8) A man on the moon with a mass of 90 kilograms weighs 146 newtons. The radius of the moon is 1.74 x 106 meters, find the mass of the moon.

7.36 x 10^(28) kg
2.4 x 10^(10) kg

7.36 x 10^(22) kg

1.43 x 10^(4) kg
i'm unsure of how to do this as well.

146=GM*90/(1.74E6)^2

M= 146*(1.74E6)^2 /90G

and I get one of the answers.

To find the mass of the moon, we can use Newton's Law of Universal Gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

We have the following information:
Mass of the man on the moon (m1) = 90 kg
Weight of the man on the moon (W) = 146 N
Radius of the moon (r) = 1.74 x 10^6 meters

Step 1: Convert the weight into mass using the acceleration due to gravity.
The weight of an object is calculated using the formula W = mg, where g is the acceleration due to gravity. On the moon, the acceleration due to gravity is approximately 1/6th of that on Earth (g = 9.8 m/s^2).

W = mg
146 N = m * (9.8 N/kg)
Solve for m: m = 146 N / 9.8 N/kg

Step 2: Substitute the known values into the equation and solve for the mass of the moon (M).

Using Newton's Law of Universal Gravitation:

W = (G * m1 * M) / r^2

Substituting the known values:

146 N = (G * 90 kg * M) / (1.74 x 10^6 m)^2

Step 3: Solve for the mass of the moon (M).

M = (146 N * (1.74 x 10^6 m)^2) / (G * 90 kg)

where G is the gravitational constant: G = 6.674 x 10^(-11) N(m/kg)^2

Substitute the value of G and calculate:

M = (146 N * (1.74 x 10^6 m)^2) / (6.674 x 10^(-11) N(m/kg)^2 * 90 kg)

M ≈ 7.36 x 10^22 kg

Therefore, the mass of the moon is approximately 7.36 x 10^22 kg.

To find the mass of the moon, we can use the universal law of gravitation, which states that the force of gravity between two objects is given by:

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

Where:
F = force of gravity
G = gravitational constant (6.67430 x 10^(-11) Nm^2/kg^2)
m1 = mass of object 1 (in this case, the man on the moon)
m2 = mass of object 2 (in this case, the moon)
r = distance between the centers of the two objects (radius of the moon in this case)

From the question, we are given the force of gravity between the man and the moon (146 N) and the mass of the man (90 kg). We are also given the radius of the moon (1.74 x 10^6 m).

Now, let's solve for the mass of the moon, which is m2:

Rearranging the formula, we have:
(m2) = (F * r^2) / (G * m1)

Substituting the given values:
m2 = (146 N * (1.74 x 10^6 m)^2) / (6.67430 x 10^(-11) Nm^2/kg^2 * 90 kg)

Calculating this, we find:
m2 ≈ 7.36 x 10^22 kg

Therefore, the correct answer is 7.36 x 10^22 kg.