gravitational force
Force between two masses, also between mass and field, considered in butiran.
When we talk about force between two masses at distance some terms come up, such gravity, gravitational force, and gravitation. Gravity is a real force but not in the traditional sense, because at fundamental level there are not any action-at-distance forces, since it just a mass creating gravitational field and then the other mass moving and interacting with this field 1. It is better to use the term gravitational force instead of gravity about the force between to masses that are not in contact 2. Newton’s law of universal gravitation usually present the force in scalar form 3, which is not easy to use for interaction more than to masses. The vector form 4 will be used here since it is more general and easier to use in calculating force superposition. There is also gravitional force on a mass in a gravitational field as weight of a mass is calculated near earth surface 5.
Mass will experience gravitational force
in gravitational field , where source of gravitational field is atually another mass or mass distribution.
Mass will experience gravitational force
due to existence of other mass , where position of mass is and position of mass is .
Relative position of mass from mass is
distance between two masses is
and
is the unit vector.
From Eqns (1) and (2) it can be obtained
as gravitational field produced by mass experienced by another mass in the surrounding of mass .
Challenge 1. Show the steps to obtained Eqn (6) from Eqns (1) and (2). If necessary use also Eqns (3) and (5).
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Tom Henderson, Trevor Fayas, “Newton’s Law of Universal Gravitation”, The Physics Class Room, Jul 2022, url https://www.physicsclassroom.com/class/circles/lesson-3/newton-s-law-of-universal-gravitation [20241013]. ↩︎
Simon Bridge, “Why is there a minus sign in front of the vector form of Newton’s law of universal gravitation?”, Quora, 27 Sep 2017, url https://qr.ae/p2UWj1 [20241013]. ↩︎
-, “Weight Equation”, Gelnn Research Center, NASA, 22 Jul 2022, url https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/weight-gravitational-force/ [20241013]. ↩︎