The methods of astrophysics

5.2.1 The moon and the falling apple

By applying his laws of mechanics and gravitation to outside the earth, Newton established the principle that the same laws govern phenomena everywhere. The apple falling from the tree, the earth orbiting the sun, the moons of Jupiter, are all subject to exactly the same laws of nature. Gravitational forces keep us in orbit, just at the right distance from the sun to give conditions suitable for life. Gravitational forces govern the motion of all the stars in the galaxy, and even the motions of the galaxies themselves.

The same principle was soon extended to other forces and other physical laws. Electromagnetic and nuclear forces all have their parts to play in the running of the universe. The sun is powered by nuclear fusion, its heat energy transported away in all directions by electromagnetic waves, subject to the laws of electromagnetism.

5.2.2 Predicting the existence of new planets

In 1781 William Herschel (1738-1822) of Bath, England, using a homemade 10 ft telescope, discovered a new planet, Uranus, about twice as far from the sun as the then-outermost known planet, Saturn, and with an orbit of about 84 years. Perhaps the most interesting thing about Uranus was that subsequent careful measurements showed that it was 'misbehaving', by not quite following the path predicted by Newton's law of gravitation. Even when the perturbing forces of the other planets had been taken into account, Uranus did not follow exactly its schedule worked out by the most careful Newtonian calculations.

One possible suggested explanation was that Newton's law of gravitation did not hold exactly at distances as large as the distance from Uranus to the sun. Such an explanation could be accepted only as a last resort. Destroying, as it would, the belief in the universal nature of the law of gravitation, it would be a huge setback to natural philosophy.

Why is Uranus 'misbehaving'?

John Couch Adams (1819-1892), a student of mathematics at Cambridge, undertook a very difficult mathematical task based on the assumption that another, as-yet-undiscovered, planet was orbiting outside Uranus. One can imagine the magnitude of the task of explaining the observed perturbations of the orbit of Uranus on the basis of three-dimensional calculations involving an unknown mass in an unknown elliptical orbit.

The calculations were, nevertheless, completed by Adams in September 1845, at which time he presented his result to George Airy (1801-1892), his professor at Cambridge, and then to James Challis, director of the Greenwich Royal Observatory. With all the confidence of youth, he proposed that "should they point their telescopes in a certain direction at a certain time they would observe a new planet hitherto unknown to man". As Adams was young and unknown, his suggestion was not taken seriously at Greenwich.

Neptune is there!

Shortly afterwards, Jean Joseph Le Verrier (1811-1877), working in France, quite independently published a result very similar to that of Adams. In his case, however, he wrote to Johann Gottfried Galle, the head of the Berlin Observatory, where he was taken seriously. Galle himself looked, apparently within an hour, and found the predicted planet. Thus another planet, Neptune, was added to the solar system in October 1846. This was a triumph for Newton's theory. Any doubt that the theory was universal evaporated.

This is a classic example of predicting an as-yet-undiscovered phenomenon. In this case, confirmation followed almost immediately. The existence of the planet was inferred independently by Adams and Le Verrier, with no instruments other than pen and paper. Le Verrier's work has been recognised with the naming of a lunar crater, Crater Le Verrier, and a street (Rue Le Verrier) in Paris.

Pluto

In more modern times, using the sophisticated telescopes of the 20th century, additional perturbations were found in the motion of both Uranus and Neptune, leading to the hypothesis that there was still another, as-yet-undiscovered, planet. Eventually, in 1930, the relatively small planet Plutof was discovered at the Lowell Observatory in Arizona.

In Table 5.1, planetary masses and sizes, together with their respective orbital parameters, are expressed in terms of the corresponding quantities for the earth.

for all the planets, to

a high degree of accuracy.

The final column gives the inclination of the plane of the orbit of the planet to the plane of the earth's orbit. With the exception of Pluto and, to a lesser extent, Mercury, all the planets orbit in approximately the same plane.

5.3 Other stars and their 'solar systems' 5.3.1 Planets of other suns

Do 'they' know about our planet earth?

If we imagine 'little green men' living on a planet similar to ours in some other solar system, it is interesting to speculate whether they see us with highly developed telescopes! The answer is that their observation technique would have to be more highly developed than ours, since the light from our sun would completely block out the relatively small intensity of light reflected from the earth. As mentioned before, unless they happen to be among our nearest neighbours in the Milky Way, their information about the earth would be out of date by tens if not hundreds of thousands of years.

Indirect evidence of planets which orbit stars other than the sun has recently become available, leading to considerable

T Following a decision of the International Astronomical Union (IAU), made in Prague on 24 August 2006, Pluto is no longer officially considered to be a planet. Its status has been changed to that of a dwarf planet (one of more than 40).

Table 5.1 Major members of the solar system (2006) and their properties.

Table 5.1 Major members of the solar system (2006) and their properties.

Semi-

Inclin.

Sidereal

major

of orbit

Diameter

Mass

period

axis a

to

Planet

(earth = 1)

(earth = 1)

T (years)

(AU)

T 2

a3

ecliptic

Mercury

0.38

0.055

0.2408

0.3871

0.0580

0.0580

7.00°

Venus

0.95

0.82

0.6150

0.7233

0.3782

0.3784

3.39°

Earth

1.00

1.00

1.0000

1.0000

1.00

1.00

0.00°

Mars

0.53

0.107

1.8809

1.5237

3.54

3.60

1.85°

Jupiter

11.2

317.8

11.86

5.2028

140.66

140.83

1.31°

Saturn

9.41

94.3

29.46

9.588

867.9

881.4

2.49°

Uranus

3.98

14.6

84.07

19.191

7.07 x 103

7.01 x 103

0.77°

Neptune

3.81

17.2

164.82

30.061

2.71 x 104

2.72 x 104

1.77°

Pluto

0.18

0.002

248.6

39.529

6.16 x 104

6.18 x 104

17.15°

excitement about what might be seen as a move from science fiction to scientific fact. Despite some over-enthusiastic early comments, the search for planets likely to support life (much less 'little green men' with whom we might communicate) is likely to be a lengthy one.

The most convincing evidence for extra-solar planets comes from the Hubble Space Telescope, which has measured a reduction in the intensity of light from a star as a result of a planet passing in front of it. In a press release on 4 October 2006, NASA reported evidence for 16 new extra-solar planets in a survey of part of the central region of the Milky Way. The candidates must be at least as massive as Jupiter to block out a measurable amount of light. An extrapolation of the survey data to the entire galaxy would seem to indicate the presence of about 6 billion Jupiter-sized planets in the Milky Way! Five of the 16 candidates belong to a new class, the 'ultra-short-period planets' (USPPs), which orbit their respective stars in about one earth day. They are quite different from planets in the solar system in that they are located only about one million miles from the parent star, a hundred times closer than the earth is from the sun.

Extra-solar planets may also be detected using the Doppler effect (a change in the frequency of light waves as a result of motion of the source, which is described in Chapter 6). This can be achieved by considering how planets and stars move relative to one another and therefore to us.

The planet and its parent star, bound together by gravitational force, orbit their common centre of mass in a manner similar to the atoms of a hydrogen molecule. (In this diatomic molecule, the two atoms rotate about their common centre of mass, midway along the line joining them.) However, the star, being much larger than the planet, is much closer to the centre of mass and the radius of its orbit is very small, as illustrated in Figure 5.6.

The star moves towards us and then away from us as it goes around in its tiny orbit. The star emits light characteristic of

Diagram not to scale. Centre of mass of star-planet system much closer to centre of star and often inside star.

orbit of star

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