Mr. Brown's Science Labs

Earth & Space Science · Regents Lab
Triangulation of Jupiter

Part 1 · Vocabulary, Reading & Practice

Tap each card to flip. Only one card opens at a time. Cards close on their own after 8 seconds — you can reopen them anytime.

Vocabulary

Match Each Term to its Meaning

Click a term on the left, then click its matching meaning on the right. 1 point per correct match · 10 total

Reading · Mapping Jupiter From a Moving Earth

For thousands of years, people watched Jupiter wander among the stars without knowing how far away it really was. Jupiter looked like a slow, bright point of light, but its true distance and the shape of its orbit were a mystery. Astronomers needed a way to measure something they could never reach.

In the late 1500s, the Danish astronomer Tycho Brahe collected the most accurate naked-eye observations of the planets ever recorded. His assistant, Johannes Kepler, used those careful measurements to figure out the shapes of the orbits. Kepler discovered that every planet, including Jupiter, travels in an ellipse, not a perfect circle. The Sun sits at one of the two foci of each ellipse. The point in the orbit closest to the Sun is called the perihelion, and the point farthest from the Sun is called the aphelion.

To find where Jupiter is in space at any moment, astronomers use a technique called triangulation. They record two things: where Earth is on its own orbit (the heliocentric longitude of Earth) and the direction we see Jupiter from Earth (the geocentric longitude of Jupiter). Because Jupiter takes about 11.86 Earth years to circle the Sun once, astronomers wait for Jupiter to return to the same spot in its orbit, then take a second observation from a different Earth position. Two sight-lines drawn from those two Earth positions cross at Jupiter's true location.

Repeating this process for six different points lets you plot the whole orbit. Then, by measuring the longest line through the ellipse (the major axis) and the offset between its center and the Sun, you can calculate Jupiter's eccentricity — a number that tells you how stretched-out the orbit is. The accepted value for Jupiter's eccentricity is about 0.048, which means Jupiter's orbit is almost (but not quite) a perfect circle.

Reading Activities

Word Bank: aphelion · perihelion · ellipse · foci · heliocentric · geocentric
1 pt
1. A planet's orbit around the Sun is shaped like an _________.
1 pt
2. The direction we see Jupiter from Earth is measured as its _________ longitude.
1 pt
3. Put the words in the correct order. Tap each word to add it to your answer. (Punctuation stays attached to the last word.)
1 pt
4. Put the words in the correct order.
1 pt
5. Expand this sentence into a full one. Use When and How.

Jupiter orbits the Sun.

1 pt
6. Expand this sentence into a full one. Use Why and Where.

Eccentricity describes orbit shape.

Part 2 · Triangulation Simulation

In this simulation you will plot four Jupiter positions using a virtual protractor. Two positions (J1 and J2) are already plotted for you as examples.

How to Use the Protractor

  1. Drag the protractor's center to place it on the Sun (or on an Earth dot).
  2. Drag the protractor's red arm to set it to the angle you want.
  3. When the arm shows the Earth heliocentric angle, click Plot Earth Position.
  4. Drag the protractor to the new Earth dot, set it to the Jupiter geocentric angle, then click Draw Sight Line.
  5. After both sight lines are drawn, click Find Jupiter to mark where they intersect.
Date:
🎯 Target Earth Heliocentric Longitude:
🎯 Target Jupiter Geocentric Longitude:
📐 Protractor arm reads:  |  Center: Sun
0° / 360° Reference Line 1 90° 180° 270° Earth's Orbit Sun

Jupiter Position Data Table 4 pts

Filled in automatically as you plot each Jupiter position. All six rows must be plotted for full credit.

Position Earth Helio (Date 1) Jupiter Geo (Date 1) Earth Helio (Date 2) Jupiter Geo (Date 2) Status

Procedure · After Plotting Jupiter's Six Positions

Once all six Jupiter positions (J1–J6) appear in the data table above, tap Connect Points → Draw Ellipse in the simulation. A dashed line will appear from J3 to J6, passing through the Sun. This line is the Major Axis of Jupiter's orbit. Continue with the steps below — you will use the on-screen measuring tool in Part 4 to find each length. All measurements are in model units (the digital equivalent of a ruler on paper).

Step 13. In Part 4, measure the total length of the Major Axis to the nearest tenth of a model unit. Record your measurement in the answer box for Step 13.
Step 14. Find the Distance Between the Foci by completing the parts below:
  • 14a. Measure the distance from J3 to the Sun to the nearest tenth. Record this value in Step 14a.
  • 14b. Measure the distance from the Sun to J6 to the nearest tenth. Record this value in Step 14b.
  • 14c. Using the two measurements above, identify which point is the Aphelion (farthest from the Sun) and which is the Perihelion (closest to the Sun). When you press Connect Points → Draw Ellipse, these labels appear automatically on the diagram.
  • 14d. Subtract the perihelion length (Sun → J6) from the aphelion length (J3 → Sun). The result is the Distance Between the Foci for this model. Record this value to the nearest tenth in Step 14d.
Step 15. Use your answers from Step 13 (major axis) and Step 14d (distance between foci) to calculate the Eccentricity of Jupiter's orbit. Show your work in the space provided and record your final answer to the nearest thousandth.

eccentricity = distance between foci ÷ major axis

📍 The measuring tool and answer boxes for all of these steps are waiting for you in Part 3.

Part 4 · Orbit Analysis

Now that you have plotted Jupiter's six positions, drawn its orbit, and calculated its eccentricity, step back and look at what the shape and your numbers reveal about Jupiter's path around the Sun.

Distance From the Sun at Each Position

The chart below shows how far each plotted Jupiter position is from the Sun in your model. A perfect circle would show six equal distances. An ellipse shows variation between aphelion (farthest) and perihelion (closest).

Tip: If your chart is empty, return to Part 2 and finish plotting all six Jupiter positions.

Analysis Questions

1 pt
7. Looking at your plotted orbit, which Jupiter position appears to be the aphelion (farthest from the Sun)?
1 pt
8. Which Jupiter position is at the perihelion (closest to the Sun)?
1 pt
9. The Sun is located at one focus of Jupiter's orbit. Looking at the shape of your plotted ellipse, is the Sun at the exact center of the orbit?

Reading Comprehension Cluster · Kepler's Three Laws of Planetary Motion

Base your answers to Questions 14 through 18 on the passage, diagrams, data table, and graph below. Each question is worth 1 point.

The Architecture of Planetary Motion

For thousands of years, astronomers believed every object in the solar system traveled along a perfect circle, with Earth fixed at the center. That picture began to fall apart in the late 1500s when the Danish astronomer Tycho Brahe spent more than twenty years recording the positions of the planets — most carefully, Mars. His measurements were the most precise of his era, accurate to within four arc-minutes (one fifteenth of a degree).

After Brahe's death in 1601, his German assistant, Johannes Kepler, inherited the data. Kepler spent eight years trying to fit Mars's path to a circle around the Sun. No matter what radius or center he chose, the model could not match Brahe's observations. In 1609 Kepler finally abandoned circles and tested another shape: the ellipse. With the Sun placed not at the center but at one of the two foci, Mars's position fell into place at every recorded date.

From that breakthrough Kepler eventually published three rules — now called the Laws of Planetary Motion — that describe how every planet orbits the Sun:

  • First Law — the orbit of each planet is an ellipse, with the Sun at one focus.
  • Second Law — an imaginary line joining a planet to the Sun sweeps out equal areas in equal intervals of time. A planet moves fastest at perihelion (nearest the Sun) and slowest at aphelion (farthest from the Sun).
  • Third Law — the square of a planet's period of revolution is proportional to the cube of its mean distance from the Sun. In equation form: T² ∝ r³. Planets farther from the Sun take dramatically longer to complete one orbit.

Kepler's three laws still describe the motion of every planet, moon, comet, and artificial satellite in our solar system, more than four centuries after they were first written down.

Diagram A · Kepler's Second Law (Equal Areas Swept in Equal Time)

Sun 2nd focus Area 1 (30 days) Area 2 (30 days) Perihelion Aphelion Both shaded sectors have equal area

Data Table A · Selected Planets (data from the 2024 ESS Reference Tables)

PlanetMean Distance from Sun (×10⁶ km)Period of Revolution (Earth years)Eccentricity of Orbit
Venus108.20.620.007
Earth149.61.000.017
Mars228.01.880.094
Saturn1432.029.50.054
Neptune4515.0163.70.009
1 pt
14. Which explanation best describes why Kepler concluded that planetary orbits are ellipses rather than perfect circles?
1 pt
15. Use Diagram A above to answer both parts.

Part A: Describe how a planet's orbital speed changes as it travels from aphelion to perihelion.

Part B: Explain how this change in speed produces equal areas swept out in equal intervals of time (Kepler's Second Law).

1 pt
16. Based on Data Table A and Kepler's Third Law, which statement correctly explains why Neptune's period of revolution is so much longer than Saturn's?
1 pt
17. Use Data Table A and the word list below to complete the passage. Place the correct term on each blank.
Word List · each blank: less or greater

Compared to Earth, the planet Mars has a mean distance from the Sun that is . According to Kepler's Third Law, the period of revolution of Mars is therefore than the period of Earth. The average orbital speed of Mars is than the average orbital speed of Earth, because planets farther from the Sun travel more slowly along their orbits.

1 pt
18. A planet orbits the Sun in an elliptical path. Based on Kepler's Second Law, which graph correctly represents the planet's orbital speed as it moves from perihelion → aphelion → perihelion over one complete orbit?

Key: P = perihelion (closest to Sun) · A = aphelion (farthest from Sun)

Part 3 · Calculations

Use the tools below to measure distances on your plotted orbit, then calculate Jupiter's eccentricity. The accepted eccentricity of Jupiter's orbit is 0.048.

Measuring Tool

📍 Loading your plotted positions…

Your six Jupiter positions and the orbit ellipse from Part 2 appear automatically below. Click Start Measuring, then click two points on the diagram. The line will snap to the Sun or a Jupiter dot if you click near it, so each measurement is precise.

Sun
📏 Last measurement: — units

Step-by-Step Calculations

Follow the steps from Part 2. Use the measuring tool above for each measurement.

1 pt
Step 13. Use the measuring tool to find the Major Axis length. Measure from J3 (aphelion) straight through the Sun to J6 (perihelion).
1 pt
Step 14a & 14b. Measure the distance from J3 to the Sun (aphelion distance) and from the Sun to J6 (perihelion distance).
1 pt
Step 14d. Subtract the perihelion length (Step 14b) from the aphelion length (Step 14a) to find the Distance Between the Foci for this model.

distance between foci = aphelion distance − perihelion distance

1 pt
Step 15. Calculate the Eccentricity of Jupiter's orbit using your values from Step 13 and Step 14d.

eccentricity = distance between foci ÷ major axis

1 pt
Step 16. Calculate the Percent Deviation of your eccentricity from the accepted value (0.048).

% deviation = |your value − 0.048| ÷ 0.048 × 100

Part 5 · Regents-Style Quiz

Five questions drawn at random from a 20-question bank, modeled on the January 2026 and June 2025 NYS Earth & Space Sciences Regents exams. You need 60% (3 out of 5) to pass. You may retake the quiz as many times as you need — a fresh set of questions will be drawn each time.

Attempt: 1
Score: / 5

Final Grade & Print Report

Triangulation of Jupiter
—%
— / 38 points

Print Your Lab Report

Tap the button below to print this lab. The print includes your data table, plotted orbit, calculations, quiz results, and final grade. Save it as a PDF and submit to Mr. Brown.

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