Trying to understand what a gravitational wave is

It seems to me that there is a great deal of interest in the possibility of gravitational waves. Several gravitational-wave detectors have been built, and there is even a branch of science with that specific goal in mind, which is gravitational-wave astronomy.

What I don’t understand is the difference between gravitational wave as produced by, say an exploding supernova, versus the change in gravitation at a fixed point in space by some other effect such as a planet (or some other dense body) passing by. Wouldn’t a passing dense body produce a single wave pulse of stronger, and then weaker gravitation, which would travel in a wave to infinity?

For example isn't the effect of Jupiter moving along its orbit producing more or less a gravitational wave which could be detected by sufficiently sensitive instruments millions of miles away?

Answer

Accelerating masses generate gravitational waves, much like accelerating charges generate electromagnetic waves.

Masses in orbit are continually accelerating, so you're right, Jupiter will generate gravitational waves by orbiting around the Jupiter-Sun centre of mass. In this case there's also gravitational radiation from the sun orbiting around the centre of mass of the Jupiter-Sun system (which is at about the radius of the sun). However the power of the wave emitted is tiny.

Wikipedia gives the following formula for the gravitational radiation of two masses in orbit around each other:

$ P = -\dfrac{32}{5} \dfrac{G^4}{c^5}\dfrac{(m_1m_2)^2(m_1+m_2)}{r^5} $

For the Jupiter-Sun system this gives about 200 Watts - less power than my fridge uses!

For two stars orbiting very closely this power can be much higher - if the two objects are both neutron stars of one solar mass and are separated by 1.9$\times$10$^8$ m, then the power radiated is around 1$\times$10$^{28}$ W, which is quite a bit higher.

Using the inverse square law, the two gravitational wave sources will have the same intensity if their distances are in the ratio 1:10$^{14}$. Since we're about 1.5$\times$10$^{11}$ metres away from the sun, a binary neutron pair's gravitational waves will overwhelm that of the Sun if they're closer than around 10$^{25}$ m away, or about 1 billion light years!