University of Washington



Lab 2: Introduction to GravityGravity is one of the most important forces in astronomy. Unlike the “strong” and the “weak” forces, it can act over the very long distances that are characteristic of Space . For this course, you will need to learn a few simple facts about gravity and how it works.Gravity is always “attractive”, meaning it can only pull objects towards each other.The gravitational force between two objects depends on only two things:How massive the two objects areHow far apart the two objects areThe gravitational force attracting two objects together increases if the mass of either object increases.The gravitational force attracting two objects together increases if the objects are closer together.The formula describing the strength of the gravitational force between two objects with masses M1 and M2, separated by a distance D isFGravity = GM1M2D2G is a constant which describes how strong the force of gravity is. It is known as “Newton’s Constant” and has a value of G = 6.67×10?11meters3/(kilogram×seconds2).The separation D between two objects is defined as the separation between their centers, not their edges. For example, if you calculate the gravitational force between two adjacent soccer balls that were touching each other, the separation would be about 22 cm, rather than zero.The equation describing the force of gravity shows thatThe force increases linearly with the mass of either object (i.e. if you double the mass of one object, the force between the objects doubles as well)The force decreases as the square of the separation (i.e. if you double the separation between the objects, the force decreases by a factor of 4 (= 22)).Sometimes (such as later in this lab), you are not interested in exactly how big a gravitational force is in absolute terms, but are instead only interested in how big it is compared to some other force. For example, suppose you wanted to compare the force of gravity that the Earth feels from the Sun to the force that the Earth feels from the Moon. The force that the Earth feels from each object is:FGravity,⊙ = GM⊙M?D⊙2 FGravity, Moon=GMMoonM? DMoon2where D⊙ and DMoon are distances measured from the center of the Earth to the center of the Sun and Moon, respectively. Dividing the force due to the Sun by the force due to the Moon gives the ratio of the two forces. A bit of simple algebra then shows that:FGravity,⊙FGravity,Moon=M⊙MMoonDMoonD⊙2Therefore, for two objects, the ratios of their masses and their distances are sufficientto tell you which object produces the stronger gravitational force, and by how much.Gravitational force has the units of mass times acceleration. Acceleration is the rate at which velocity changes and has units of (meters/second)/second, or meters×seconds-2. Force therefore has units of kilograms×meters×seconds-2. This combination of units is sometimes called “a Newton”, after Sir Isaac Newton. One Newton of force can accelerate a 1 kilogram mass by 1 meter per second every second. ................
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