I'm not sure if my answers are correct. Your help will be greatly appreciated. Thanks in advanced!

1. two very large cruise ships each have a mass of 415000 tonnes. If they were docked side by side, 1.0m apart, their centres would be 60m apart. What is the force of gravitational attraction putting them together? (hint: 1 tonne=1000kg)

2. On Earth, the gravitational field intensity is 9.8 N/kh. Mercury has a mass of 3.28x10^23kg abd a radius of 2.57x10^6m/ Calculate the gravitational field intensity on Mercury N/kg.

3. What would the weight of the dog be if it was taken to Mercury? (the weight of the dog is 245N and the mass is 25kg)

for #1 I got 3x10^-9, for #2 i got 8.5x10^15 and for #3 I got 2.1x10^17. I don't think I got these answers correct.

1.

F =G•m₁•m₂/R²
the gravitational constant G =6.67•10⁻¹¹ N•m²/kg²,
F =G•m₁•m₂/R²=
=6.67•10⁻¹¹•(4.15•10⁸)²/60²=3191 N
2.
g`=GM/R²=
=6.67•10⁻¹¹•3.28•10²³/(2.57•10⁶)²=3.31 N/kg
3.
W(Mercury)=mg`=25•3.31=82.75 N

To calculate the force of gravitational attraction in problem #1, you need to use Newton's Law of Universal Gravitation, which states that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

The equation for gravitational force is:

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

Where:
F is the force of gravitational attraction
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2)
m1 and m2 are the masses of the two objects
r is the distance between their centers

Given the masses of the two cruise ships (415,000 tonnes each) and the distance between their centers (60 m), we can convert the masses to kilograms:

m1 = 415,000 tonnes * 1000 kg/tonne = 415,000,000 kg
m2 = 415,000 tonnes * 1000 kg/tonne = 415,000,000 kg

Plugging the values into the equation, we have:

F = (6.67430 × 10^-11 N(m/kg)^2 * 415,000,000 kg * 415,000,000 kg) / (60 m)^2

Calculating this expression will give you the correct force of gravitational attraction.

For problem #2, you need to use the same formula for gravitational force, but you'll need to calculate the mass of Mercury. Given the mass of Mercury (3.28x10^23 kg) and the radius (2.57x10^6 m), you can use the formula for the gravitational field intensity, g, which is the gravitational force per unit mass:

g = (G * M) / r^2

Where:
g is the gravitational field intensity
G is the gravitational constant
M is the mass of the astronomical body (Mercury in this case)
r is the distance from the center of the astronomical body

The gravitational field intensity on Mercury (g) can be calculated using the given values and the formula above.

For problem #3, the weight of an object on a different planet can be calculated using the formula for weight:

weight = mass * gravitational field intensity

Given the weight of the dog (245 N) and its mass (25 kg), you can calculate the weight of the dog on Mercury using the gravitational field intensity you calculated in problem #2.

By following these steps and using the correct formulas, you should be able to obtain accurate solutions to each problem.