Learning Goal: To understand Newton\'s law of universal gravitation and be able

Question

Learning Goal:

To understand Newton's law of universal gravitation and be able to apply it in two-object situations and (collinear) three-object situations; to distinguish between the use of G and g.

In the late 1600s, Isaac Newton proposed a rule to quantify the attractive force known as gravity between objects that have mass, such as those shown in the figure. (Figure 1) Newton's law of universal gravitation describes the magnitude of the attractive gravitational force F g between two objects with masses m1 and m2 as

Fg=G(m1m2r2),

where r is the distance between the centers of the two objects and G is the gravitational constant.

The gravitational force is attractive, so in the figure it pulls to the right on m1 (toward m2) and toward the left on m2 (toward m1). The gravitational force acting on m1 is equal in size to, but exactly opposite in direction from, the gravitational force acting on m2, as required by Newton's third law. The magnitude of both forces is calculated with the equation given above.

The gravitational constant G has the value

G=6.67×1011Nm2/kg2

and should not be confused with the magnitude of the gravitational free-fall acceleration constant, denoted by g, which equals 9.80 m/s2 near the surface of the earth. The size of G in SI units is tiny. This means that gravitational forces are sizeable only in the vicinity of very massive objects, such as the earth. You are in fact gravitationally attracted toward all the objects around you, such as the computer you are using, but the size of that force is too small to be noticed without extremely sensitive equipment.

Consider the earth following its nearly circular orbit (dashed curve) about the sun.(Figure 2) The earth has mass mearth=5.98×1024kg and the sun has mass msun=1.99×1030kg. They are separated, center to center, by r=93millionmiles=150millionkm.

Part A

What is the size of the gravitational force acting on the earth due to the sun?

Explanation / Answer

Mass of earth,Me = 5.98*10^24 kg

mass of sun, Msun = 1.99*10^30 kg

distance between sun and earth, r = 150 Mkm

= 150*10^6*10^3 m

= 1.5*10^11 m

the size of the gravitational force acting on the earth due to the sun, F = G*Me*Msun/r^2

= 6.67*10^-11*5.98*10^24*1.99*10^30/(1.5*10^11)^2

= 3.53*10^22 N <<<<<<-------Answer

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