2.1: Newtonian Gravitation

Astronomy 10: The Solar System (Workbook) · LibreTexts

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    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    2.1.1 Gravity and No Gravity

    Model

    A satellite orbits around the Earth on the path shown. On the figure, draw an arrow on the satellite to show the direction it is moving at this snapshot in time.

    Satellite orbiting Earth with position marked for analyzing motion under changing gravity.

    Satellite orbiting Earth with position marked for analyzing motion under changing gravity.

    1. Imagine that at this moment in time, the force of gravity increased. Draw the path the satellite would travel and label the path “More Gravity.” Explain your thinking. How did you determine this path?
    2. Imagine that at this moment in time, the force of gravity decreased. Draw the path the satellite would travel and label the path “Less Gravity.” Explain your thinking. How did you determine this path?
    3. Imagine that at this moment in time, the force of gravity was turned off. Draw the path the satellite would travel and label the path “No Gravity.” Explain your thinking. How did you determine this path?

    Summary

    When there are no forces acting on an object in motion, that object will:

    Forces cause objects to:

    2.1.2 Force of Gravity: Mass and Distance

    Model

    In the model below, pairs of objects are shown at different distances. The arrows represent the gravitational force between the objects. A larger arrow means more force.

    N Gravity LC.png

    Object pairs A, B, and C comparing masses, distances, and gravitational forces.

    1. Identify the following comparisons. These do not need to be CER format:
      1. Compare A and B. What changed about the distance between the objects and the masses of the objects? What changed about the force of gravity between the objects?
      2. Compare A and C. What changed about the distance between the objects and the masses of the objects? What changed about the force of gravity between the objects?
      3. For each pair of objects, how does the force experienced by the object on the left compare to the force experienced by the object on the right?
    2. Summarize as a CER (you might use your comparisons as evidence): What makes the force of gravity go up? What makes the force of gravity go down?

    Summary

    Forces are interactions between two objects that push or pull the objects. These forces change the way an object moves. Forces always come in pairs. In any interaction, each object experiences the same force in opposite directions. This equal and opposite relationship is called Newton’s Third Law.

    The strength of the force of gravity is related to the mass of the interacting objects and the distance between the center of mass of those objects. Both objects experience the same force but in opposite directions. The strength of this force is represented by the relationship:

    \(F_{\text{gravity}} \propto \frac{m_1 \times m_2}{r^2}\)

    Apply

    Rank the following pairs of objects from lowest gravitational force to highest gravitational force. Try putting the values given into the proportional relationship above. You may use a calculator.

    Gravitational force ranking activity comparing object masses and distances.

    Gravitational force ranking activity comparing object masses and distances.

    Image Credit: Astronomy Interactives from the Astronomy Education Department at the University of Nebraska-Lincoln (https://astro.unl.edu/interactives/)

    2.1.3 Force and Motion

    Model

    In the model below, the force of gravity and acceleration of gravity are shown for three objects. On each object, the top arrow represents the force of gravity that we just explored. The bottom arrow represents the acceleration of the object, which represents how the motion changes based on the force of gravity.

    Earth and three objects showing gravity force arrows and acceleration arrows.

    Earth and three objects showing varying gravity force arrows and equal acceleration arrows.

    1. For each Earth–object pair, how does the force of gravity on the object compare to the force of gravity on the Earth?
    2. Compare across objects. Rank the forces of gravity that each object experiences.

    Same F for all Objects OR Greatest ____________________ ____________________ ____________________ Least

    1. Based on your responses, predict how the masses of the three objects (not Earth) compare.

    Same M for all Objects OR Greatest ____________________ ____________________ ____________________ Least

    1. Compare across objects. Rank the acceleration of gravity that each object experiences.

    Same a for all Objects OR Greatest ____________________ ____________________ ____________________ Least

    1. Use your responses to make a connection between force, mass, and acceleration. Circle the statement that best matches the patterns you see:
    • Mass does not affect acceleration.
    • With more mass you need more force to get the same acceleration.
    • With more mass you need less force to get the same acceleration.

    Summary

    The net force (\(\Sigma F\)) acting on an object is equal to the product of the mass of the object and the object's acceleration. This relationship is called Newton’s Second Law.

    \(\Sigma F = ma\)

    The net force causes this acceleration. When objects have more mass, they experience less acceleration for the same net force. You can say this another way by rearranging the equation:

    \(a=\frac{\Sigma F}{m}\)

    To get the same acceleration, you need more force on objects with more mass. For curved motion, acceleration points inward toward the center of the curve.

    With gravity, more mass leads to more force, so the mass of the object ends up canceling out. The acceleration is only based on the mass of the other object and the distance between the two objects.

    \(F_g \propto \frac{m_1 \times m_2}{d^2}\)

    \(a_1 \propto \frac{m_2}{d^2}\)

    2.1.4 Multiple Forces

    Model

    In this model, there are three objects that exert gravitational forces on each other.

    Three-object gravity system used to analyze combined gravitational forces.

    Image Credit: Astronomy Interactives from the Astronomy Education Department at the University of Nebraska-Lincoln (https://astro.unl.edu/interactives/)

    1. Draw a force arrow on each middle object. Make the length represent the strength of the force, so if the force to the left is greater than to the right, make the arrow to the left longer than the arrow to the right.
    2. Next to each object, write what direction it will change its motion.
    3. Next to the objects on the left, draw an arrow to represent the force from both the middle and right-most object. Scale them to show which force is bigger.
    4. Next to the objects on the right, draw an arrow to represent the force from both the middle and left-most object. Scale them to show which force is bigger.
    5. When an object interacts with two other objects, do you simply add the forces together? If not, explain how you identify the change in motion of an object when there is more than one force acting on that object.

    Summary

    Forces have ____________________ and ____________________. When adding two or more forces together, you need to take both into account.

    The change in motion of the object is based on the ____________________ force acting on that object.

    This page titled 2.1: Newtonian Gravitation was last modified on Sat, 01 Aug 2026 14:37:31 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Andrew Totah-McCarty.