Earth, Moon, Sun & Space Models — Print · Science 6: Matter, Energy & Earth Systems, Grade 6

Their mass stays at 60 kg because mass measures the amount of matter, which does not change with location. Their weight falls from about 588 N to about 98 N, because weight is the gravitational force between them and the body they stand on, and the Moon's mass is far smaller than Earth's. The astronaut has not lost any matter.

Because they are falling along with their spacecraft. Both are in continuous free fall around Earth at the same rate and along the same curved path, so there is no floor pushing up against them and nothing to produce the sensation of weight. Gravity is acting the whole time; it is what curves the path into an orbit.

Because it has a much longer path and travels it more slowly. Neptune is about thirty times further from the Sun, so its orbit is far larger, and the Sun's pull at that distance is roughly a nine-hundredth of its strength at Earth, so a slower speed of about 5.4 km per second is enough to hold it in orbit against Earth's 30.

From the discrepancy in Uranus's orbit. Uranus was not quite where gravitational calculations placed it, and instead of discarding the theory astronomers asked what additional mass would produce exactly that error. Le Verrier calculated where such a planet must be, and Neptune was found within a degree of the predicted position in 1846.

Because a swinging pendulum keeps swinging in the same plane unless something pushes it sideways. Foucault's pendulum appeared to rotate its swing through the day, and since nothing was pushing it, the only explanation is that the building and the ground beneath it were turning underneath the pendulum.

Because both hemispheres are the same distance from the Sun at any moment. If distance caused the seasons, Sydney and London would be warm together and cold together. They are not: December is midsummer in one and midwinter in the other, so whatever causes seasons must act differently on the two halves of the planet, which tilt does and distance cannot.

Because the same beam is spread over a larger area. Light arriving perpendicular to the ground concentrates its energy on the smallest possible patch, while a beam arriving at 30 degrees covers roughly twice that area, so each square metre receives about half as much. Low-angle light also travels through more atmosphere, losing more on the way.

Because it is 90 degrees minus the 23.5 degree axial tilt. That is the latitude at which, on the day the hemisphere leans furthest towards the Sun, the Sun just fails to set, and six months later just fails to rise. A different tilt would place the circle at a different latitude, so the number comes directly from the tilt.

Because a full moon is opposite the Sun as seen from Earth. At midday the Sun is high in the southern or northern sky, so the point opposite it is below the horizon. A full moon therefore rises around sunset and sets around sunrise, and is only ever up during the night.

First, a full moon occurs when Earth is between the Sun and the Moon, which is exactly when the shadow explanation predicts the Moon should be darkest, so it predicts the opposite of what happens. Second, the Moon is often visible in daylight showing a clear phase, at times when Earth is nowhere between it and the Sun and could cast nothing onto it.

It is a waxing gibbous moon: gibbous because more than half is lit, waxing because the lit area is growing, which in the northern hemisphere shows as light on the right. Over the following days the lit portion will keep growing until the whole disc is lit at full moon, a few days later.

Because the far side is not permanently dark. It receives as much sunlight as the near side over the course of a month, including full sunlight at new moon when the near side is unlit. What is true is that we never see it from Earth, because the Moon rotates once per orbit, so the correct term is the far side.

Because of the relative sizes of the shadows. Earth's shadow is large enough to cover the Moon completely, so anyone on the night side of Earth can see the darkened Moon at the same time. The Moon's shadow on Earth has an umbra at most about 270 km wide, so only people inside that narrow track see a total solar eclipse.

Because the targets are very small in angular terms. The Sun and Moon each appear about half a degree across, so an alignment must be accurate to within roughly that much for a shadow to land. A 5 degree tilt means the Moon usually passes well above or below the line, and the shadow misses Earth or the Moon entirely.

Because the ocean bulges on both sides of Earth. The Moon pulls the near ocean more strongly than it pulls the planet, and pulls the planet more strongly than the far ocean, so water heaps up both towards the Moon and away from it. Earth's rotation then carries each coast through both bulges in a little over 24 hours.

Because the two mechanisms demand different precision. Tides depend on gravity, which acts whatever the exact alignment, so the Sun's and Moon's pulls combine at every new and full moon. An eclipse requires a shadow to actually land on a target half a degree wide, so the alignment must be accurate to within about that, which happens only a few times a year.

Because the two differ by an enormous factor. At that scale Earth is 0.127 mm across, about the thickness of paper, while the Sun is 150 cm away. Making Earth large enough to see clearly, say 1 cm, would multiply every distance by about eighty, putting the Sun over 100 m away and off any page or table.

Because the diagrams compress the distances to fit the page. The belt contains a great many objects spread through an enormous volume, with an average separation of something close to a million kilometres, so a spacecraft crossing it is very unlikely to come near any of them. The crowded appearance is an artefact of drawing, not a feature of the belt.

Because it predicted planetary positions accurately enough for the purposes of the time, which is what a model is judged by. It needed steadily more complicated adjustments as observations improved, and it was replaced when Galileo's telescope revealed things it could not accommodate at all, such as moons orbiting Jupiter and the complete set of phases of Venus.

Because a model used outside its limits gives wrong answers while appearing to work. Knowing that the particle model fails on ice floating at 0.92 g/cm3, or that a food chain cannot represent an animal with many prey, is what tells you when to stop relying on it. The limit is part of understanding the model, not a criticism of it.