Lab 5 Extrasolar Planets complete
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Astronomy
Date
Jan 9, 2024
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Extrasolar Planets
Remember to type your answers in blue text
Background Material
Complete the following after reviewing everything in the links under Background Materials.
Question 1:
The left side of the diagram below depicts the radial velocity curve of a star that is
orbited by an extrasolar planet.
The right side is a top-down view of the orbital motion of the
star and planet. The small circle represents the star’s motion, and the larger circle represents the
planet’s motion as both objects move around a common center of mass. The view from Earth is
in the plane of the page, so we are viewing the system edge-on from the left side of the page.
Radial velocity is positive when the star is moving away from Earth and negative when the star
is moving towards Earth. In the boxes provided, label the positions on the
star’s
orbit with the
letters corresponding to the labeled positions of the radial velocity curve.
NAAP – ExtraSolar Planets 1/9
+
-
Question 2:
Label the positions on the
planet’s
orbit with the letters corresponding to the
labeled positions of the radial velocity curve.
Part I: Exoplanet Radial Velocity Simulator
Introduction
Open up the exoplanet radial velocity simulator. You should note that there are several distinct
panels:
a
3D Visualization
panel in the upper left where you can see the star and the planet
(magnified considerably). Note that the orange arrow labeled
earth view
shows the
perspective from which we view the system.
o
The
Visualization Controls
panel allows one to check
show multiple views
. This
option expands the 3D Visualization panel so that it shows the system from three
additional perspectives.
a
Radial Velocity Curve
panel in the upper right where you can see the graph of radial
velocity versus phase for the system. The graph has
show theoretical curve
in default
mode. A readout lists the
system period
and a cursor allows you to measure radial
velocity and thus the
curve amplitude
(the maximum value of radial velocity) on the
graph. The scale of the y-axis renormalizes as needed and the phase of perihelion (closest
approach to the star) is assigned a phase of zero. Note that the vertical red bar indicates
the phase of the system presently displayed in the 3D Visualization panel. This bar can be
dragged and the system will update appropriately.
There are three panels which control system properties.
o
The
Star Properties
panel allows you to control the mass of the star. Note that
the star is constrained to be on the main sequence – so the mass selection also
determines the radius and temperature of the star.
o
The
Planet Properties
panel allows you to select the mass of the planet, the semi-
major axis, and the eccentricity of the orbit.
o
The
System Orientation
panel controls the two perspective angles.
Inclination
is the angle between the Earth’s line of sight and the plane of
the orbit. Thus, an inclination of 0º corresponds to looking directly down
NAAP – ExtraSolar Planets 2/9
-
+
on the plane of the orbit and an inclination of 90º is viewing the orbit edge
on.
Longitude
is the angle between the line of sight and the long axis of an
elliptical orbit. Thus, when eccentricity is zero, longitude will not be
relevant.
There are also panels for
Animation Controls
(start/stop, speed, and phase) and
Presets
(preconfigured values of the system variables).
NAAP – ExtraSolar Planets 3/9
Exercises
Select the preset labeled
Option A
and click
set
. This will configure a system with the following
parameters – inclination: 90º, longitude: 0º, star mass: 1.00 M
sun
, planet mass: 1.00 M
jup
,
semimajor axis: 1.00 AU, eccentricity: 0 (effectively Jupiter in the Earth’s orbit).
Question 3:
What is the amplitude of the radial velocity curve? Remember that the amplitude in
this case is the speed of the star.
What is the orbital (system) period?
Increase the planet mass to 2.0 M
jup
and note the effect on the system. Now increase the planet
mass to 3.0 M
jup
and note the effect on the system.
Question 4:
In general, how does the amplitude of the radial velocity curve change when the
mass of the planet is increased?
Explain why the amplitude changes.
Return the simulator to the values of
Option A
. Increase the mass of the star to 1.2 M
sun
and note
the effect on the system. Now increase the star mass to 1.4 M
sun
and note the effect on the system.
Question 5
: How is the amplitude of the radial velocity curve affected by increasing the star’s
mass? Explain why the amplitude changes.
Return the simulator to the values of
Option A
.
Question 6:
How is the amplitude of the radial velocity curve affected by decreasing the semi-
major axis of the planet’s orbit? How is the period of the system affected? Explain why these
values change.
NAAP – ExtraSolar Planets 4/9
The Amplitude of the radial velocity curve is 28.5 and the orbital period is one year-365 days.
The amplitude of the radical velocity curve increases when you increase the planets mass. The
amplitude changes because if the planet is more massive then the center of mass moves closer
to the planet and the star moves more, so it increases the velocity overall.
As the mass of the star increases the amplitude of the radical velocity curve decreases. And
when you increase the mass of the star its speed or velocity will decrease.
As you decrease the semi-major axis of the planets orbit the amplitude of the radial velocity
curve will increase. The period of the system decreases when you decrease the semi-major axis
of the planets orbit. Changing the way the planet orbits cause the amplitude of the radial
velocity to change.
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