Earth, Moon & Solar System — Problem set, Grade 9

Model sky patterns, seasons, tides, and predictable orbital motion.

Review the key ideas

Earth, Moon & Sun: Moon Phases

Moon phases come from watching different portions of the Moon's always-half-lit surface as it orbits Earth — eclipses are the rarer case when Earth's shadow or the Moon itself actually blocks the light.

Seasons & Earth's Tilt

Earth's 23.5° axial tilt — not its distance from the Sun — determines the seasons, by changing how directly sunlight strikes each hemisphere throughout the year.

The Solar System

The solar system is organized by distance and composition — rocky terrestrial planets close in, gas and ice giants farther out — and astronomical units (AU) keep its huge distances easy to compare.

Gravity, Orbits & Tides

Gravity supplies the net force that curves orbital motion. Differences in lunar and solar gravitational effects across Earth produce tides; local coastlines shape the observed pattern.

Predicting Orbits with Mathematical Models

Gravity provides inward acceleration; orbital period and orbital size follow a predictable relationship under stated assumptions.

Problem 1

In your own words, what part of the Moon is always lit by the Sun?
Answer and explanation

Half of the Moon — whichever half faces the Sun — is always lit.

Just like Earth, the Moon is a sphere lit by the Sun on whichever half faces it at any moment. That's always exactly half of the Moon's surface. What changes is how much of that lit half faces Earth as the Moon orbits us, which is what creates the phases.

Problem 2

Tonight is a full moon. About how many days until the next new moon?
Answer and explanation

About 14-15 days

A full moon is roughly halfway through the 29.5-day cycle, and a new moon marks the start/end point. From full moon to the next new moon is the remaining half of the cycle: 29.5 ÷ 2 ≈ 14.75, so about 14-15 days.

Problem 3

Explain the difference between a lunar eclipse and a regular full moon.
Answer and explanation

A full moon is just the phase where we see the Moon's fully lit side; a lunar eclipse is the rarer event when Earth's shadow actually falls on the Moon.

Every month there's a full moon, when the Moon's entire sunlit half faces Earth. A lunar eclipse can only happen at full moon, but it additionally requires the Sun, Earth, and Moon to be almost perfectly lined up so Earth's shadow falls on the Moon. Since the Moon's orbit is tilted about 5° relative to Earth's orbit around the Sun, that precise alignment only happens a couple of times a year, not every month.

Problem 4

What season is it in the Northern Hemisphere around June 21, and why?
Answer and explanation

Summer

June 21 is the summer solstice. Earth's fixed tilt has the Northern Hemisphere leaning most directly toward the Sun on this date, giving it the most direct sunlight and the longest day of the year.

Problem 5

Explain why a low, glancing angle of sunlight heats the ground less than a direct, high angle of sunlight, even though it's the same sunlight.
Answer and explanation

The same amount of energy is spread over a larger area at a low angle, so each patch of ground gets less energy.

Picture a flashlight beam hitting a wall straight-on versus at a steep sideways angle: straight-on, the light forms a small, bright, concentrated circle; at an angle, the same beam stretches into a larger, dimmer oval. Sunlight works the same way — direct, high-angle rays concentrate their energy over a small area, while indirect, low-angle rays spread that same energy over a bigger area, so each square meter of ground receives less heating.

Problem 6

It is December 21. Describe the season and day length in both the Northern and Southern Hemispheres, and explain why they differ.
Answer and explanation

Winter and short days in the Northern Hemisphere; summer and long days in the Southern Hemisphere.

December 21 is the Northern Hemisphere's winter solstice: Earth's tilt points the North Pole away from the Sun at this point in the orbit, so the Northern Hemisphere gets indirect sunlight and its shortest day. Since Earth's tilt direction is fixed in space, the Southern Hemisphere is tilted toward the Sun at the very same time, getting direct sunlight and its longest day — summer. The hemispheres always have opposite seasons for this reason.

Problem 7

List the four terrestrial (inner) planets in order from the Sun.
Answer and explanation

Mercury, Venus, Earth, Mars

The four rocky, dense inner planets — closest to the Sun and separated from the outer planets by the asteroid belt — are Mercury, Venus, Earth, and Mars.

Problem 8

Mars orbits the Sun at about 1.5 AU, and Earth orbits at 1 AU. About how many times farther from the Sun is Mars than Earth?
Answer and explanation

About 1.5 times farther

Divide Mars's distance by Earth's distance: 1.5 AU ÷ 1 AU = 1.5. So Mars orbits about 1.5 times farther from the Sun than Earth does.

Problem 9

The Sun contains about 99.8% of all the mass in the solar system. About what percent of the solar system's mass is contained in everything else combined (all 8 planets, moons, asteroids, comets, etc.)?
Answer and explanation

About 0.2%

If the Sun holds 99.8% of the mass, everything else must make up the remaining share: 100% − 99.8% = 0.2%.

Problem 10

What is gravity?
Answer and explanation

An attractive force between any two masses.

Gravity is the pulling force that every object with mass exerts on every other object with mass. It gets stronger when the masses are larger and weaker, quickly, as the distance between them increases.

Problem 11

A friend says, 'The Sun causes tides, not the Moon, because the Sun is so much bigger.' What is wrong with this claim?
Answer and explanation

Tidal effects depend on the difference in gravity across Earth, not just the total gravitational force. The nearby Moon has the larger tidal effect, while the Sun also contributes.

The Sun exerts a larger total gravitational force on Earth, but its gravitational field varies less across Earth relative to its total. The closer Moon produces the stronger tidal effect.

Problem 12

It's the first quarter moon. Are we experiencing a spring tide or a neap tide? Explain using the positions of the Sun, Earth, and Moon.
Answer and explanation

Neap tide

At first quarter (and also third quarter), the Moon is 90° away from the Sun as seen from Earth — the Sun, Earth, and Moon form a right angle instead of a straight line. The Sun's and Moon's gravitational pulls on Earth's oceans point in different directions and partly cancel each other out, producing a smaller-than-usual tidal range: a neap tide. Spring tides, with the biggest range, happen instead at new and full moon, when the Sun, Earth, and Moon line up and their pulls combine.

Problem 13

A waxing moon is one that is
  1. getting smaller
  2. getting larger
  3. not visible
  4. always full
Answer and explanation

getting larger

Waxing means the lit fraction is increasing toward full.

Problem 14

Explain how you could tell from a single observation whether the Moon is waxing or waning.
Answer and explanation

Note which side is lit and the time of day it is visible. From the northern hemisphere a waxing moon is lit on the right and is visible in the evening sky after sunset, while a waning moon is lit on the left and is visible in the morning before sunrise. A single observation of both the lit side and the time therefore settles it.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the data, mechanism, or calculation that supports it.
  • Include units, conditions, or limits where relevant.

Problem 15

Chapter review: A student argues that first quarter must show one quarter of the lunar disk lit and every new Moon causes a solar eclipse. Correct both statements with geometry.
Answer and explanation

First quarter describes about one-quarter of the phase cycle and the visible disk is roughly half lit. New Moon alone does not guarantee a solar eclipse because the tilted lunar orbit usually misses the shadow line; alignment near a node is also needed.

First quarter describes about one-quarter of the phase cycle and the visible disk is roughly half lit. New Moon alone does not guarantee a solar eclipse because the tilted lunar orbit usually misses the shadow line; alignment near a node is also needed.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 16

At the June solstice, the hemisphere tilted toward the Sun is
  1. northern
  2. southern
  3. both
  4. neither
Answer and explanation

northern

The northern hemisphere is tilted sunward, giving its longest day.

Problem 17

A student says summer happens because Earth is closer to the Sun. Give the evidence that disproves this.
Answer and explanation

Earth is closest to the Sun in early January, when the northern hemisphere is in winter, so distance cannot be the cause. The decisive evidence is that the two hemispheres have opposite seasons at the same moment: a single Earth–Sun distance cannot produce summer in one place and winter in another, whereas the tilt explains it exactly.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the data, mechanism, or calculation that supports it.
  • Include units, conditions, or limits where relevant.

Problem 18

Chapter review: Under a simple comparison, two surfaces receive equal absorbed power per square metre, but one receives it for 9 hours and the other 15. Compare energy received and explain why this still does not uniquely fix their temperatures.
Answer and explanation

The second receives 15/9 = 5/3, about 1.67 times the energy per area under the assumptions. Temperature also depends on heat capacity, mass, losses, prior conditions and varying real radiation.

The second receives 15/9 = 5/3, about 1.67 times the energy per area under the assumptions. Temperature also depends on heat capacity, mass, losses, prior conditions and varying real radiation.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 19

Which object is at the centre of the Solar System and holds it together?
  1. Earth
  2. Jupiter
  3. The Sun
  4. The asteroid belt
Answer and explanation

The Sun

The Sun holds nearly all the system's mass and its gravity governs the orbits.

Problem 20

Explain why a scale model of the Solar System rarely shows both sizes and distances correctly.
Answer and explanation

The distances are enormously larger than the objects: at a scale where Earth is a small bead, the Sun is metres away and Neptune is kilometres distant. A diagram that fits on a page must either exaggerate the planet sizes or compress the distances, so most do both. Saying which has been distorted is part of reading the model honestly.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the data, mechanism, or calculation that supports it.
  • Include units, conditions, or limits where relevant.

Problem 21

Chapter review: A Solar System distance model places a body at a = 10 AU. Convert that scale to kilometres using 1 AU ≈ 150 million km. Explain why the distance and an image of a water-related feature do not alone establish its size or life.
Answer and explanation

The scale is about 1.5 billion km. It is an orbital distance, not a diameter. A water-related surface interpretation concerns geological conditions and does not alone prove organisms or all habitability requirements.

The scale is about 1.5 billion km. It is an orbital distance, not a diameter. A water-related surface interpretation concerns geological conditions and does not alone prove organisms or all habitability requirements.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 22

Neap tides, with the smallest range, occur when the Sun and Moon are
  1. aligned
  2. at right angles as seen from Earth
  3. both new
  4. closest
Answer and explanation

at right angles as seen from Earth

Their tidal effects partly cancel at first and third quarter.

Problem 23

Explain why there are two tidal bulges rather than one.
Answer and explanation

On the near side the Moon's pull is strongest and draws water toward it. At Earth's centre the pull is intermediate, and on the far side it is weakest, so that water is effectively left behind as the solid Earth is pulled away from it. The result is a bulge on both sides, which is why most coasts experience two high tides as Earth rotates through them each day.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the data, mechanism, or calculation that supports it.
  • Include units, conditions, or limits where relevant.

Problem 24

Chapter review: At fixed central mass, a satellite’s center separation doubles while its mass triples. Find the gravitational-force factor. Explain why this does not uniquely give the new orbit or period.
Answer and explanation

The force factor is 3/2² = 3/4. A trajectory also needs velocity/initial conditions and an appropriate orbital model; force ratio alone does not define an entire new orbit.

Apply the mass factor 3 and separation-square factor 1/4.

Multiply to obtain 3/4.

Distinguish force ratio from full motion and request the needed initial/model conditions.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 25

A student doubles a from 1 AU to 2 AU and predicts P doubles. Evaluate using P² = a³.
Answer and explanation

At 2 AU, P = √8 ≈ 2.83 years, so period does not scale linearly with orbital size.

Problem 26

Chapter review: In the ideal same-Sun model, a body has a = 6.25 AU. Find P and the transformed pair (a³, P²). Explain why the same numerical constant need not apply around another star.
Answer and explanation

a³ = 244.140625, so P = 15.625 years and the transformed pair is (244.140625 AU³, 244.140625 years²). The proportional constant depends on the dominant central mass; the convenient solar years/AU form is not universal.

Compute 6.25³ = 244.140625.

Take its square root: 15.625 years.

Keep transformed units and identify the central-mass assumption.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.
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