Question

At its greatest distance from Earth, the moon experiences a gravitational force of 1.78 E 20 N. The mass of the Earth is 5.97 E24 kg. The mass of the moon is 7.35 E22 kg. What is the distance between the Earth and the moon at that point if G = 6.67 E−11 N*m2/kg2?4.06 E 5 km1.65 E 17 km1.65 E 8 km4.06 E 14 km

Answer 1

The distance between the Earth and the Moon at the point where the opposing gravitational forces are equal is approximately 4.06E14 km.

Step-by-step explanation:

To find the distance between the Earth and the Moon at the point where the opposing gravitational forces are equal, we can use the principle that the force of gravity is inversely proportional to the square of the distance between two objects. Let's call the distance between the Earth and the Moon at that point 'd'.

Using Newton's law of universal gravitation, we can set up the following equation: Fe / Fm = (d / r)2, where Fe is the gravitational force of the Earth, Fm is the gravitational force of the Moon, and r is the distance between the Earth and the Moon.

Plugging in the given values, we get the following: 1.78E20 N / (6.67E-11 N*m2/kg2) = (d / 3.80E5 km)2

Simplifying the equation, we can solve for 'd' by taking the square root of both sides and converting the units:

d = sqrt((1.78E20 N / 6.67E-11 N*m2/kg2) * (1 km / 1000 m) * (1E5 m / 1 km))

Calculating this expression, we find that the distance between the Earth and the Moon at the point where the opposing gravitational forces are equal is approximately 4.06E14 km.

Answer 2

Given

F = 1.78e20 N

m_e = 5.97e24 kg

m_m = 7.35e22 kg

G = 6.67e-11 nm2/kg2

Procedure

`\begin{gathered} F=(Gm_em_m)/(r^2) \\ r=\sqrt[]{(Gm_em_m)/(F)} \\ r=\sqrt[]{(6.67e-11\cdot5.97e24\cdot7.35e22)/(1.78e20)} \\ r=4.06e8\text{ m} \end{gathered}`