Physics 1A: Gravitation & Fundamental Forces

What gravity actually does

Gravity is the force of attraction between any two objects that have mass. Every particle of matter in the universe pulls on every other particle. The pull is strongest when the objects are massive and close together; it fades quickly with distance. On Earth’s surface it dominates our daily experience — the reason cups fall off tables, planets orbit stars, and satellites stay in orbit is the same one equation, applied at different scales.

Isaac Newton, in the late 1600s, proposed that the same force that pulls apples toward the Earth also holds the Moon in orbit. This unification of "heavenly" and "earthly" motion was one of the great insights in the history of physics. The equation he wrote down is still the one you use for every gravity problem on the Physics Semester A CBE.

The law of universal gravitation

Newton’s law of universal gravitation states:

F = G · (m₁ · m₂) / d²

Where:

• F is the gravitational force between the two objects, measured in newtons (N).
• m₁ and m₂ are the two masses, measured in kilograms (kg).
• d is the distance between the centers of the two objects, measured in meters (m).
• G is the universal gravitational constant: G = 6.67 × 10⁻¹¹ N·m²/kg². It is one of the smallest constants in physics, which is why you feel a strong pull toward the Earth (which is enormous) but essentially no pull toward the person sitting next to you.

The force acts along the line connecting the two masses. Each mass pulls the other with equal magnitude — this is Newton’s third law showing up again. You are pulled toward the Earth with the same force the Earth is pulled toward you. The Earth just does not accelerate much because its mass is so much greater than yours.

The inverse-square law — small distance changes, big force changes

Look carefully at the denominator: d², not d. This is what physicists call an inverse-square law, and it is a source of many CBE errors. The gravitational force does not simply drop off with distance — it drops off with distance squared.

Practical consequence: if you double the distance between two objects, the force between them drops to (1/2)² = 1/4 of the original. If you triple the distance, force drops to (1/3)² = 1/9. Halve the distance, and force jumps to 4× the original.

A common CBE question phrases this trap as: "If the distance between two objects is doubled, what happens to the gravitational force?" The distractor is usually "halved" (which would be true if the law were 1/d, not 1/d²). The correct answer is one-fourth. Do not answer the question you wish it asked; answer the one it did.

Weight — gravity at Earth’s surface

On or near Earth’s surface, the universal gravitation formula simplifies beautifully. Consider an object of mass m sitting at Earth’s surface. The Earth’s mass is M_Earth ≈ 5.97 × 10²⁴ kg, and the distance from the object’s center to Earth’s center is essentially Earth’s radius, R_Earth ≈ 6.37 × 10⁶ m. Plug into F = GmM/d²:

F = m · [G · M_Earth / R_Earth²] = m · g

The bracketed quantity is what we call the surface gravitational acceleration, g ≈ 9.8 m/s². It is not a fundamental constant; it is a derived quantity that depends on which planet you are standing on and how far you are from its center. On the Moon, g ≈ 1.62 m/s². On Jupiter’s surface, g ≈ 24.8 m/s². Same you, same mass, wildly different weights.

This is where the CBE separates students who understand from those who memorized:

• Mass (kg) — how much matter is in the object. Never changes based on location.
• Weight (N) — the gravitational force on that mass. Depends on the local g.

A student who weighs 588 N on Earth (mass 60 kg × 9.8 m/s²) weighs about 97 N on the Moon (60 kg × 1.62 m/s²) — but still has 60 kg of mass. When the CBE asks about "weight on the Moon," they want you to recompute F = mg with the new g. When they ask about mass, it stays fixed.

Orbits — falling forever

An orbit is what happens when an object is falling toward another mass but moving fast enough sideways that it keeps missing. The Moon orbits the Earth because gravity pulls it toward the Earth continuously — but the Moon’s sideways velocity is exactly matched to that pull so that its path curves around rather than crashes in. Satellites, planets, and moons all follow the same principle.

You do not need the full derivation for Physics 1A, but three qualitative facts show up on the CBE:

• Higher orbits move slower. A satellite at 400 km altitude moves at about 7.7 km/s. A satellite in geostationary orbit at 36,000 km altitude moves at about 3.1 km/s. Distance up = speed down.
• Kepler’s third law: the square of an orbital period is proportional to the cube of the orbital radius. For any two bodies orbiting the same center: T² ∝ r³. Doubling the orbital distance more than doubles the orbital period.
• Orbits are ellipses, not perfect circles. Most artificial satellites are near-circular by design, but the natural shape of an orbit under gravity is an ellipse with the central body at one focus.

The four fundamental forces

Gravity is one of four fundamental forces that describe every interaction in the universe. The Physics Semester A CBE expects you to know them qualitatively — you will not be asked to calculate strong-force values, but you should be able to identify each one and its relative strength.

• Gravitational — attractive only, acts on anything with mass, infinite range, extremely weak on small scales. Dominates at astronomical scales because there is no negative mass to cancel it out.
• Electromagnetic — attractive or repulsive between electric charges, infinite range, roughly 10³⁶ times stronger than gravity for equivalent objects. Everything you touch, feel, or see involves EM forces at the atomic level. You will meet this force formally in Physics Semester B.
• Strong nuclear — very short range (about 10⁻¹⁵ m — the size of a nucleus). Holds protons and neutrons together in atomic nuclei. Vastly stronger than EM at that range; falls off to zero above it.
• Weak nuclear — even shorter range than the strong force. Responsible for certain kinds of radioactive decay. Weaker than EM but stronger than gravity at the same range.

Historically, physicists have found that some of these forces are unified at very high energies — electromagnetism and the weak force merge into the "electroweak" force in extreme conditions. Grand unification of all four is an active area of theoretical research and is worth knowing about even if it does not appear on the CBE.

Where students lose points on gravity questions

• "Half the distance, half the force." Wrong — the law is 1/d², not 1/d. Half the distance means 4× the force.
• Confusing the constant G with the acceleration g. G is universal (6.67 × 10⁻¹¹). g is the local acceleration on a planet’s surface (9.8 on Earth). Same letter, very different quantities.
• Ignoring the mass of the object you are computing weight for. Weight = mg is not just g. If the mass is 60 kg, weight is 588 N, not 9.8 N.
• Assuming zero gravity in space. Astronauts on the ISS are not in "no gravity" — they are in free fall, which feels like weightlessness. Actual gravitational acceleration at ISS altitude is still about 8.7 m/s², or ~89% of surface gravity. They fall, and their spacecraft falls with them.
• Using diameter instead of radius. When a problem gives you the diameter of a planet, remember to divide by 2 before plugging into d² in the gravitation formula.

Worked example — surface gravity on a different planet

A hypothetical planet has 2 times the mass of Earth and 3 times the radius. What is the surface gravitational acceleration on this planet, in terms of Earth’s g?

Step 1 — Use the surface-gravity formula g = GM/R².

Step 2 — Set up the ratio. If M' = 2M and R' = 3R:

g' / g_Earth = (M' / M_Earth) · (R_Earth / R')² = 2 · (1/3)² = 2/9

Step 3 — Numerical value. g' ≈ 2/9 × 9.8 ≈ 2.18 m/s².

Common distractors on this problem: (a) 2 · 9.8 = 19.6 m/s² (multiplied mass only, ignored radius entirely); (b) 2/3 · 9.8 ≈ 6.5 m/s² (used first power of radius, forgot to square); (c) 2/9 with sign confusion. If you see any of these, retrace which factor got mishandled.

Check yourself

1. Write the law of universal gravitation from memory, including units on every quantity.
2. If the distance between two objects doubles, what happens to the force? What if it triples? What if it halves?
3. Explain the difference between G (the universal constant) and g (Earth’s surface gravity).
4. State how your mass and weight compare between Earth and the Moon.
5. List the four fundamental forces from strongest to weakest at atomic scales.
6. Explain why astronauts on the International Space Station feel weightless even though gravity is still acting on them.

Practice with CBE-style questions

Gravitation questions on the CBE tend to test either the inverse-square dependence or the mass-vs-weight distinction. Work through the practice bank filtered by Gravitation & Fundamental Forces — each question includes a full worked solution and identifies which conceptual error each distractor represents.

Independent practice content aligned to Texas Essential Knowledge and Skills (TEKS) §112.39(c)(5)(A), (c)(5)(B), (c)(5)(H). Not affiliated with TTU K-12, UT High School, UT-Austin, the Texas Education Agency, or any Credit by Examination administrator. Texas CBE™ does not administer any exam or grant academic credit.