To solve this problem, use the law of universal gravitation.

Remember that  is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

Now that we know the force, we can find the acceleretion. Remember that weight is equal to the mass times acceleration due to gravity.

Set our two forces equal and solve for the acceleration.

To solve this problem, use the law of universal gravitation.

Remember that  is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

Now that we know the force, we can find the acceleretion. Remember that weight is equal to the mass times acceleration due to gravity.

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Set our two forces equal and solve for the acceleration.

The formula for force is given by Newton's second law:

Both rocks will experience the same acceleration, , or the acceleration due to gravity.

Use the mass of each rock in this equation to find which rock experiences a greater force.

We can see that the force on the rock with mass of is equal to three times for the force on the rock with mass of . The heavier rock experiences the greater force.

Even though the rocks have different masses, the acceleration on both will be , the acceleration due to gravity. We can look at Newton's second law to see the force experienced by the rocks:

When objects are in free-fall, the acceleration will be equal to the acceleration from gravity, regardless of the mass of the object.

Newton's second law states:

In this case the acceleration will be the constant acceleration due to gravity on Earth.

Use the acceleration of gravity and the mass of the ball to solve for the force on the ball.

The answer is negative because the force is directed downward. Since gravity is always acting downward, a force due to gravity will always be negative.

First we need to find the mass of the astronaut using Newton's second law.

We know the total weight of the astronaut and the acceleration due to gravity on Earth, allowing us to solve for her mass.

Now that we know her mass, we can look at her weight on the distant moon. We know her weight and mass, allowing us to solve for the acceleration due to gravity in this new environment.

Newton's second law states that:

We know from the problem that the acceleration due to gravity on the moon is less than the acceleration due to gravity on Earth. The mass of the object, however, will remain constant. The result is that the force of gravity on the object while on the moon will be less than the force on the object while on Earth.

This means that the weight of the object while on the moon must be less than . Since the object has a weight on Earth, however, we know that its weight on the moon cannot be zero. This would imply that either the acceleration due to gravity on the moon is zero, or that the mass is zero, neither of which is possible. This allows us to eliminate from the answers.

The only other option that is less than is .

Weight is a very specific force, determined by the acceleration due to gravity acting on a given mass. Using Newton's second law, we can see that weight will be equal to the equation:

We are given the mass of the astronaut and the acceleration due to gravity on Mars. Using these values, we can calculate her weight on Mars.