There's a point between Earth and the Moon where net gravitational field= 0, Mass of Earth =6.0 ×10^24 kg, mass of the Moon =7.3 ×10^22 kg and radius of the Moon’s orbit = 3.8 ×10^8 m, what's the distance of this point from the center of Earth?
To find the distance from the center of Earth to the point between Earth and the Moon where the net gravitational field is zero, we can use the concept of gravitational forces. At this point, the gravitational forces of the Earth and the Moon counterbalance each other, resulting in a net gravitational field of zero.
To begin, we need to understand the equation for the gravitational force between two objects:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force between the two objects,
G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
In this case, we have the following information:
Mass of Earth (m1) = 6.0 x 10^24 kg
Mass of the Moon (m2) = 7.3 x 10^22 kg
Radius of Moon's orbit (r) = 3.8 x 10^8 m
Now we can solve for the distance from the center of Earth to the point where the net gravitational field is zero.
To do this, we first set the gravitational forces of the Earth and the Moon equal to each other:
G * (m1 * m2) / r^2 = G * (m1 * m2) / (R - r)^2
Where R is the total distance between Earth and the Moon (radius of the Moon's orbit).
From this equation, we can calculate the distance (r) from the center of Earth to the desired point.
Now, let's substitute the values into the equation:
G * (m1 * m2) / r^2 = G * (m1 * m2) / (R - r)^2
Cancelling out the common terms:
r^2 = (R - r)^2
Expanding the right side of the equation:
r^2 = R^2 - 2Rr + r^2
Simplifying the equation:
2Rr = R^2
Dividing both sides by 2R:
r = R / 2
Substituting the known values for R:
r = (3.8 x 10^8 m) / 2
Calculating the result:
r = 1.9 x 10^8 m
Therefore, the distance from the center of Earth to the point between Earth and the Moon where the net gravitational field is zero is approximately 1.9 x 10^8 meters.