Discover how mass and distance control the pull of gravity, run two orbit simulations, and calculate gravitational field strength and force — even for the same object at perihelion and aphelion.
Tap any card to flip it. Only one card opens at a time and each closes after 8 seconds — you can reopen any card as many times as you like.
Tap a term on the left, then tap its definition on the right. Correct matches turn green.
Every object that has mass pulls on every other object that has mass. We call this pull gravity. It is the weakest of nature's forces, yet it is the force that holds you to the ground, keeps the Moon orbiting Earth, and keeps Earth orbiting the Sun.
In the 1600s, Isaac Newton realized that the strength of this pull depends on just two things: the masses of the two objects and the distance between their centers. The more mass an object has, the stronger its gravitational pull. The farther apart two objects are, the weaker the pull becomes — and it weakens very quickly. This is called an inverse-square relationship: if you double the distance, the force drops to one-fourth of its value.
Scientists describe the pull at any location using gravitational field strength (the symbol g), measured in newtons per kilogram (N/kg). On the New York State reference tables, the model for this is g = Gm/r², where G is the universal gravitational constant (6.67 × 10-11 N·m²/kg²), m is the mass of the large object, and r is the distance from its center. At Earth's surface, g is about 9.8 N/kg.
This is the model used on the NYS reference tables. Learn to read it, then use the simulator.
| g | gravitational field strength — the pull per kilogram at that spot (N/kg) |
| G | universal gravitational constant = 6.67 × 10-11 N·m²/kg² (never changes) |
| mE | mass of Earth (the large object) = 5.97 × 1024 kg |
| r | distance between the center of Earth and the center of the satellite (m) |
Slide to change the distance r. Watch the satellite move and the field strength g update. Earth's radius is 6.378 × 106 m.
Use the simulation above to gather data. For each distance r, press Set sim to move the satellite to that distance, read the g value the simulation shows, and record it in the table. Then check your data and plot it.
| r (×106 m from center) | Move the sim | g (N/kg) — you record |
|---|---|---|
| 10 | ||
| 20 | ||
| 30 | ||
| 40 | ||
| 50 | ||
| 60 |
Plot your recorded data to see the shape of the relationship between gravitational field strength and distance from the center.
The Hubble Space Telescope (HST) circles Earth about 540 km above the surface. The Moon circles Earth far beyond that — roughly 384,000 km away. Both are held in their paths by the same force: Earth's gravity.
If gravity still pulls on the HST, why do astronauts inside a spacecraft appear to float? It is not because gravity is missing. It is because the spacecraft and everything in it are in free fall — they are all falling toward Earth at the same time while also moving sideways fast enough to keep missing it. Falling together is what makes them look weightless. This continuous “falling around” the planet is what an orbit really is.
Because the HST is much closer to Earth than the Moon, Earth's gravitational field is stronger at the HST. A stronger pull means the HST must travel faster and completes an orbit in about 95 minutes, while the Moon takes about 27 days. This matches Kepler's idea that objects closer to the body they orbit have shorter orbital periods. The same pattern explains perihelion and aphelion: a comet feels a much stronger pull and moves fastest at its closest point to the Sun, and a weaker pull and slower speed at its farthest point.
Practice plugging numbers into the gravity equations. Use the calculators to check your thinking, then answer the questions. Tip: to enter powers of ten, use e — for example type 2e7 for 2 × 107, or 6e24 for 6 × 1024.
Find g at Earth's surface. Use m = 5.97 × 1024 kg, r = 6.378 × 106 m, G = 6.67 × 10-11.
e — for example 5.97e24 for 5.97 × 1024 and 6.378e6 for 6.378 × 106.Read the mass and distance off the diagram, type them into the calculator, and compute g. With these friendly numbers your answer should come out to a nice round value.
e — type 6e24 for 6 × 1024 or 2e7 for 2 × 107.Read the two masses off the diagram (they never change). Enter the distance for Position A (r = 2 m) and for Position B (r = 4 m), then compute each one and compare what doubling the distance does to the force.
e — type 4e5 for 4 × 105. Whole numbers like 2 and 4 can be typed normally.Use the quick calculators below to fill in each table. Table 1 changes the world (different mass and radius); Table 2 changes the distance for one comet. A correctly completed data table is worth 4 points. Round answers; the lab accepts close values.
In Section 3 you changed the distance from one planet. Here the object changes instead — each world has its own mass and radius. Calculate the field strength g = Gm/r² right at each surface (use the world's radius for r). Enter N/kg. This is the “gravity you would feel standing there.”
| World | Mass m (kg) | Radius r (m) | g (N/kg) — you calculate |
|---|---|---|---|
| Earth's Moon | 7.35 × 1022 | 1.74 × 106 | |
| Mars | 6.42 × 1023 | 3.39 × 106 | |
| Jupiter | 1.90 × 1027 | 6.99 × 107 | |
| The Sun | 1.99 × 1030 | 6.96 × 108 |
A comet (mass 2.2 × 1014 kg) orbits the Sun (mass 1.99 × 1030 kg). Calculate the gravitational force F = Gm₁m₂/r² between the Sun and the comet at each point. Enter in newtons (N).
| Orbit point | r (m, comet to Sun) | F (N) — you calculate |
|---|---|---|
| Perihelion (closest) | 8.8 × 1010 | |
| Aphelion (farthest) | 5.3 × 1012 |
Base your answers on the diagram below and what you have learned. The diagram stays on this page so you never have to click back.
Base your answers on the orbit model below. Not drawn to scale.
5 questions are drawn at random from a 20-question bank. Score at least 60% (3 of 5) to master this lab. Unlimited retries — each retry draws a fresh set.
Your printable report includes your name and grade at the top, your data tables, the diagrams, and every question with your answer.