Gravity, Circular Motion, and Orbits

An orbiting satellite is falling. It keeps missing the ground because its sideways motion carries it around Earth while gravity bends its path inward.

This lesson supports Chapter 5 of Physics for Beginners. Keep the physical picture in view, write the units, and check the direction of every vector before trusting a calculation.

Gravity acts between masses

Newton’s law of gravitation is \[F_g=G\frac{m_1m_2}{r^2}.\] Larger masses create a stronger gravitational force. Greater center-to-center distance weakens the force according to an inverse-square relationship. Doubling the distance reduces the force to one fourth of its original value.

Circular motion needs an inward net force

An object moving in a circle changes direction every moment, so it accelerates toward the center. The centripetal acceleration is \[a_c=\frac{v^2}{r}.\] “Centripetal force” is the name for the inward net force. It may be supplied by tension, friction, gravity, or another real force.

Weight and mass are different

Mass measures inertia and does not change when you move to another world. Weight is a gravitational force, \(W=mg\), so it depends on the local gravitational field. Astronauts in orbit still experience gravity. Their apparent weightlessness comes from continuous free fall with their spacecraft.

Worked example

A \(2\text{ kg}\) object moves at \(6\text{ m/s}\) in a circle of radius \(3\text{ m}\). Its centripetal acceleration is \(a_c=6^2/3=12\text{ m/s}^2\). The required inward net force is \(F=ma=24\text{ N}\).

Watch the idea in action

Khan Academy gives a focused explanation of the chapter’s central idea. Pause before each calculation and predict the next step on paper.

Practice questions

1. How does gravitational force change when distance doubles?
2. Which way does centripetal acceleration point?
3. Write the formula for centripetal acceleration.
4. What is the difference between mass and weight?
5. What force keeps a satellite in orbit around Earth?
6. Are orbiting astronauts beyond Earth’s gravity?

Answers

1. It becomes one fourth as large.
2. Toward the center.
3. \(a_c=v^2/r\).
4. Mass measures inertia, while weight is gravitational force.
5. Gravity.
6. No. They are in continuous free fall.

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