### Lunar Leaper

Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?

### Which Twin Is Older?

A simplified account of special relativity and the twins paradox.

### Whoosh

A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?

# Construct the Solar System

##### Stage: 4 and 5 Challenge Level:

The following table comprises real astronomical data (compiled from Wikipedia) which describe the elliptical paths taken by some key objects in our solar system:

 Name Diameter relative to Earth Average distance from the sun (in AUs) Time to orbit the sun (years) Inclination of orbit to sun's equator (in degrees) Orbital Eccentricity e Time to spin on axis (days) The Sun 109 -- -- -- -- 26.38 Mercury 0.382 0.39 0.24 3.38 0.206 58.64 Venus 0.949 0.72 0.62 3.86 0.007 -243.02 Earth 1.00 1.00 1.00 7.25 0.017 1.00 Mars 0.532 1.52 1.88 5.65 0.093 1.03 Jupiter 11.209 5.20 11.86 6.09 0.048 0.41 Saturn 9.449 9.54 29.46 5.51 0.054 0.43 Uranus 4.007 19.22 84.01 6.48 0.047 -0.72 Neptune 3.883 30.06 164.8 6.43 0.009 0.67

The actual numbers for the earth are

 Diameter Mass kg Distance from sun Orbital period Rotation time 12756 km 5.9736 E10 147.1-152.1 million km 365.256366 days 23 hours 56 minutes

Make an accurate top down drawing of the solar system on, for example, a piece of A4 paper.

You will first need to try to make sense of the data in the table!

You could either assume that the orbits are all circular, centred on the sun. Or (a lot more tricky) you could take into account the eccentricity of the orbit: $e = \frac{r_{max}-r_{min}}{r_{max}+r_{min}}$ where $r_{max}$ and $r_{min}$ are the maximum and minimum distances from the sun respectively.

Once you have made your drawing, you can make a side-view to show the effects of inclination of the orbits.

In late April 2002 a grand conjunction occurred in which Mercury, Venus, Mars, Saturn and Jupiter were all visible from various places on Earth at night. What does this tell us about the possible range of locations of these planets of their orbits?

From this information, for which of the planets could you meaningfully predict their locations relative to earth now?

Extension:Estimate how often you would expect Mercury, Venus, Mars, Saturn and Jupiter to line up. How often might you expect all of the planets to line up?

NOTES AND BACKGROUND

Planetary conjunctions are beautiful to observe, as planets are the brightest 'stars' in the sky. You can see an image of a planetery conjunction here