HS-ESS1-4: Predicting Orbits with Gravity
Also called NGSS HS-ESS1-4 · Topic: Space Systems · Earth and Space Science
The Official Wording
Use mathematical or computational representations to predict the motion of orbiting objects in the solar system.
Clarification statement: Emphasis is on Newtonian gravitational laws governing orbital motions, which apply to human-made satellites as well as planets and moons.
Assessment boundary: Mathematical representations for the gravitational attraction of bodies and Kepler’s Laws of orbital motions should not deal with more than two bodies, nor involve calculus.
NGSS Lead States, 2013 · Read it on nextgenscience.org · checked October 15, 2026
What HS-ESS1-4 Means in Plain English
Students use math, or a simple computer model, to predict how objects orbit in the solar system. They apply Newton's law of gravity and Kepler's laws to planets, moons and satellites, finding orbit periods, speeds and distances from the mass being orbited.
Problems involve only two bodies, such as a moon and its planet, and use algebra rather than calculus. The work rests on Newton's law of gravitation (HS-PS2-4) and on middle school models of gravity in the solar system (MS-ESS1-2).
HS-ESS1-4 I Can Statements
- I can use Newton's law of gravity to describe an orbit.
- I can use Kepler's third law to relate period and distance.
- I can predict a satellite's orbit height from its period.
HS-ESS1-4 Worked Example
One worked problem: how high a weather satellite must orbit to stay over the same spot.
A geostationary weather satellite circles once every 23 hours 56 minutes (86,160 s), matching Earth's spin. Earth's GM is 3.986 × 10¹⁴ m³/s² and its radius is 6,371 km. How high above the surface does it orbit?
- Set gravity equal to the force needed to keep the satellite on a circle, then solve for the radius.GMm/r² = m(2π/T)²r, so r³ = GMT² ÷ 4π²
- Plug in Earth's GM and the period.r³ = (3.986 × 10¹⁴)(86,160)² ÷ 39.48 ≈ 7.50 × 10²² m³
- Take the cube root to find the distance from Earth's center.r ≈ 4.216 × 10⁷ m = 42,160 km
- Subtract Earth's radius to get the height above the surface.42,160 − 6,371 ≈ 35,790 km
Check it: Putting r back in, T = 2π√(r³/GM) = 2π√(1.88 × 10⁸) ≈ 86,200 s, which matches the 23 hour 56 minute period.
Common Mistakes with HS-ESS1-4
Thinking satellites float with no gravity
“Up there, there's no gravity, so the satellite just floats.”
Try this: Gravity at orbit height is still strong and supplies the centripetal pull. Without it, the satellite would fly off in a straight line.
Using height instead of radius
Plugging 35,790 km straight into Kepler's third law
Try this: Orbit equations use the distance from the center of the planet, so add the planet's radius to the height before calculating.
Expecting the satellite's mass to matter
“A heavier satellite needs a lower orbit.”
Try this: The satellite's mass cancels from both sides of the equation, so any object at that distance has the same orbital period and speed.
Where HS-ESS1-4 Fits
Practice HS-ESS1-4
Quick Check
- If a moon orbited twice as far from its planet, would its period be longer or shorter?
- Why do two satellites at the same height move at the same speed even if one is heavier?
- What force keeps the Moon moving in a curve around Earth?