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



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


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.


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


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)


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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The EIA Team / Tel:+44 (0)1274 234082 / 25 Sept 1995