Larry weighs 300 N at the surface of the earth. what is the weight of the earth in the gravitational field of Larry?

-force= GMm/d^2
would i set it up like force= (9.8m/s^2)(300 N)?

an astronaut lands on a planet that has twice the mass as earth and twice the diameter. how does the astronaut weight differ from that on earth? (this one i don't get still)

if the moon pulls the earth as strongly as the earth pulls the moon, why doesnt the earth rotate around the moon, or why don't both rotate around a point midway between them?
-the earth doesnt rotate around the moon because the moon is not center of gravity and they both don't rotate around a point midway between them because of the center of gravity.

To find the weight of the earth in the gravitational field of Larry, you can use the formula for gravitational force:

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

where G is the gravitational constant, m1 and m2 are the masses of the objects (in this case Larry and the earth), and r is the distance between the centers of the objects.

In this scenario, Larry weighs 300 N at the surface of the earth. The weight of an object is the force with which it is pulled by gravity. So, the weight of Larry is equal to the force of gravity between him and the earth.

Therefore, you would set it up as:

300 N = (G * m1 * m2) / r^2

Now, to find the weight of the earth in the gravitational field of Larry, you would rearrange the formula:

300 N * r^2 = G * m1 * m2

Note that the mass of Larry is negligible compared to the mass of the earth, so m1 can be ignored. The distance from the center of the earth to the surface is the same as the radius of the earth. Therefore, the equation can be simplified to:

300 N * (radius of the earth)^2 = G * m2 (mass of the earth)

Now you can solve for the weight of the earth.

Regarding the question about an astronaut landing on a planet with twice the mass and twice the diameter of the earth, the weight of the astronaut will be greater than on earth. This is because the gravitational force is directly proportional to the mass of the object attracting the astronaut. So, with double the mass, the gravitational force will be twice as strong. The weight is proportional to the gravitational force, so the weight of the astronaut will also be doubled.

Lastly, the reason why the earth doesn't rotate around the moon or both rotate around a point midway between them is due to the difference in mass between the moon and the earth. The center of gravity of a system depends on the masses and their distribution. In the case of the earth-moon system, the center of mass is much closer to the center of the earth due to its significantly larger mass. Therefore, the earth exerts a stronger gravitational force on the moon, causing the moon to orbit around the earth. The earth's rotation is not affected because the gravitational force of the moon is not strong enough to overcome the earth's rotational motion.

To find the weight of the earth in the gravitational field of Larry, you would need to use Newton's law of universal gravitation formula:

force = G * (m1 * m2) / d^2

In this formula, G is the gravitational constant, m1 is the mass of the first object (in this case, Larry), m2 is the mass of the second object (in this case, the earth), and d is the distance between the centers of the two objects.

However, in this case, we are given the weight of Larry (300 N), not his mass. The weight of an object is the force with which it is pulled towards the center of the Earth due to gravity, and it is given by the formula:

weight = mass * acceleration due to gravity

In this case, we know that his weight is 300 N, and the acceleration due to gravity on the surface of the Earth is approximately 9.8 m/s^2. Therefore, we can rearrange the formula to solve for the mass of Larry:

mass = weight / acceleration due to gravity

mass = 300 N / 9.8 m/s^2

Now that we have the mass of Larry, we can substitute it into the formula to find the force between Larry and the Earth:

force = G * (mass of Larry * mass of Earth) / d^2

Please note that force here represents the gravitational force between Larry and the Earth, not Larry's weight. The weight of the Earth would be equal in magnitude but opposite in direction.

Regarding the second question about an astronaut landing on a planet with twice the mass and diameter of Earth, the astronaut's weight would be different because weight depends on the mass and the gravitational field strength. The gravitational field strength (acceleration due to gravity) depends on the mass of the planet and the distance from its center.

In this case, if the planet has twice the mass of Earth and twice the diameter, it means that its volume would be 2^3 = 8 times larger than Earth. Therefore, the density of the planet would be the same as Earth since density = mass/volume.

Since weight is proportional to mass and gravitational field strength, and the mass of the planet is twice that of Earth, the weight of the astronaut on this new planet would be twice as much compared to their weight on Earth.

When it comes to the third question about the rotation between the Earth and the Moon, it is essential to consider the concept of the center of gravity. The center of gravity is the point at which the entire weight of an object can be considered to act. In the case of the Earth-Moon system, the center of gravity is closer to the Earth due to its much larger mass.

Both Earth and the Moon exert gravitational forces on each other because every object with mass exerts a gravitational force on every other object with mass. However, the Earth's mass is significantly larger than the Moon's mass, which means that the gravitational force exerted by the Earth on the Moon is stronger than the force exerted by the Moon on the Earth.

As a result, the Moon orbits around the Earth in what we observe as the Moon revolving around the Earth. If the Moon's gravitational force were strong enough to overcome the Earth's gravitational force, then the Earth and Moon could potentially rotate around a point midway between them, called the barycenter. However, in this case, the Earth's gravitational force is dominant due to its much larger mass, causing the Moon to revolve around the Earth instead.