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NYS Earth & Space Science

Mr. Brown's Science Labs

Gravity & Gravitational Field Strength

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.

g = Gm/r²Inverse-Square LawKeplerOrbitsPerihelion / Aphelion
Section 1

Vocabulary & Matching

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.

Key Terms

Matching Practice (1 pt each · 8 pts)

Tap a term on the left, then tap its definition on the right. Correct matches turn green.

Terms

Definitions

Section 2

Reading: The Force That Shapes the Universe

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.

Reading Activities (1 pt each)

Complete the Sentence
As the distance between two objects increases, the gravitational force between them .
Build the Sentence
Tap the words in the correct order to form a complete sentence.
Expand the Sentence
Start with this bare-bones sentence: “Gravity pulls objects together.”
Rewrite it as one longer sentence that adds WHERE this happens and WHY it matters.
Section 3

The Gravitational Field Model

This is the model used on the NYS reference tables. Learn to read it, then use the simulator.

How to Read the Model

Gravitational Field Model (recreation of the NYS Regents diagram)
g = GmE ⁄ r²
ggravitational field strength — the pull per kilogram at that spot (N/kg)
Guniversal gravitational constant = 6.67 × 10-11 N·m²/kg² (never changes)
mEmass of Earth (the large object) = 5.97 × 1024 kg
rdistance between the center of Earth and the center of the satellite (m)
Notice r is in the bottom of the fraction and is squared. That is the inverse-square law: as the satellite moves farther out, g shrinks fast.

Simulation: Move the Satellite

Slide to change the distance r. Watch the satellite move and the field strength g update. Earth's radius is 6.378 × 106 m.

6.92
r (×10⁶ m from center)
540
altitude above surface (km)
8.32
g (N/kg)
85%
of surface gravity
At the Hubble Space Telescope's orbit (540 km up), gravity is still about 85% as strong as on the ground!

Collect Your Data (4 pts)

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.

Press a “Set sim” button to move the satellite, then read the g value here and in the simulation above.
r (×106 m from center)Move the simg (N/kg) — you record
10
20
30
40
50
60

Graph: How Gravity Changes with Distance

Plot your recorded data to see the shape of the relationship between gravitational field strength and distance from the center.

Press “Plot My Data” after filling in the table. The dashed line shows the expected curve from g = Gm/r².

How Did Gravity Change? (1 pt each)

Section 4

Reading: Orbits & Why Astronauts Float

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.

The Orbits Model

Orbits of HST and the Moon Model (recreation of the NYS Regents diagram · not to scale)

Reading Activities (1 pt each)

Complete the Sentence
Astronauts inside the orbiting Hubble Telescope appear weightless because they are .
Build the Sentence
Tap the words in the correct order to form a complete sentence.
Expand the Sentence
Start with this bare-bones sentence: “The Moon orbits Earth.”
Rewrite it as one longer sentence that adds WHY the Moon stays in orbit and HOW its distance compares to the Hubble Telescope.
Section 5

Calculation Simulator

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.

Worked Example

Find g at Earth's surface. Use m = 5.97 × 1024 kg, r = 6.378 × 106 m, G = 6.67 × 10-11.

g = (6.67×10-11)(5.97×1024) ⁄ (6.378×106)² ≈ 9.79 N/kg
That matches the “about 9.8 N/kg” you feel every day. Now try the calculators below. Remember: when typing into a calculator, write powers of ten with e — for example 5.97e24 for 5.97 × 1024 and 6.378e6 for 6.378 × 106.

Field-Strength Calculator  g = Gm / r²

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.

g = — N/kg
Tip: enter powers of ten with e — type 6e24 for 6 × 1024 or 2e7 for 2 × 107.

Force Calculator  F = Gm₁m₂ / r²

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.

FA = — N
FB = — N
Tip: enter powers of ten with e — type 4e5 for 4 × 105. Whole numbers like 2 and 4 can be typed normally.
Position A (r = 2 m) gives F ≈ 2.0 N. Position B (r = 4 m) gives about 0.50 N — exactly one-fourth, because the distance doubled (inverse-square law).

Check Your Understanding (1 pt each)

Section 6

Data Tables: Calculate g and F

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.

Quick g calculator:
g = —
Quick F calculator:
F = —

Table 1 — Surface Gravity of Different Worlds (4 pts)

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.”

WorldMass m (kg)Radius r (m)g (N/kg) — you calculate
Earth's Moon7.35 × 10221.74 × 106
Mars6.42 × 10233.39 × 106
Jupiter1.90 × 10276.99 × 107
The Sun1.99 × 10306.96 × 108
A bigger mass pulls harder, but a bigger radius spreads that pull over more distance — both matter. That is why giant Jupiter's surface g is only a few times Earth's, while the dense, smaller Sun is enormous.

Table 2 — Same Comet at Perihelion vs. Aphelion (4 pts)

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 pointr (m, comet to Sun)F (N) — you calculate
Perihelion (closest)8.8 × 1010
Aphelion (farthest)5.3 × 1012
Interpret
At which point is the Sun's gravitational pull on the comet stronger, and what does this mean for the comet's speed?
Section 7 · Regents-Style Cluster

Cluster A: The Gravitational Field Model

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.

Gravitational Field Model · g = GmE/r²
Section 8 · Regents-Style Cluster

Cluster B: Orbits of HST & the Moon

Base your answers on the orbit model below. Not drawn to scale.

Orbits of HST and the Moon Model
Section 9

Quiz — Test Bank

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.

Section 10

Your Grade & Lab Report

FINAL GRADE
0%
0 of 40 points

Print / Save as PDF

Your printable report includes your name and grade at the top, your data tables, the diagrams, and every question with your answer.