physics

posted by .

Somewhere between the Earth and the Moon, the gravitational pull exerted by these two bodies on a space pod would cancel. Is this location nearer the Earth or nearer the Moon?
A) Nearer the Earth.
B) Nearer the Moon.
C) At the half-way point.

  • physics -

    Stated another way, "At what distance from the earth toward the moon will the gravitational force of attraction towards the moon be equal and opposite to the gravitational force of attraction towards the earth?

    The Law of Universal Gravitation states that each particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Expressed mathematically,
    F = GM(m)/r^2
    where F is the force with which either of the particles attracts the other, M and m are the masses of two particles separated by a distance r, and G is the Universal Gravitational Constant. The product of G and, lets say, the mass of the earth, is sometimes referred to as GM or mu (the greek letter pronounced meuw as opposed to meow), the earth's gravitational constant. Thus the force of attraction exerted by the earth on any particle within, on the surface of, or above, is F = 1.40766x10^16 ft^3/sec^2(m)/r^2 where m is the mass of the object being attracted and r is the distance from the center of the earth to the mass.
    The gravitational constant for the earth, GM(E), is 1.40766x10^16ft^3/sec^2. The gravitational constant for the moon, GM(M), is 1.7313x10^14ft^3/sec^2. Using the average distance between the earth and moon of 239,000 miles, let the distance from the moon, to the point between the earth and moon, where the gravitational pull on a 32,200 lb. satellite is the same, be X, and the distance from the earth to this point be (239,000 - X). Therefore, the gravitational force is F = GMm/r^2 where r = X for the moon distance and r = (239000 - X) for the earth distance, and m is the mass of the satellite. At the point where the forces are equal, 1.40766x10^16(m)/(239000-X)^2 = 1.7313x10^14(m)/X^2. The m's cancel out and you are left with 81.30653X^2 = (239000 - X)^2 which results in 80.30653X^2 + 478000X - 5.7121x10^10 = 0. From the quadratic equation, you get X = 23,859 miles, roughly one tenth the distance between the two bodies from the moon. So the distance from the earth is ~215,140 miles.
    Checking the gravitational pull on the 32,200 lb. satellite, whose mass m = 1000 lb.sec.^2/ft.^4. The pull of the earth is F = 1.40766x10^16(1000)/(215,140x5280)^2 = 10.91 lb. The pull of the moon is F = 1.7313x10^14(1000)/(23858x5280)^2 = 10.91 lb.
    This point is sometimes referred to as L2. There is an L5 Society which supports building a space station at this point between the earth and moon. There are five such points in space, L1 through L5, at which a small body can remain in a stable orbit with two very massive bodies. The points are called Lagrangian Points and are the rare cases where the relative motions of three bodies can be computed exactly. In the case of a body orbiting a much larger body, such as the moon about the earth, the first stable point is L1 and lies on the moon's orbit, diametrically opposite the earth. The L2 and L3 points are both on the moon-earth line, one closer to the earth than the moon and the other farther away. The remaining L4 and L5 points are located on the moon's orbit such that each forms an equilateral triangle with the earth and moon.

  • physics -

    nearer the earth

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    You are flying to the Moon. Find the point at which the gravitational attractions of Earth and Moon on you will be equal and opposite. Given: radius of the moon: 1.74*10^6 m radius of the earth: 6.38*10^6 m orbital radius of the moon: …
  2. science

    Somewhere between Earth and the Moon, gravity from these two bodies on a space pod would canel. Is it closer to the Earth or the Moon?
  3. physics

    somewhere between earth and the moon gravity from these two bodies on a space pod would cancel. Is this location nearer to earth or the moon?
  4. physics help please!

    A spacecraft is on a journey to the moon. At what point, as measured from the center of the earth, does the gravitational force exerted on the spacecraft by the earth balance that exerted by the moon?
  5. physics

    Calculate the magnitudes of the gravitational forces exerted on the Moon by the Sun and by the Earth when the two forces are in direct competition, that is, when the Sun, Moon, and Earth are aligned with the Moon between the Sun and …
  6. Physics

    Consider a space pod somewhere between earth and the moon, at just the right distance so that the gravitational attractions to Earth and Moon are equal. Is this location nearer Earth or Moon?
  7. physics

    Which of the following correctly describe the gravitational attraction between Earth and the Moon?
  8. Physics

    When a spacecraft travels from the Earth to the Moon, both the Earth and the Moon exert a gravitational force on the spacecraft. Eventually, the spacecraft reaches a point where the Moon's gravitational attraction overcomes the Earth's …
  9. physics

    A spacecraft is on a journey to the moon. At what point, as measured from the center of the earth, does the gravitational force exerted on the spacecraft by the earth balance that exerted by the moon?
  10. Physics

    The earth has about 80 times the mass of the earth’s moon. The gravitational force exerted on the moon by the earth has what relation to the gravitational force exerted on the earth by the moon?

More Similar Questions