dwarf that orbits Sirius a in a very elliptical path, moving much faster when it's closer to Sirius a than when it's further away.

However, if it's two equal-size stars circling a common center of gravity, then... I suppose it would extrapolate to be the same - each star would move faster the closer it was to the center of gravity for the system. If the stars were far apart, they would circle each other slowly; if they were very close, they would circle each other extremely quickly. (There are some stars that circle each other in a matter days.)

Answer 3

It is the same to the planet-sun system. Now there are binary stars and if the masses are similar, both star have elliptic orbits and the focus for both orbits is the center of mass of the system that may be between the stars or inside one of them. The same happened with double planetoids as Pluto and Caronte: Both turn around the common mass center. If we see the Jupiter-Sun orbits, something similar happen there: the Sun-Jupiter mass center lay a little above the Sun's surface, so a star and a planet can turn around their barycenter. The period is the same: the Sun would have a 12 years 'year', yes?. yyyyyeah

Answer 4

a million. now no longer some thing transformations 2. now no longer some thing transformations. Kepler's 0.33 regulation is era squared (in earth years) = semi-important axis cubed. Mass isn't lined. as quickly as you make the main of Newton's version, the loads cancel out, as quickly as you do the mathematics suitable. countless people shrink lower back to rubble on the instruments whilst utilising Kepler's regulation the 1st few situations. I did that lots whilst i grew to become into in a junior element introductory astrophysics course on the college of Arizona. That course taught me to continually shop song of the instruments, and to double and triple examine each and each issue whilst the instruments are no longer any further optimal magnificent, AND to double and triple examine the unit conversion too.

Answer 5

From Wikipedia:
"The third law : The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits."

The orbital period is just the time it takes the satellite to travel around the Earth once. This is the same for a planet traveling around the sun. I would imagine it would be the same for a star orbiting another star. (Often denoted "T" or the greek letter tau.)

The semi-major axis is part of an ellipse's geometry. It is half the distance of the longest axis of the ellipse. If the orbit is a circle the semi-major axis is just the radius. (Often denoted "a" for ellipse, "r" for circle.)

So basically:
T^2 is proportional to a^3

Answer 6

ummmm. actually no