Gravity and gravitational fields Notes

What Is Gravity And How Does It Act Between Objects With Mass?

1. Gravity is one of the four fundamental interactions in nature.
2. Unlike the strong and weak nuclear interactions, gravity has an unlimited range.
3. Gravitational forces act between any two objects that have mass.
4. The gravitational interaction is always attractive and never repulsive.
5. Although gravity acts between all masses, the force between everyday objects is extremely small and usually unnoticeable.

Gravity as a Force Between Masses

1. Gravity acts between any two objects with mass.
2. The gravitational force between everyday objects is extremely small.
3. The force becomes noticeable when at least one object is very massive.
4. Planets and stars experience strong gravitational attraction.

Everyday Experience of Gravity

1. Gravity pulls objects toward the centre of the Earth.
2. Objects fall to the ground when released because the Earth exerts a gravitational force on them.
3. Humans experience gravity constantly, which is why its effects are often unnoticed.
4. Gravity provides the force that gives objects weight.

Weightlessness and Freefall

1. Astronauts in space often appear weightless.
2. This does not mean gravity is absent.
3. Astronauts experience weightlessness because they are in continuous freefall around the Earth.
4. In freefall, gravity still acts, but there is no supporting force pushing back on the body.

Newton’s Ideas About Gravity

1. Isaac Newton proposed that the same force responsible for an apple falling also governs the motion of the Moon and planets.
2. This idea unified motion on Earth and motion in space under a single explanation.
3. Newton suggested that gravity acts between all objects with mass.
4. He also reasoned that gravity must weaken with distance to explain planetary orbits.

Newton’s Law of Gravitation

1. Newton showed that gravitational force depends on:
   1. The masses of both objects
   2. The distance between them
2. The relationship follows an inverse square pattern.
3. As distance increases, force decreases rapidly.
4. The gravitational force between two objects is given by: $$F = G \frac{m_1 m_2}{r^2}$$
5. Where:
   1. F = gravitational force between the objects (in newtons, N)
   2. G = gravitational constant
   3. m_1 and m_2= masses of the two objects (in kilograms, kg)
   4. r = distance between the centres of the two masses (in metres, m)

Gravitational Field Explains How Gravity Acts Through Space

1. To describe "action at a distance," physicists use the idea of a field.
2. A massive object (like Earth) creates a gravitational field in the space around it.
3. If another mass enters that region, it experiences a force pulling it toward the massive object.
4. A helpful way to visualize a gravitational field is with field lines:
   1. The arrows show the direction a small test mass would accelerate (toward the center of the planet).
   2. The "crowding" of lines represents strength: closer to Earth, the field is stronger.

Gravitational field strength

1. Earth produces a gravitational field that pulls objects toward its center.
2. This field extends far into space, well beyond Earth’s surface.
3. Objects near Earth experience a nearly constant gravitational pull.
4. Near earth's surface, it is $$g \approx 9.8\ \text{N kg}^{-1}$$

$$g = \frac{W}{m}$$

Weight is the gravitational force on an object

1. Weight depends on both the object’s mass and the gravitational field strength.
2. The relationship between weight, mass, and gravitational field strength is: W = mg where,
   1. $W$ is weight (N)
   2. $m$ is mass (kg)
   3. $g$ is gravitational field strength ($\text{N kg}^{-1}$)

Mass vs weight

1. Mass is an intrinsic property: it does not change when you travel.
2. Weight depends on the local gravitational field: it changes from place to place.

Gravity and Orbits

1. Gravity is responsible for keeping objects in orbit.
2. An orbit occurs when an object is constantly falling toward another object but keeps missing it due to its forward motion.
3. The gravitational force provides the centripetal force needed to keep an object moving in a curved path.

Satellites and Orbital Motion

1. A satellite is an object that orbits a larger body.
2. Artificial satellites orbit the Earth due to gravitational attraction.
3. The balance between forward motion and gravitational pull allows satellites to remain in orbit.

Gravitational Fields of the Moon and the Sun

1. The Moon has its own gravitational field.
2. The Moon’s gravitational field is weaker than Earth’s due to its smaller mass.
3. The Sun’s gravitational field is much stronger than Earth’s and dominates the solar system.
4. The Sun’s gravity keeps planets in orbit.

Tides and Gravitational Effects

1. Tides on Earth are caused mainly by the Moon’s gravitational field.
2. The Moon pulls more strongly on the side of the Earth closest to it.
3. This difference in gravitational pull causes the oceans to bulge, producing tides.
4. The Sun also affects tides, but its effect is smaller due to distance.