HS-ESS1-4: Predicting orbits with mathematics
What students must show for performance expectation HS-ESS1-4, with a lesson sequence built on live data, the misconceptions to expect, and assessment questions with answers.
Last updated . Curriculum links last reviewed November 2026.
What students must show
Our summary- Students use equations or computer models to predict how planets, moons and human-made satellites move in their orbits.
Newton's law of gravitation governs orbits, for satellites as well as planets and moons.
Two-body systems only, and no calculus.
Our summary, in our own words. Read the official wording.
The three dimensions
High schoolUsing mathematics and computational thinking
Use mathematical representations of phenomena to describe explanations.
ESS1.B Earth and the solar system
Kepler's laws describe common features of orbits, including elliptical paths; gravity or collisions can change an orbit.
Scale, proportion and quantity
Algebra can predict the effect of changing one variable.
Live tools for this standard
3 toolsLesson sequence
Engage to evaluate- Engage10 min
The ISS goes round in about 92 minutes, a GPS satellite in about 12 hours and a geostationary satellite in a day. Predict: what decides the period?
- Explore30 min
The Kepler sheet: five satellites' heights and periods from the directory. Plot the period squared against the radius cubed: a straight line. Find its slope.
- Explain20 min
Derive T^2 = (4 pi^2 / GM) r^3 by setting gravity equal to the centripetal force. Use the slope to find Earth's mass (about 6 x 10^24 kg).
- Elaborate15 min
Predict the period of an orbit 1,000 km up, then check it against a satellite at that height in the directory. Then try the geostationary sheet.
- Evaluate15 min
Ellipses: a near-Earth asteroid moves fastest when it is closest to the Sun. Which of Kepler's laws describes that?
Common misconceptions
3 to watch forHeavier satellites orbit more slowly.
A satellite's period depends only on the mass of what it orbits and its distance, not on its own mass.
Find two satellites at the same height with very different masses in the directory.
Satellites stay up because there is no gravity in orbit.
Gravity supplies the centripetal force; take it away and a satellite heads off along a straight path.
The ball-on-a-string demonstration.
Orbits are perfect circles.
Orbits are ellipses. Many are close to circles, but comets and some asteroids have very stretched orbits.
Look at a near-Earth asteroid's path.
Assessment questions
Answers folded awayHS-ESS1-4: Predicting orbits with mathematics · orbitalradar.com/schools/us/standards/hs-ess1-4
- Which change makes a satellite's orbit take longer?
- A bigger satellite
- A higher orbit
- A faster launch into the same orbit
- For satellites around Earth, the period squared divided by the radius cubed is:
- The same for all of them
- Larger for heavier satellites
- Zero
- Show that an orbit about 35,800 km above the surface takes one day.
- An asteroid moves faster near the Sun than far from it. Which law describes this?
- Pick a satellite in the directory and predict its period from its height. How close is your prediction?
Answer key
- A higher orbit.
- The same for all of them.
- With r = 42,164 km from Earth's center, T^2 = 4 pi^2 r^3 / GM gives about 86,160 s: one sidereal day.
- Kepler's second law: equal areas in equal times.
- Within about 1 to 2 percent for orbits close to circular.
Worksheet
US LetterOne page on US Letter, filled in with live numbers when you open it. Teacher notes and answers included.
The same idea in state standards
Texas, Florida, Georgia- Texas: Astronomy 11A, Physics 5H
- Florida: SC.912.E.5.6
- Georgia: SAST1.d, SP2.d
Related, not equivalent: each state words and groups its standards differently.
More standards pages
High schoolAbout these codes
These are our suggestions for where each tool fits. Always preview a page before using it with a class: some tools show ads, these school pages do not.
Codes are performance expectations of the Next Generation Science Standards*, for example 5-ESS1-2. Each summary is our own wording; follow the link on a standard page for the official text.
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Pick a style, then copy it or download it for your reference manager.Orbital Radar. (2026, November 6). HS-ESS1-4: Predicting orbits with mathematics. Retrieved November 6, 2026, from https://orbitalradar.com/schools/us/standards/hs-ess1-4
“HS-ESS1-4: Predicting orbits with mathematics.” Orbital Radar, 6 Nov. 2026, orbitalradar.com/schools/us/standards/hs-ess1-4. Accessed 6 Nov. 2026.
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Orbital Radar. “HS-ESS1-4: Predicting orbits with mathematics.” Last modified November 6, 2026. https://orbitalradar.com/schools/us/standards/hs-ess1-4.
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* Next Generation Science Standards is a registered trademark of WestEd. Neither WestEd nor the lead states and partners that developed the Next Generation Science Standards were involved in the production of this product, and do not endorse it.