OK - let's use what we've just worked out to work out how
heavy the planet is around this pulsar
First some data: we can measure the orbital
period, how long the pulsar takes to wobble backwards and forwards
which is the same time as it takes the planet to orbit backwards and forwards
for one of the planets: this pulsar actually has three planets, but just take one of them
25.626 bdays plus or minus 003 - look at that
beautiful precision. You can also measure
in addition to how long it takes to do one oscillation, ow big the oscillation
is, that is to say, how much sooner than average the pulses
arrive at one end, and how much later at the other, and that truns out to be a whopping 3.0
micro-seconds. OK
so that's our data, what do we do from here? Well, the first thing to do is
take this orbital period and use this to find out how far out the planet is
We use the equation we derived earlier
We need to factor in the mass of the neutron star, which is about 1.4 times
the mass of the Sun probably, as we will discuss in the violent universe course.
and that will give us a value of
2.8 by ten to the ten
metres, which is about
0.2 astronomical units. So
this planet is 20% as far out as
the Earth is from the Sun. OK - so that's got how far
out it is, how about its mass? Well, for that we use
the fact that the mass of the star over
mass of the planet equals the radius of the planet's orbit
divided by the radius of the star's orbit.
Now we know the radius of the planet's orbit - we've just computed it up here. We know
the mass of the star, what we need is the radius of the reflex
motion of the star, and we get that from the timing oscillation.
If the star timing varies by
three microseconds, we're going to assume the orbit is edge-on here
that means that the radius is the distance light travels
in three microseconds, so r star is
three by ten to the minus six - that's the time
times the speed of light, which is three by ten to the eight
metres per second, which comes out as about nine hundred
metres, so the reflex motion of the star is backwards and forwards
and a radius of about nine hundred metres. So what we could
learn from that is that m planet sine
i is
about 0.02
times the mass of the Earth.
So - this is probably a little baby planet
If the orbit is edge on, so sine i is one, then the mass of the planet
is only two percent that of the Earth. If the sine inclination is larger
so it's nearer to a face-on orbit, it could be heavier than that, it could be all the way up to infinity in principle
but odds are its a pretty small planet.