Gravitational waves might be slowing them down?

[Rosanella]

Am I missing something here?

With my writing hand in heavy bandage after Tuesday's operation, I have time to catch up with a few books on the 'to-read' list, audiobooks and podcasts on the 'to-listen-to' list. Incidentally, Relativity has been on my 'how-does-it-work?' list and there's one thing that really baffled me was finding out that gravitational waves might be the cause of the slowing down of the binary system PSR1913+16 when the two stars pass close to each others -- apparently, this binary system has been under study for 25 years. It is thought that in closer proximity they both emit large amounts of gravitational radiation.

What? Slowing down when they pass close to each other??? How? Should they not speed up, rather, due to the stronger gravitational field between the two? Am I missing something here?

Gravitational waves are not still proven to exist BUT...I'm confused

[George Jones]

I'm not sure what you mean by "the slowing down."

The energy of the gravitational radiation comes from orbital energy, so gravitational radiation that streams away from the system causes orbital energy to decrease. This causes orbital radius and period to decrease, and orbital speed to increase.

[Rosanella]

I'm not sure what you mean by "the slowing down."

That's what I don't quite understand...

The energy of the gravitational radiation comes from orbital energy, so gravitational radiation that streams away from the system causes orbital energy to decrease. This causes orbital radius and period to decrease, and orbital speed to increase.

I'm sorry, but I still don't quite get it

[George Jones]

I hope your hand is healing well

Let's step back from gravitational radiation for a bit and break things down into bits.

First, consider speeds in orbits. For concreteness, take orbit 1 to be the orbit of the ISS about the Earth, and orbit 2 to a hypothetical larger orbit of the ISS about the Earth at the Moon's distance.

In which orbit, 1 or 2, does the ISS have the greater speed? The answer to this question can worked out using Newton's laws, or using Kepler's third law, which comes from Newton's laws. I think that I want to use Kepler.

Let the period and radius of orbit 1 be p and r, and the period and radius of orbit 2 be P and and R. Kepler's second law gives

p^2/r^3 = P^2/R^3.

Now, the period of each orbit is the distance around the orbit divided by the speed of ISS in orbit,

P = 2 pi R/V and p = 2 pi r/v.

I have used poor notation in that it is difficult to distinguish between upper case and lower case letters. Everything to with the larger orbit is upper case; everything to with lsmaller orbit is lower case.

What happens when the expressions for the period are put into the expression fro Kepler's third law? Can R > r be used to tell which of v and V is bigger?

[Rosanella]

I hope your hand is healing well

I think it is, thank you I'm catching up with lots of reading and podcasts but feeling restless ... ... the stationary bike helps though

..Let's step back from gravitational radiation for a bit and break things down into bits.

First, consider speeds in orbits. For concreteness, take orbit 1 to be the orbit of the ISS about the Earth, and orbit 2 to a hypothetical larger orbit of the ISS about the Earth at the Moon's distance.

In which orbit, 1 or 2, does the ISS have the greater speed? The answer to this question can worked out using Newton's laws, or using Kepler's third law, which comes from Newton's laws. I think that I want to use Kepler.

Let the period and radius of orbit 1 be p and r, and the period and radius of orbit 2 be P and and R. Kepler's second law gives

p^2/r^3 = P^2/R^3.

Now, the period of each orbit is the distance around the orbit divided by the speed of ISS in orbit,

P = 2 pi R/V and p = 2 pi r/v.

I have used poor notation in that it is difficult to distinguish between upper case and lower case letters. Everything to with the larger orbit is upper case; everything to with lsmaller orbit is lower case.

What happens when the expressions for the period are put into the expression fro Kepler's third law? Can R > r be used to tell which of v and V is bigger?

Thank you for the break down...thinking cap on ....If I'm looking at the equations correctly, I see that the

(2*pi*r) is directly proportional to (p * v) (and likewise (2*pi*R) is directly prop. to (P*V) for the larger orbit 2) , that is

(p * v)=(2*pi*r) and (P*V) = (2*pi*R) , so the orbit increases as period and velocity increase too. Also, orbit 1 (2*pi*r), being smaller than orbit 2 (2*pi*R) it would have a shorter radius -- r<R or R>r.

Then it follows that when ISS goes around a larger orbit, the radius R increases with velocity increasing too. Or vice versa, when ISS has a shorter orbit (as in orbit 1) having a shorter radius, then velocity decreases.

Have I got that?.....

[George Jones]

I see that the

(2*pi*r) is directly proportional to (p * v) (and likewise (2*pi*R) is directly prop. to (P*V) for the larger orbit 2) , that is

(p * v)=(2*pi*r) and (P*V) = (2*pi*R) ,

Yes, good.

so the orbit increases as period and velocity increase too. Also, orbit 1 (2*pi*r), being smaller than orbit 2 (2*pi*R) it would have a shorter radius -- r<R or R>r.

Then it follows that when ISS goes around a larger orbit, the radius R increases with velocity increasing too. Or vice versa, when ISS has a shorter orbit (as in orbit 1) having a shorter radius, then velocity decreases.

Have I got that?.....

Let's check this by eliminating p and P in Kepler's third law. I get

   2*pi*r              2*pi*R
 (--------)^2  =  (----------)^2
      v                        V
------------          ------------ .
      r^3                 R^3

Does this make sense? If not, ask some more questions. If so,

rearrange this so that v^2 and V^2 are on one side of the equation, and r and R are on the other side.

[Rosanella]

I'm enclosing my workings (in case I've made some errors) and my calculations give me something that I've seen before:

V^2/v^2 = r/R

I seeee! The velocities are inversely proportional to their respective radii, that is when ISS's orbit 1 (the smaller orbit) increases its velocity v decreases and the same applies to orbit 2 and V...

BUT, in the case of the binary system PSR1913+16 the two stars slow down (velocity decreases) when they pass each other and I understand 'pass each other' as being closer or is that not necessarily the case?

SGL_GravitationalWavesstuff.doc

[vhbelvadi]

...gravitational waves might be the cause of the slowing down of the binary system PSR1913+16 when the two stars pass close to each other...

I've read a couple of papers related to a 'slowing down' phenomenon in the PSR 1913+16 system, but all papers (such as Dworak, T. Z. and Kulak, A.'s "The pulsar PSR 1913 + 16 in a binary system and gravitational waves" in Postepy Astronomii) only talk about a decrease in the orbital period.

I expect you know that in such cases, radial velocity is measured indirectly, by using pulses of light emitted by the two stars. Due to an increase in gravitational force when these stars are close to each other, gravitational time dilation occurs, as predicted by Einstein, and this, in turn, affects the time period between the emitted pulses, which means we percieve the radial velocity decreasing.

It is being debated that this effect of gravity is due to the hypothetical 'gravitational waves'.

Hope I've made myself clear.

[Take a look at the attached document, though. I picked up some graphs which I thought would explain it better]

Gravitational waves are slowing them down.doc

[Rosanella]

Thank you George & vhbelvadi for shedding some light to my earlier confusion