The gravitational attraction force between the Earth and the Moon is approximately 1.982 × 10^20 Newtons.
The gravitational attraction force between the Earth and the Sun is approximately 3.52 × 10^22 Newtons.
The gravitational attraction between two objects can be calculated using Newton's law of universal gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The equation for the gravitational force (F) is given by:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the objects,
G is the gravitational constant (approximately 6.67430 × 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.
Gravitational attraction between Earth and Moon:
The mass of the Earth is approximately 5.972 × 10^24 kg, and the mass of the Moon is approximately 7.342 × 10^22 kg. The average distance between the Earth and the Moon is about 384,400 kilometers (or 384,400,000 meters).
Plugging in these values into the equation, we can calculate the gravitational attraction force between the Earth and the Moon:
F = (G * m1 * m2) / r^2
= (6.67430 × 10^-11 * 5.972 × 10^24 * 7.342 × 10^22) / (384,400,000)^2
Calculating this, we find that the gravitational attraction force between the Earth and the Moon is approximately 1.982 × 10^20 Newtons.
Gravitational attraction between Earth and Sun:
The mass of the Sun is about 1.989 × 10^30 kg, and the average distance between the Earth and the Sun (known as an astronomical unit or AU) is about 149.6 million kilometers (or 149,600,000,000 meters).
Using the same equation as above:
F = (G * m1 * m2) / r^2
= (6.67430 × 10^-11 * 5.972 × 10^24 * 1.989 × 10^30) / (149,600,000,000)^2
Calculating this, we find that the gravitational attraction force between the Earth and the Sun is approximately 3.52 × 10^22 Newtons.