The following table gives information about the ORBITS of the NINE planets of the SOLAR SYSTEM. The force of GRAVITY makes the planets move in orbits that are nearly circular around the SUN.
Planet Distance Mass Time for 1 from of Planet Orbit Sun (x10 ^22 kg) of Sun (million km) (days) Mercury 58 33.0 88.0 Venus 108 487 224.7 Earth 150 598 365.2 Mars 228 64.2 687.0 Jupiter 778 190,000 4332 Saturn 1,429 56,900 10760 Uranus 2,871 8,690 30700 Neptune 4,504 10,280 60200 Pluto 5,913 1.49 90600
1. a. Plot a graph of the DISTANCE from the SUN (on the x-axis)
against the TIME for
one ORBIT (on the y-axis) for each of the nine PLANETS.
Join the points together
to produce a SMOOTH curve.
b. Write down what you can CONCLUDE from the graph.
c. It was once thought that a tenth planet should have an orbit of 420 million km from the Sun. Use your graph to predict how long a YEAR will be on this planet.
2. a. Calculate the SPEED of each of the nine planets using the formulae
SPEED = DISTANCE TRAVELLED /TIME
1) Distance travelled around an orbit = 2IIr
2) r = distance from the Sun
The best units of speed to use are millions of km per day.
Put these in a table
THE SPEEDS OF THE PLANETS
Planet Distance from sun Speed of planet (millions of km) (million km day -1) Mercury 58 4.14 Venus 108 etc. etc.
b. Write down what you can CONCLUDE from this table.
c. Newton's Law of Gravitation states that the force of gravity becomes SMALLER the further the planet is from the Sun. Use this fact and what you know about circular motion to explain why Mercury has such a HIGH speed and why Pluto has such a LOW speed.
THE MOONS OF JUPITER
Name of Distance Mass of Time for 1 Orbit Satellite from Satellite of Jupiter of Jupiter Jupiter (x10^18) (days) (million km) Sinope 23.70 0.078 758.00 Carme 22.60 0.096 692.50 Elara 11.74 0.78 259.65 Himalia 11.48 9.56 250.57 Callisto 1.88 108,000 16.69 Ganymede 1.07 148,000 7.15 Europa 0.67 48,000 3.55 Io 0.42 89,400 1.77 Amalthea 0.18 7.17 0.50
3. The above nine moons of JUPITER form a mini-solar system.
a. Plot a graph of DISTANCE from Jupiter (on the x-axis)
against TIME for one orbit
(on the y-axis) for each of the SATELLITES in the
above table. Join these points to
produce a SMOOTH curve.
b. In what way is the curve SIMILAR to the curve for the PLANETS?
c. In what way is the curve DIFFERENT from the curve for the planets?
d. The radius of SINOPE's orbit around Jupiter is VERY ROUGHLY the same as the radius of Mercury's orbit around the Sun. Explain why Sinope takes so long to complete one orbit whereas Mercury only takes 88 days.
4. Surprisingly, the MASS of the planets does not affect the orbit at all. You should
DEMONSTRATE this by plotting a graph of DISTANCE from the Sun (on x-axis) against the MASS of the planet (on y-axis). The points should be in a RANDOM scatter showing that there is NO relation between the two VARIABLES.
5. JOHANN BODE noticed that if you measure the orbital RADII of the planets in the Solar System in AU (1 AU is the mean distance from the Earth to the Sun) then the radii of the orbits seem to obey a MATHEMATICAL rule called BODE'S LAW.
Take the number 0, 3, 6, 12 ... doubling at each step. Add 4 to each number, then divide by 10. This is the predicted radius in AU.
a. Check Bode's Law by constructing the following table of Actual Radius (in AU) and radius predicted by Bode's Law for all nine planets
THE ORBITAL RADII OF THE PLANETS
Planet Orbital Radius Radius from Radius (AU) Bode's Law (million km) Mercury 58 0.39 0.40 Venus 108 0.72 0.70 Earth 150 1.0 etc
b. Using his Law, Bode predicted there should be a "missing" planet. What should be the ORBITAL RADIUS of this planet? What would be the TIME it takes to orbit the Sun? (So convinced were astronomers that this missing planet must exist that it was given the name CERES. In fact there are just ASTEROIDS at this orbital radius)
c. If Bode's Law were true, it would have to apply to other planetary systems such as the moons of Saturn and Jupiter. Try to find a RULE that would fit the ORBITAL RADII of moons (the rule R = (n + 10) / 10 where n = 0, 3, 6 .. fits the first few)
THE ORBITAL RADII OF THE MOONS OF SATURN
Moon of Saturn Orbital Orbital Radius from Radius Radius Rule (thousand km) (Scaled) Mimas 186 1.0 Enceladus 238 1.28 Tethys 295 1.59 Dione 377 Rhea 527 Titan 1,222 Hyperion 1,481 Iapetus 3,561 Phoebe 12,952
N.B. Saturn has at least 25 moons, but most are no more than lumps of rock. Those above are over 200 km across).
CLEARLY, Bode's Law is NOT true in general and it is just COINCIDENCE that the planets orbital radii fall close to his numbers.
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