Question

The mass of the earth is 6×10²⁴kg and that of the moon is 7.4×10²²kg.if the distance between the earth and the moon is 3.84×10⁵km,calculate the force exerted by the earth on the moon.(Take G=6.7×10‐¹¹ Nm²kg²)

Answer 1

The gravitational force exerted by the Earth on the Moon is approximately 2.016 x 10^20 Newtons, calculated using Newton's law of gravitation with given masses, the gravitational constant, and the distance between the Earth and the Moon.

The gravitational force between two objects can be calculated using Newton's law of gravitation:

`\[ F = (G \cdot m_1 \cdot m_2)/(r^2) \]`

Where:

- F is the gravitational force between the two objects,

- G is the gravitational constant
`(\(6.7 * 10^(-11) \, \text{Nm}^2/\text{kg}^2\))`,

- m_1 and m_2 are the masses of the two objects,

- r is the distance between the centers of the two masses.

In this case, m_1 is the mass of the Earth
`(\(6 * 10^(24) \, \text{kg}\)), \( m_2 \)` is the mass of the Moon
`(\(7.4 * 10^(22) \, \text{kg}\))`, and r is the distance between the Earth and the Moon
`(\(3.84 * 10^5 \, \text{km}\))`.

However, it's important to convert the distance from kilometers to meters:

`\[ r = 3.84 * 10^5 \, \text{km} * 10^3 \, \text{m/km} \]`

Now, substitute the values into the formula:

`\[ F = \frac{(6.7 * 10^(-11) \, \text{Nm}^2/\text{kg}^2) \cdot (6 * 10^(24) \, \text{kg}) \cdot (7.4 * 10^(22) \, \text{kg})}{(3.84 * 10^5 \, \text{km} * 10^3 \, \text{m/km})^2} \]`

Let's calculate the gravitational force using the provided values:

`\[ F = \frac{(6.7 * 10^(-11) \, \text{Nm}^2/\text{kg}^2) \cdot (6 * 10^(24) \, \text{kg}) \cdot (7.4 * 10^(22) \, \text{kg})}{(3.84 * 10^5 \, \text{km} * 10^3 \, \text{m/km})^2} \]`

First, convert the distance from kilometers to meters:

`\[ r = 3.84 * 10^5 \, \text{km} * 10^3 \, \text{m/km} = 3.84 * 10^8 \, \text{m} \]`

Now substitute the values:

`\[ F = \frac{(6.7 * 10^(-11) \, \text{Nm}^2/\text{kg}^2) \cdot (6 * 10^(24) \, \text{kg}) \cdot (7.4 * 10^(22) \, \text{kg})}{(3.84 * 10^8 \, \text{m})^2} \]`

`\[ F = ((6.7 * 10^(-11)) \cdot (6 * 10^(24)) \cdot (7.4 * 10^(22)))/((3.84 * 10^8)^2) \]`

`\[ F \approx ((4.02 * 10^(14)) \cdot (7.4 * 10^(22)))/(1.4736 * 10^(17)) \]`

`\[ F \approx (2.9688 * 10^(37))/(1.4736 * 10^(17)) \]`

`\[ F \approx 2.016 * 10^(20) \, \text{N} \]`

So, the gravitational force exerted by the Earth on the Moon is approximately
`\(2.016 * 10^(20)\)` Newtons.