What are Kepler
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University of New South Wales *
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Course
1160
Subject
Astronomy
Date
Dec 6, 2023
Type
docx
Pages
2
Uploaded by MegaMagpie1368
1.
What are Kepler’s laws?
Kepler’s law of ellipses states that planets orbit a star in an elliptical orbit with the
star at one of two foci. Ellipses are geometric shapes which are an stretched circle
where instead of a centre there are two foci.
Kepler’s second law, the law of periods states that when a line is drawn from the suns
focus point to a planet will always sweep an equal amount of area in an equal amount
of time. Based of this, the planet will move at a greater orbital velocity when it is
closer in its orbit to the star and slower when it is further away from it.
Kepler’s third law states that the average distance from the sun and the orbital period
of a planet are directly proportional to one another. This relationship was written in an
equation as the orbital period squared is equal to a proportionality constant multiplied
by the average distance from the sun cubed. This infers that a planets orbital velocity
will be smaller, if it orbits the star at a large distance.
2.
Switch to the planet and moon scenario.
a.
Does the planet move as the moon orbits?
As the moon orbits the planet, the planet also moves in a very small circular
orbit due to the gravitational pull from the moon. The planet moves in a small
orbit due to the small gravitational pull it experiences from the moon.
b.
How is this different to the Sun-planet scenarios above?
In the sun-planet scenario, the Sun was the central body, however, the it did
not move as the planet orbited it. This happened because the mass ratio
between the Sun and planet is much larger than that of the planet and moon.
c.
Where are the centres of mass in each scenario from Questions 1, 4, and 7?
In questions 1,4 and 7, the centre of mass was the sun regardless of its mass
being increased or decreased as it was still larger than that of the planet
orbiting it.
3.
Take the star and planet in the standard configuration to be the Sun and the Earth.
a.
When the gridlines are turned on, what is the distance between each
marking,
in AU? The distance you are considering is shown in red below.
When the gridlines are turned on in the simulation, the standard distance
between each grid marking is approximately 74 million km which is also equal
to 0.5 astronomical units.
4.
Record the time it takes each planet at those orbital distances to complete one orbit, in
a table like the one below.
a.
Planet distance (AU)
Orbital period (days)
0.5
68
1
367
1.25
869
1.5
1996
Do these results follow Kepler’s third law? Planet Distance (AU) Orbital
Period (days)?
These results do follow Kepler’s third law as the orbital period increases as the
planets distance from the star increases. Moreover, the relationship between
the planets distance from the star and the orbital period is increasing in a non-
linear manner which is consistent with the mathematical equation of Kepler’s
third law which states that the orbit period squared is equal to a constant
multiplied by the planets distance from the star cubed.
5.
Which planet in our Solar System do you expect to have the fastest orbital velocity?
a.
Which planet would you expect to have the slowest orbital velocity?
Neptune is the planet furthest away from the sun and hence should have the
slowest orbital velocity.
b.
What is the reason for this?
Kepler’s second law of areas states that a planets orbital period increases as its
orbital radius increases. Neptune is the planet furthest from the sun and hence
has the greatest orbital period. Since the orbital velocity is inversely
proportional to the orbital period, a large orbital period results in a small
orbital velocity.
6.
What did you learn in this experiment?
Through the simulations, I was able to solidify my understanding of Kepler’s laws
and how it predicts the orbits and nature of planetary bodies in space.
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