The earth has a mass = 5.98 X 10^24 kg and the sun has a mass = 1.99 X 10^30 kg. They are separated, center to center, by r= 93 million miles = 150 million km.

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

Very confused by this problem. May someone walk me through the problem step by step? Thank you

Anyone know the answer to this question? According to scientists, the Earth's mass is 5.98 x 1024 kilograms. The mass of the Sun is 1.989 x 1030 kilograms. How many times greater is the mass of the Sun than the mass of the Earth?

F =G•m1•m2/R²

the gravitational constant G =6.67•10^-11 N•m²/kg²,
m1 = 5.98 X 10^24 kg
m2 = 1.99 X 10^30 kg
R=1.5•10^11 m

Sure! Let me walk you through it step by step, but with a little humor sprinkled in!

First, we need to calculate the gravitational force using Newton's law of gravitation. The formula is:

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

Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.674 × 10^-11 N(m/kg)^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.

Okay, so let's plug in the values:

m1 = mass of the Earth = 5.98 × 10^24 kg
m2 = mass of the Sun = 1.99 × 10^30 kg
r = distance between Earth and Sun = 150 million km = 150 × 10^6 km = 150 × 10^9 m

Now, we can calculate the force. Get ready, it's going to be an astronomical number! Drumroll, please...

F = (6.674 × 10^-11 N(m/kg)^2) * (5.98 × 10^24 kg * 1.99 × 10^30 kg) / (150 × 10^9 m)^2

And the answer, my friend, is approximately...

F ≈ 3.52 × 10^22 N

That's a huge number, isn't it? The gravitational force between the Earth and the Sun is so strong that it keeps us nicely in orbit, preventing us from drifting away like a lost balloon at a birthday party!

I hope that helps! Let me know if you have any other cosmic conundrums to be solved. Just remember, even if the numbers sound astronomical, I'm here to clown around and make it fun!

Sure! I'd be happy to walk you through the problem step by step.

To find the size of the gravitational force acting on the Earth due to the Sun, we need to use Newton's Law of Universal Gravitation. This law 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.

Step 1: Convert the distance between the Earth and the Sun from kilometers to meters. 1 kilometer is equal to 1000 meters. Therefore, 150 million kilometers is equal to 150 million multiplied by 1000 meters, which is 1.5 x 10^11 meters.

Step 2: Calculate the gravitational force using the formula for Newton's Law of Universal Gravitation:

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

where F is the gravitational force, G is the gravitational constant (approximately 6.674 x 10^-11 N m^2 / kg^2), m1 is the mass of the Earth, m2 is the mass of the Sun, and r is the distance between their centers.

Step 3: Now substitute the given values into the formula:

F = (6.674 x 10^-11 N*m^2/kg^2) * (5.98 x 10^24 kg) * (1.99 x 10^30 kg) / (1.5 x 10^11 m)^2

Step 4: Simplify the expression:

F = (6.674 x 5.98 x 1.99 * 10^-11 * 10^24 * 10^30) / (1.5 * 1.5 * 10^11 *10^11) N

F = (7.92529 x 10^44) N / (2.25 * 10^22) m^2

F = 3.51135 x 10^22 N

Therefore, the size of the gravitational force acting on the Earth due to the Sun is approximately 3.51135 x 10^22 Newtons.