Consider the Earth and the Moon as a two-particle system.
(a) Find the gravitational field of this two-particle system at the point that is exactly halfway between the Earth and the Moon. (Assume a radial direction r̂ from the Earth to the Moon. Express your answer in vector form.)
g =
N/kg
(b) An asteroid of mass 6.16 ✕ 1015 kg is at the point exactly halfway between the Earth and the Moon. What is the magnitude of the gravitational force on it?
Because earth is far more massive than moon, net force would be toward earth.
if d = distance to earth and distance to moon (in other words d = distance between/2)
ME = mass earth and MM = mass moon
F/m = G(ME/d^2 - MM/d^2) = (G/d^2)(ME-MM)
a=-.0107r
b=.0107*6.16*10^15=6.59*10^13
To find the gravitational field of the two-particle system at the point exactly halfway between the Earth and the Moon, we can use the concept of superposition. The gravitational field at this point is the vector sum of the gravitational fields created by the Earth and the Moon.
(a) The gravitational field at the halfway point is given by:
g = g_earth + g_moon,
where g_earth is the gravitational field created by the Earth and g_moon is the gravitational field created by the Moon.
The gravitational field created by a point mass is given by:
g = GM/r^2,
where G is the universal gravitational constant, M is the mass of the object creating the gravitational field, and r is the distance from the object to the point where the field is being measured.
The mass of the Earth, M_earth, is approximately 5.97 x 10^24 kg, and the mass of the Moon, M_moon, is approximately 7.34 x 10^22 kg. The distance between the Earth and the Moon, d, is approximately 3.84 x 10^8 m.
The gravitational field created by the Earth at the halfway point is given by:
g_earth = (G * M_earth) / (d/2)^2.
The gravitational field created by the Moon at the halfway point is given by:
g_moon = (G * M_moon) / (d/2)^2.
Therefore, the gravitational field of this two-particle system at the halfway point is:
g = g_earth + g_moon.
(b) To find the magnitude of the gravitational force on the asteroid at the halfway point, we can use the equation:
F = m * g,
where F is the gravitational force, m is the mass of the asteroid, and g is the gravitational field.
Given that the mass of the asteroid is 6.16 x 10^15 kg, and the calculated gravitational field at the halfway point is g, we can substitute these values into the equation to find the magnitude of the gravitational force.
exactly half way? zero, there is no net force either. Remember E is a vector, and is pointing in the direction of the mass. for halfway between, the E's add to zero.
b. hmmmm, just answered.