Universal Gravitation Homework Questions?

My teacher gave us review question for an upcoming test, and I thought I understood but I guess I don't. I don't understand how to do the following questions.

1)The intensity of light from a central source varies inversely as the square of the distance. If you lived on a planet only half as far from the sun as our earth, how would the light intensity compare with that on earth? How about a planet ten times as far away as the earth?

2)Calculate the force of gravity between the earth (mass = 6x10^24 kg) and the sun (mass = 2x10^30 kg, distance = 1.5x 10^11 m).

3)To better comprehend the magnitude of the gravitational force between the earth and the sun, pretend gravity is turned off and the pull replaced by the tension in a steel cable joining them. How thick would such a cable need to be? You can estimate the diameter by knowing the tensile strength of steel cable is about 4.5x10^8 N/m^2 (each square meter cross section can support a 4.5x10^8 newton force).

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  • Steve
    Lv 7
    1 decade ago
    Favorite Answer

    All these ?s are readily answered using only the gravity equation: F = G*M1*M2/r²

  • 1 decade ago

    1) In equation this means

    I = K / r^2 where

    I is luminous intensity

    K is some constant

    r is distance

    so if r is divided by 2 you get

    I = K/(r/2)^2 = 4 x K/r^2

    Intensity is multiplied by 4

    similarly if r is multiplied by 10 you get

    I = K/(10r)^2 = 1/100 x K/r^2

    Intensity is divided by 100

    2) The force is

    F = G*m1*m2/r^2

    where

    G is universal gravitational constant 6.673 × 10^-11 m^3/(kg. s^2)

    m1 is mass of earth

    m2 is mass of sun

    r is distance from earth to sun

    so

    F = 6.673e-11*6e24*2e30/(1.5e11)^2

    F = 2.25e22 N = 22 500 000 000 000 000 000 000 N

    3) The cross section of the steel cable would be

    A = 2.25e22/4.5e8 = 5e13 m^2 = 50 000 000 km^2

    In other words the cable would be as thick as 5 times the surface of Canada.

  • 4 years ago

    So truthfully, pumpkin! the image voltaic purely has a negligible impact on earth. Heliocentrists do in assessment to records and modern-day technological guidance getting indoors the way of their nineteenth century theories. And heliocentrism and gravity are purely theories - they have not graduated yet.

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