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Empty Space in our Solar System

There is a lot of empty space in our solar system. In a scale model where the sun is represented by a weather balloon 1 meter in diameter sitting in the Baird Auditorium of the Smithsonian's Museum of Natural History, Jupiter would be a grapefruit orbiting at a distance of 500 meters, as far away as the Federal Triangle Metro stop. The earth would be the size of a beer nut, orbiting well outside the museum, say at the distance of Constitution Avenue (see Table 1 for more details).




Model Diameter

Orbital Size




1 m



88 d


3 mm

40 m


224 d


8 mm

70 m


365 d


8 mm

100 m


687 d


4 mm

150 m


12 yr


10 cm

500 m


29 yr


9 cm

1 km


84 yr


3 cm

2 km


165 yr


3 cm

3 km


249 yr


2 mm

4 km

Table 1. Our Solar System

In contrast to our own solar system, the first extrasolar planets were found in tight, short-period orbits. For example, 51 Pegasi was found to have a companion similar in mass to Jupiter,Mayor, M. & Queloz, D. 1995, Nature, 378, 355but orbiting with a period of only 4 days. In our scale model, that planet would be represented by a grapefruit with an orbit about the same size as the stage of the Baird Auditorium. In retrospect it should not have been a surprise that massive planets in short-period orbits were the first to be discovered, because they are the easiest to detect with the Doppler technique being used. This is an indirect technique. We do not see the light reflected (or heat emitted) by the planet itself, but instead we detect the reflex motion that the gravitational pull of the planet induces in its parent star. Just as the planet sweeps around in its orbit, so the parent star must respond with a counterbalancing motion. Of course, the amplitude of the star's motion is much smaller and harder to detect, by the ratio of the masses. Jupiter orbits at 12 kilometers per second, but the sun's raction is 12 meters per second, not much faster than a sprinter can run. But, if you move Jupiter in 100 times closer, the orbital velocity must go up by a factor of 10. If you make the planet 10 times more massive than Jupiter, this also makes the Doppler signature go up by a factor of 10.

Therefore, the first planetary companions discovered by the Doppler technique were in very tight orbits and/or were considerably more massive than Jupiter. This is illustrated in Figure 3, where I have plotted the 20 planets discovered so far using the Doppler technique, together with Jupiter and Saturn. The vertical axis is the semi-major axis of the planet's orbit (a measure of the size of the orbit) in Astronomical Units (AU, the distance of the earth from the sun). At 5.2 and 9.5 AU, Jupiter and Saturn (plotted as filled circles near the top of the figure) have considerably larger orbits than any of the extrasolar planets. The planets at the bottom of the diagram have such small orbits that the periods are as short as 3 or 4 days, and the shapes of the orbits have been circularized by tidal forces.

The horizontal axis in Figure 3 is the mass the planetary companion would have if the orbit happens to be oriented so that we view it edge-on. The actual inclination of the orbit to the line of sight, i, can not be determined from Doppler measurements alone, and thus is usually unknown. If the orbit is actually tilted up to the line of sight, then our estimate of the mass of the planet is too small by the factor 1/sin(i).

Figure 3

In Figure 3 I have only plotted the planet candidates with minimum masses less than 10 Jupiter masses (MJ). There are also a few companions with minimum masses in the range between 10 MJ and the substellar limit at about 75 MJ, but they seem to be relatively rare. It is almost as if the process that makes planets does not produce companions much bigger than 10 or 20 MJ, while the process that makes stars does not produce companions much smaller than 75 MJ.Mazeh, T., Goldberg, D., & Latham, D. W. 1998, ApJL, 51, L199

Contributed by: Dr. David Latham

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David Latham

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