Astronomy Exam 3

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Newton himself considered the most productive time of his life for mathematics and science (natural philosophy) to have been when he was

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home at Woolsthorpe during the plague years

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Newton’s Principia originated

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as a followup to a conversation among members (Fellows) of the Royal Society – Wren, Hooke, and Halley

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Which of the following did Halley not do in connection with Newton’s Principia?

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write a considerable portion of it

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The methodology employed by Newton in his Principia was

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a combination of the inductive and deductive methods

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The mathematics of Principia was

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almost calculus, but not quite, yet very difficult

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According to Newton’s Laws of Motion, an object is not being acted on by a net external force so long as

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its velocity isn’t changing

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Which is accelerated more by their forces on each other, the Earth or the Moon? (Earth is more massive than the Moon.)

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the Moon

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Uniform circular motion is caused by the operation of a

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centripetal force

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If two planets have the same mass but different radii, which will have the larger surface gravity?

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the smaller one

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Which of the following orbits is a periodic orbit in the two-body problem?

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ellipse

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According to Newton, an object fired from the Earth with exactly the escape velocity will follow a trajectory that is part of a

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parabolic orbit

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The Earth’s mass is about 81 times greater than the Moon’s. Then the center of mass of the Earth-Moon system is located

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near the center of the Earth

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Newton showed that Kepler’s Law of Areas (Second Law) is actually a result of the conservation of

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angular momentum

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Which of the following quantities doesn’t appear in Newton’s version of Kepler’s Third Law?

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eccentricity

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(I suggest drawing a diagram on your question sheet.) The tidal force caused by the Moon at the place on Earth farthest from the Moon is directed

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away from the Moon

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The tides that occur when the Sun, Moon, and Earth lie nearly along a straight line are called

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spring tides

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The Earth’s oblateness is caused by

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its rotation and the resulting centrifugal ”force”

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The Earth’s precession (of the equinoxes) is caused by

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tidal forces of the Sun and Moon trying to pull its equatorial bulge into alignment with the ecliptic plane

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To measure the shape of the Earth, one measures the length of a degree of latitude at different latitudes. If the Earth is oblate, a degree of latitude is

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shorter at the Equator than at the poles

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Toward the end of Newton’s life he precipitated the great controversy over priority in inventing the branch of mathematics now known as calculus; his antagonist was

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Leibniz

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The first expedition to bring back accurate data which indicated the actual oblateness of the Earth was that headed by

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Godin, La Condamine, and Bouguer

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The branch of astronomy that deals with the positions
of astronomical bodies on the sky is

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astrometry

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The "Great Inequality" is a 900-year cycle associated with a resonance between the planets

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Jupiter and Saturn

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A numerical calculation of the orbit of Halley’s Comet that accurately predicted the comet’s return in 1759 was carried out by

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Clairaut, Madame Lepaute, and Lalande

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The fact that the "fixed" stars actually shift their positions on the celestial sphere very slowly because of their individual motions through space
(the shifts we call proper motions) was discovered by

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Halley

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The first proof that the Earth goes around the Sun was the aberration of starlight discovered by

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Bradley

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Longitude on the Earth is determined by

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comparing local time with time at the Prime Meridian

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Mayer’s tables of the Moon’s motion were

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calculated using Mayer’s lunar theory with many parameters determined from ob- servation (semi-empirical)

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Halley pointed out that observations of the transits of Venus in 1761 and 1769 would give an accurate value for

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the length of the astronomical unit (AU)

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The Treatise on Celestial Mechanics which was the high point of eighteenth-century celestial mechanics was written by

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Laplace

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Newton’s theory of gravitation was finally shown to be incomplete or incorrect when which of the following was explained?

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advance of Mercury’s perihelion

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The refracting telescope having a convex objective lens and a concave eyepiece lens is known as the

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Galilean refractor

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The reflecting telescope having a concave primary mirror and a concave secondary mirror is the

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Gregorian

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The problem with the refracting telescope that causes color fringes around images and motivated Newton to turn to mirrors for the main optical element instead of lenses was

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chromatic aberration

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The solution to the problem of chromatic aberration (though only partially) was the achromatic refractor patented by

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Dollond

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The instrument used to discover the aberration of starlight and nutation was the

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zenith sector

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The approximate date of Newton is

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1690

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The size of a planet's elliptical orbit is given by its

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semimajor axis a

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Which of the following discoveries made by Galileo using the telescope was not highly controversial?

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there are many stars too faint to be seen with the naked eye

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Galileo's work in which he laid the foundations for Newton's work by proposing a version of inertia (later in Newton's First Law of Motion) and presenting the law of falling bodies in mathematical form was

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Discourses on Two New Sciences

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Which of the following scientific societies played a role in the events leading to Newton's writing his Principia?

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Royal Society of London

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Philosophical Transactions

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is the research journal of the Royal Society

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The methodology employed by Newton in his Principia was

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a combination of the inductive and deductive methods

Front 44

The problem with the refracting telescope that causes color fringes around images and motivated Newton to turn to mirrors for the main optical element instead of lenses was

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chromatic aberration

Front 45

Which is accelerated more by their forces on each other, the Earth or the Moon?

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the moon

Front 46

If two planets have the same mass but different radii, which will have the smaller surface gravity?

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the larger one

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Which of the following orbits in the two-body problem is an unbound orbit?

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parabola

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The Earth's precession (of the equinoxes) is caused by

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tidal forces of the Sun and Moon trying to pull its equatorial bulge into alignment with the ecliptic plane

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The first measurements to show (not very accurately) that the Earth is oblate rather than prolate were made by an expedition to

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Lapland led by Maupertuis

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Three areas that Newton worked in:

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Mathematics, dynamics, optics

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Newton called calculus:

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fluxions

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To calculate the moon's acceleration, you need to know:

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the earth's radius

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Newton proved the amount of refraction is characteristic of:

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each color no matter how many times it passes through a prism

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Newton called particles of light:

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corpuscles

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Most famous example of spherical aberration:

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hubble telescope

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After Newton's vacation he returned to Cambridge and was elected:

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Fellow of Trinity

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Newton was not the first to make a reflector, who was?

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James Gregory

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Gregorian telescope

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concave primary and secondary

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Cassegrain telescope

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concave primary, convex secondary

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Newtonian telescope

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concave primary, simplest

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Isaac Barrow resigned as Lucasian Professor and suggested _______ as his successor.

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Newton

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Newton did not believe in Trinity.
True or False?

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True

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As a result of his telescope, Newton was elected:

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Fellow of Royal Society

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Newton requested to be dropped from the Royal Society.
True or False

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True

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What type of religion was Newton interested in?

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Scripture, learned Hebrew, Book of Daniel, alchemy

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Most important book in the history of science.

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Mathematical Principals of Natural Philosophy, 1687

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Who encouraged Newton to write Principia?

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Halley

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Newton's 1st law

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law of inertia - body at rest or in motion remains that way unless acted upon by a force

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Newton's 1nd law

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Force = mass x accelertion

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Newton's 3rd law

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every force has an equal and opposite force

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Motion of a circle is at constant speed not:

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constant velocity

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Possible orbital paths:

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ellipse (bound) - periodic
parabola (unbound)) - one time
hyperbola (unbound) - one time

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Newton's law of gravity tells us the moon's gravity is stronger on the side of the earth:

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closest to the moon

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High tides occur every:

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12 hrs 25 min

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When the sun and moon pull in the same direction:

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high tide higher, low tide lower

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When the sun and moon pull at right angles:

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high tide lower, low tide higher

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Earth is oblate due to

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centrifugal force

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Regression works same as precession but:

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shorter timescale, 18.6 years

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How was Principia received?

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- difficult to understand
- earth oblate rejected by french
- Huygens didn't understand gravity across empty space

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Longitude at sea is necessary for:

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maritime power

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John Flamsteed is famous for:

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Right ascension, 61 Cygni - first star measured with heliocentric parallax, Atlas Coelesits

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Flamsteed established:

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Royal Greenwich Observatory

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Newton became the Master of the Mint during his:

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London years

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Newton became President of the Royal Society during his:

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London years

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Opticks was:

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published in 1703, was in english and not deductive

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Gottfried Leibniz was the first to publish papers on:

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calculus

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The Europeans supported _____ and not ______ over calculus papers

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Leibniz, Newton

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Two reasons the French disagreed with Newton:

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the shape of the earth (prolate), inverse square law of attraction

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Voltaire popularized Newton in:

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France

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Lunar Theory proposed by:

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Clairut, D'Alembert adn Euler

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Lunar Theory

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moons motion taking sun's planets effects into account; related problem of three-body's

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Lunar theory was developed to the point of being usable for the moon clock.
True or False

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True

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Tobias Mayer famous for:

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semi-empirical lunar theory - coefficients to give good fit for data

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Pierre Laplace (1749-1827) famous for:

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"Great Inequality", Treatise on Celestial Mechanics, Exposition of System of World

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Planetary Theory

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Jupiter and Saturn don't behave

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Great Inequality

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acceleration of Jupiter and retardation of Saturn due to their mutual attraction

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Halley discovered what stars?

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Aldebaran, Sirius, Arcturus

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Halley established that:

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the fixed stars shift on the celestial sphere arises from their own motion through space

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Halley succeeded _____ as Astronomer Royal

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Flamsteed

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James Bradley was:

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the 3rd Royal Astronomer

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James Bradley responsible for:

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aberration of starlight, nutation, accuracy of star positions and distances of stars

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Aberration of Starlight important because

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- 1st proof of Copernican theory
- gave improved value to speed of light
- correction of positions of stars

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Nutation

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nodding - changing geometry of moon's tidal forces acting to drive precession

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Graham

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Zenith Sector

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Astronomical Branches

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Observational - measurments of positions of sun, moon, planets, stars and their changes.
Theoretical - celestial mechanics mathematical analysis of orbital motions.

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Achromat

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George Bass made lenses, John Dollond patented

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Three Body Problem

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"Restricted Circular Planar-Three-Body System

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Venus' Transits:

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used to pin down astronomical unit

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Date of Laplace

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1780

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Date of Bradley

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1730