Laws of Motion and gravity

June 14, 2015


An unfortunate epiphany of


  • It wasn't long before astronomers had applied Newton's Laws to determine the masses of the known planets, by observing and with each other.
  • In 1781, an amateur astronomer named William Herschel, who had built one of the most powerful telescopes of the time, noticed "a curious either nebulous star or perhaps a comet".

Subsequent observations revealed that this object moved relative to the stars, although more slowly than a comet.

Herschel soon realized that he had discovered a seventh planet, Uranus (and the first in recorded history!).

At its brightest, Uranus is barely visible to the naked eye in a dark sky.

Because of its slow motion, however, Uranus was always mistaken for a star by earlier observers.

  • Uranus has an orbital period of 84 years, but after 50 years it was clear that it wasn't following its predicted orbit.

Astronomers applied Newton's Laws to account for the gravitational pulls of Jupiter and Saturn, but that still did not remove all of the discrepancies.
John Couch Adams and Urbain-Jean-Joseph Le Verrier independently realized that a new planet beyond Uranus might cause these deviations.

In 1843 and 1845, respectively, they applied Newton's Laws to determine its position.

In 1846 Galle and d'Arrest at the Berlin Observatory followed up on Le Verrier's prediction, and quickly identified the eighth planet, Neptune.

Neptune moves even more slowly than Uranus, and it has an orbital period of 165 years.

Question: in the picture shown, looking down on the solar system, what effect would the gravity of the outer planet (Neptune) have on the speed of the inner planet (Uranus)?

  • After some years, positional errors in Neptune's predicted orbit again suggested the presence of another large planet further out.

In 1905, another amateur astronomer, Percival Lowell, who had built his own observatory in Arizona, began a search for this planet, which he called Planet X.

After Lowell died in 1916, his successors at the Lowell Observatory continued the search.
Finally, in 1930, Clyde Tombaugh discovered Pluto, but its observation was fortuitous because its mass is so small that it doesn't have a significant effect on Neptune.

Better measurements of the outer planets' masses (by the Voyager spacecraft in 1970s and 1980s) have now removed the errors in Neptune's position.

  • Generally speaking, a planetary orbit should be fixed in space.

Question: what physical principle requires this?

However, another planet's gravitational pull can make a planet's orbit precess around the Sun.

Question: where have we already seen an example of a precessing orbit?

In 1845, Le Verrier discovered that Mercury's orbit also precesses around the Sun (note the changing orientation of the semimajor axis in the picture).

This is a very small effect, only 0.10 seconds of arc per orbit (43" per century), but even so it could not be explained by the other planets.

Le Verrier hypothesized that there might be another planet inside of Mercury's orbit, so close to the Sun that it was difficult to observe.

This planet, which Le Verrier called Vulcan, has never been found.

So, there was no good explanation for Mercury's precession using Newton's laws, but, like Neptune, the effect was small enough to attribute to measurement errors, and was largely ignored.

Source: www.opencourse.info
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What are Newton's laws of motion and gravity?

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