UNL2207 - The Nature of Natural Law: Tutorial 6
Kepler’s Laws and More Gravity
1)
Compare and contrast the models of the solar system due to Ptolemy, Copernicus
and Kepler; list the most significant features of each. Which model do you think is the
‘simplest’ and why?
2)
On average, the earth’s orbit around the Sun has a radius of about 150 million
kilometers and it moves around the Sun at about a speed of 30km/s. More precisely, at
different points in its orbit it moves faster than this and at other points slower. When is the
earth moving fastest around the Sun and when the slowest? Hint: the earth’s perihelion is
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1.471 x 10 km while it’s aphelion is 1.521 x 10 km.
3)
If the earth were suddenly stopped in it’s orbital movement, how long would it take to
fall into the Sun? Hint: imagine a highly elongated elliptical orbit with eccentricity almost 1.
4)
Kepler’s Second law states that the imaginary line between any planet and the
Sun sweeps equal areas in equal times as it orbits the Sun. If the gravitational attraction
between the Sun and the planets were somehow switched off and the planets no longer
followed elliptical paths, would Kepler’s equal area in equal time law still hold true?
5)
If a body is more than 259,000 km from the earth, it is attracted more strongly by the
Sun than by the earth (as you can verify by applying the inverse square law of universal
gravity to the two-body earth-Moon system and to the Sun-Moon system). The average
distance from the earth to the Moon is 384,400 km, which is much larger than 259,000 km –
therefore the Moon is pulled more by the Sun than by the earth, about twice as much in fact.
Why doesn’t the Sun ‘steal’ the Moon from the earth?
6)
The diagram below shows a section of the earth’s orbit around the Sun and the
Moon’s orbit around the earth (ignore that the diagram is not drawn to scale). Sketch the
trajectory of the Moon with respect to the Sun. Hint: use the results you have obtained in the
previous question.
SUN
Moon
Earth
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7)
The engines of a spacecraft in a circular orbit about the earth are fired briefly to give
the craft an outward radial thrust as shown in (a) below. Will this thrust produce orbit (b) or
(c)?
(b)
(a)
(c)
8)
As you move away from the Sun its gravity gets weaker. But suppose it did not;
suppose it got stronger. If that fictitious law were true, would it be possible for bodies such as
the planets to orbit the Sun? Hint: assume that a planet could still execute uniform circular
motion.
a) Yes, just as they presently do
b) Yes, but unlike as they presently do
c) No, orbital motion could not occur
9)
The ocean tide produced by the Moon is deepest on the side of the earth
a) under the Moon
b) away from the Moon
c) about equally deep on both sides
How many high tides and low tides are there each day - why this number?
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10)
Consider once again (see Tutorial 2) a projectile falling out of an aeroplane flying
uniformly in a straight line at a fixed altitude. To the pilot the projectile’s trajectory would
appear to be vertical, while to an observer on the ground it would appear parabolic.
What can you say if you observed the motion from the freely falling projectile itself?
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