Identifying the guilty party was mainly based on eyewitness accounts during what time period?
2 answers:
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Answer:
E) are almost circular, with low eccentricities.
Explanation:
Kepler's laws establish that:
All the planets revolve around the Sun in an elliptic orbit, with the Sun in one of the focus (Kepler's first law).
A planet describes equal areas in equal times (Kepler's second law).
The square of the period of a planet will be proportional to the cube of the semi-major axis of its orbit (Kepler's third law).
Where T is the period of revolution and a is the semi-major axis.
Planets orbit around the Sun in an ellipse with the Sun in one of the focus. Because of that, it is not possible to the Sun to be at the center of the orbit, as the statement on option "C" says.
However, those orbits have low eccentricities (remember that an eccentricity = 0 corresponds to a circle)
In some moments of their orbit, planets will be closer to the Sun (known as perihelion). According with Kepler's second law to complete the same area in the same time, they have to speed up at their perihelion and slow down at their aphelion (point farther from the Sun in their orbit).
Therefore, option A and B can not be true.
In the celestial sphere, the path that the Sun moves in a period of a year is called ecliptic, and planets pass very closely to that path.
(a) Both the girl and the boy have the same nonzero angular displacement.
Explanation:
The angular displacement of an object moving in uniform circular motion, as the boy and the girl on the merry-go-round, is given by
where
is the angular speed
t is the time interval
For a uniform object in uniform circular motion, all the points of the object have same angular speed. This means that the value of is the same for the boy and the girl.
Therefore, if we consider the same time interval t, the boy and the girl will also have same nonzero angular displacement.
(b) The girl has greater linear speed.
Explanation:
The linear (tangential) speed of a point along the merry-go-round is given by
where
is the angular speed
r is the distance of the point from the centre of the merry-go-round
In this problem, the girl is near the outer edge, while the boy is closer to the centre: since the value of is the same for both, this means that the value of r is larger for the girl, so the girl will also have a greater linear speed.