Universal Gravity 1. The force of gravity between two objects depends on what factors? 2. Two objects each of mass m are placed a distance d apart and the force of gravity between them has magnitude F_(9) Determine the new force of gravity when: a) the mass of one object is doubled b) the mass of both objects is doubled c) the distance between them is doubled d) the distance between them is doubled and the mass of both objects is doubled 3. Suppose you went to a planet that had twice the mass of the Earth with the same radius. How would your weight compare? 4. Suppose you were to stand on a magic ladder that reached up so you were one Earth radius 4. Supper the surface (you're 2 Re from the center of the Earth). How would your weight compare to your weight online the surface of the Earth?

### 1. The force of gravity between two objects depends on what factors?The force of gravity between two objects depends on:- **Masses of the two objects**: The gravitational force is directly proportional to the product of the masses of the two objects.- **Distance between the objects**: The gravitational force is inversely proportional to the square of the distance between the centers of the two objects.This relationship is described by Newton's Law of Universal Gravitation: Where:- is the gravitational force,- is the gravitational constant ( ),- and are the masses of the two objects,- is the distance between the centers of the two objects.---### 2. Two objects each of mass are placed a distance apart, and the force of gravity between them has magnitude . Determine the new force of gravity in the following cases:#### (a) The mass of one object is doubled:If the mass of one object is doubled, the new force becomes: So, the new force of gravity is **twice the original force** ( ).---#### (b) The mass of both objects is doubled:If the mass of both objects is doubled, the new force becomes: So, the new force of gravity is **four times the original force** ( ).---#### (c) The distance between them is doubled:If the distance between the objects is doubled, the new force becomes: So, the new force of gravity is **one-fourth the original force** ( ).---#### (d) The distance between them is doubled and the mass of both objects is doubled:If the distance is doubled and the mass of both objects is doubled, the new force becomes: So, the new force of gravity is **the same as the original force** ( ).---### 3. Suppose you went to a planet that had twice the mass of the Earth with the same radius. How would your weight compare?Weight is the gravitational force acting on an object, given by: Where:- is the mass of the planet,- is the radius of the planet,- is your mass.If the planet has **twice the mass of the Earth** but the **same radius**, the new weight becomes: So, your weight would be **twice as much as it is on Earth**.---### 4. Suppose you were to stand on a magic ladder that reached up so you were one Earth radius away from the surface (you're from the center of the Earth). How would your weight compare to your weight while on the surface of the Earth?The gravitational force decreases with the square of the distance from the center of the Earth. If you're at a distance of (twice the Earth's radius), the new weight becomes: So, your weight would be **one-fourth of your weight on the surface of the Earth**.---### Summary of Results:1. Gravitational force depends on the masses of the objects and the square of the distance between them.2. New forces of gravity: - (a) , - (b) , - (c) , - (d) .3. Your weight on a planet with twice Earth's mass and the same radius would be **twice as much**.4. Your weight at a distance of from Earth's center would be **one-fourth** of your surface weight.