Download The Sun and Planets Class Exercise 1.

The Sun and Planets
Class Exercise 1.
Exercise 1.
Spring Semester 2017
Prof Dr Ravit Helled
The view from Earth
The Solar System is a planetary system with one star (the Sun) and eight planets.1 The
four planets nearest to the Sun are rocky planets. We call these these the terrestrial
planets. In order of increasing distance from the Sun, these are: Mercury, Venus, Earth,
and Mars. The remaining outer four planets are the gas giants. Continuing outwards
from Mars, they are Jupiter, Saturn, Uranus, and Neptune.
In this exercise we will gain a more intuitive understanding of sizes and distances in the
Solar System. To achieve this, we begin by converting the typical units of measurement
to a scale better suited to astronomical distances and sizes. We do this by normalizing
the SI units (e.g., meters, kilograms) into Earth masses and Earth radii (i.e., 1 distance
unit ≡ 1 Earth radii and 1 mass unit ≡ 1 Earth mass). Use this new system of units to
complete the following table:
Table 1. — Fill in the missing values
Object
Radius (km)
Radius (R⊕ )
Earth
6’378.14
1.0
Moon
1’737.5
Mercury
2’439.7
Venus
6’051.8
Mars
3’389.5
Jupiter
69’911
Saturn
58’232
Uranus
25’362
Neptune
24’622
Sun
695’700
†
Ganymede
2’634.1
Mass (1024 kg)
5.97219
0.07346
0.330104
4.86732
0.641693
1’898.13∗
568.319∗
86.8103
102.410
1’989’000∗
0.14819
Mass (M⊕ )
1.0
† Ganymede is the largest and most massive moon of Jupiter
∗ Corrected masses for Jupiter, Saturn, and the Sun
Exercise 2.
“To infinity... and beyond!”
In astronomy and physics, we can measure distances by the time that it takes light to
travel between two points. We can do this because the speed of light is finite and we have
measured its value to great accuracy. The most common unit in this distance scale is
the lightyear (sometimes abbreviated as “ly”), which is just short of 9 trillion kilometers
(1 ly = 9.461 × 1012 km). As defined by the International Astronomical Union (IAU), a
lightyear is the distance that light travels in vacuum in one Julian year (365.25 days).
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Sorry, Pluto.
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For instance, the distance between Earth and the Sun is 149.6 billion meters. The speed
of light is c = 3 × 108 m/s.
tlight =
149.6 × 109 m
= 498.7 s
3 × 108 m/s
(1)
Therefore it takes 8 minutes and 19 seconds for sunlight to reach the Earth.
We will now use this distance scale to understand some distances in the Solar System.
In the following table calculate the time it takes light to travel between (or traverse) the
object(s):
Table 2. — Light Travel Time
Scale
Distance (m)
Sun–Earth
1.47 × 1011
Sun diameter
1.39 × 109
Earth diameter
1.27 × 107
Earth–Moon
3.69 × 108
Sun–Mars
2.17 × 1011
Sun–Jupiter
7.79 × 1011
Sun–Pluto
5.91 × 1012
Nearest star (Prox. Cen.) 4.02 × 1016
Milky Way diameter†
9.50 × 1020
Milky Way–Andromeda† 2.37 × 1022
Milky Way–GN-z11†
1.27 × 1023
light travel time
8m19s
† Ignore all cosmological effects (e.g., expansion, general relativity, etc.).
Exercise 3.
The Scale of Systems
The satellite (i.e., moon) systems of giant planets are often referred to as “miniature
solar systems”. In this exercise we will make a few calculations to test whether or not
this comparison makes sense.
Calculate the ratio of the mass of the Sun to the total mass of the planets. Compare it
to the ratio of the mass of Jupiter to the mass of its satellites. Use whichever mass units
you are most comfortable with.
Table 3. — Ratios
Central Body Planets/Satellites
Sun
planets
Jupiter
Jovian moons
Mass Ratio
Note that you can neglect the masses of the terrestrial planets because they are very small
compared to the mass of the gas giants.
How similar are these two ratios? What does this mean for the comparison above?
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