Classical Mechanics
# Newton's Law of Gravity

What is the approximate gravitational potential energy of the two-particle system, of masses $5.4\text{ kg}$ and $2.9 \text{ kg},$ separated by a distance of $15.0\text{ m}?$

**Assumptions and details**

- The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.$

Consider an $xy$-plane in deep space, where two particles **A** and **B** are located. Particle **A** is fixed at the origin and particle **B** is apart from particle **A** with a distance of $3.6\text{ m}.$ The masses of particles **A** and **B** are $24\text{ kg}$ and $12\text{ kg},$ respectively. If particle **B** is released from rest, what is the kinetic energy of **B** when it has moved $0.1\text{ m}$ toward **A**?

**Assumptions and Details**

- The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.$

The mean diameter of Mars is $6.7\times 10^3\text{ km}$ and its mass is $6.7\times 10^{23}\text{ kg}.$ What is the approximate escape speed on Mars?

**Assumptions and Details**

- The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.$

$12.0\text{ m},$ as shown in the above figure. Then the side length of the square is reduced to $4.0\text{ m}.$ If the mass of each particles is $19.0\text{ kg},$ approximately how much gravitational potential energy of the four-particle system is reduced, assuming that the four particles are point particles?

Four identical particles are forming a square with side length**Assumptions and Details**

- The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2 ?$

If a $6000 \text{ kg}$ space rocket is launched vertically from the surface of the Earth with initial energy $7.0 \times 10^{11} \text{ J},$ what will be the kinetic energy of the space rocket when it is $1.4 \times 10^7 \text{ m}$ from the center of the Earth, assuming that the mass and the radius of the Earth are $6.0 \times 10^{24}\text{ kg}$ and $6.4 \times 10^6 \text{ m},$ respectively?

**Assumptions and Details**