Consider the earth following its nearly circular orbit (dashed curve) about the sun.(Figure 2) The earth has mass mearth=5.98×1024kg and the sun has mass msun=1.99×1030kg. They are separated, center to center, by r=93millionmiles=150millionkm.

What is the size of the gravitational force acting on the earth due to the sun?

ZAzA

Well, the gravitational force acting on the earth due to the sun is pretty impressive, I must say! It's like the sun is giving the earth a cosmic bear hug!

But let's get to the numbers. We can use Newton's law of universal gravitation, which states that the gravitational force (F) between two objects is given by the equation F = (G * m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.

So, plugging in the numbers we have, G = 6.67430 × 10^-11 N(m/kg)^2, m1 = 5.98 × 10^24 kg, m2 = 1.99 × 10^30 kg, and r = 150 million km = 150 × 10^9 m.

Calculating this cosmic bear hug force, we find that the gravitational force acting on the earth due to the sun is approximately 3.52 × 10^22 Newtons. That's one strong hug!

To calculate the size of the gravitational force acting on the Earth due to the Sun, we can use the formula for gravitational force:

F = (G * m1 * m2) / r^2

Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2)
m1 is the mass of the first object (in this case, the Earth)
m2 is the mass of the second object (in this case, the Sun)
r is the distance between the centers of the two objects

Given:
m1 (mass of Earth) = 5.98 × 10^24 kg
m2 (mass of Sun) = 1.99 × 10^30 kg
r (distance between Earth and Sun) = 150 million km = 150 × 10^9 meters

Plugging in the values into the formula:

F = (6.67430 × 10^-11 N(m/kg)^2) * (5.98 × 10^24 kg) * (1.99 × 10^30 kg) / (150 × 10^9 meters)^2

Calculating this equation:

F = (6.67430 × 10^-11 N(m/kg)^2) * (5.98 × 10^24 kg) * (1.99 × 10^30 kg) / 22500 × 10^18 meters^2

F ≈ 3.52 × 10^22 N

Therefore, the size of the gravitational force acting on the Earth due to the Sun is approximately 3.52 × 10^22 Newtons.

To calculate the size of the gravitational force acting on the Earth due to the Sun, we can use Newton's law of universal gravitation:

F = G * (m1 * m2) / r^2

Where:
F is the gravitational force between two objects,
G is the gravitational constant (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.

In this case, the mass of the Earth (m1) is 5.98 × 10^24 kg, the mass of the Sun (m2) is 1.99 × 10^30 kg, and the distance between the centers of the Earth and the Sun (r) is 150 million km.

First, we need to convert the distance from kilometers to meters:
r = 150 million km * 1000 m/km = 150 billion meters.

Now we can plug the values into the formula to calculate the gravitational force:

F = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.98 × 10^24 kg) * (1.99 × 10^30 kg) / (150 billion meters)^2

Calculating this expression will give you the size of the gravitational force acting on the Earth due to the Sun.