Newtonian Gravitation
In 1687, Sir Isaac Newton published his law of universal gravitation, which states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
$$F_g = G\frac{m_1m_2}{r^2}$$
where:
- $F_g$ is the gravitational force between the two particles
- $G$ is the gravitational constant, which is $6.674 × 10^{-11} \text{ N} \cdot \text{m}^2/\text{kg}^2$
- $m_1$ and $m_2$ are the masses of the two particles
- $r$ is the distance between the two particles
Applications of Newtonian Gravitation
Newtonian gravitation has a wide range of applications, including:
- Calculating the force between two planets
- Determining the mass of a planet
- Predicting the trajectory of a projectile
- Designing spacecraft trajectories
New Applications of Newtonian Gravitation
Scientists are constantly exploring new applications of Newtonian gravitation. One promising area of research is the use of gravity to generate electricity. This technology, known as gravitational energy storage, could provide a clean and renewable source of energy.
Tables
| Quantity | Symbol | Units |
|---|---|---|
| Gravitational force | $F_g$ | N |
| Gravitational constant | $G$ | N m$^2$/kg$^2$ |
| Mass | $m$ | kg |
| Distance | $r$ | m |
| Planet | Mass (kg) |
|---|---|
| Earth | $5.972 × 10^{24}$ |
| Mars | $6.417 × 10^{23}$ |
| Jupiter | $1.898 × 10^{27}$ |
| Saturn | $5.684 × 10^{26}$ |
| Uranus | $8.683 × 10^{25}$ |
| Neptune | $1.024 × 10^{26}$ |
| Projectile | Velocity (m/s) | Angle (degrees) |
|---|---|---|
| Baseball | 30 | 45 |
| Golf ball | 50 | 30 |
| Bullet | 1000 | 0 |
| Gravitational energy storage system | Capacity (MWh) | Efficiency (%) |
|—|—|
| Flywheel | 100 | 90 |
| Pumped hydro | 1000 | 80 |
| Compressed air | 10 | 60 |
Tips and Tricks
- When solving problems involving gravitation, it is helpful to draw a free-body diagram of the objects involved.
- The gravitational force between two objects is always attractive.
- The gravitational force between two objects is independent of the medium between them.
- The gravitational force between two objects is not affected by the motion of the objects.
Common Mistakes to Avoid
- Do not confuse the gravitational force with the weight of an object. Weight is the force of gravity acting on an object.
- Do not forget to include the gravitational constant in your calculations.
- Do not assume that the gravitational force between two objects is always constant. The force can change if the distance between the objects changes.
Why Newton’s Law of Gravitation Matters
Newton’s law of gravitation is one of the most important laws in physics. It has played a key role in our understanding of the universe and has been used to make many important discoveries.
Benefits of Newton’s Law of Gravitation
Newton’s law of gravitation has many benefits, including:
- It provides a simple and accurate way to calculate the force between two objects.
- It can be used to determine the mass of a planet.
- It can be used to predict the trajectory of a projectile.
- It can be used to design spacecraft trajectories.
- It has helped us to understand the structure of the universe.
