Physics of Gravity and Orbits

At what depth below the Earth's surface does gravity decrease by 10% of its surface value?

What would be the escape speed from a wooden Earth with a mass that is 10% of the actual Earth, assuming the diameter remains unchanged?

Calculate the kinetic energy of an artificial satellite with a mass of 2000 kg orbiting at a height of 3600 km.

What is the potential energy of a satellite of mass 2000 kg at a height of 3600 km?

What is the total energy of the artificial satellite orbiting at a height of 3600 km above the Earth?

Gravity and Acceleration

The acceleration due to gravity decreases as distance from the Earth's center increases.
At a distance of 640 km below the Earth's surface, the acceleration due to gravity is 10% less than at the surface.

Escape Speed

Escape speed is the minimum speed an object needs to escape the gravitational pull of a planet.
If the Earth were made of wood, its mass would be 10% of its current mass, but its diameter would remain the same.
The escape speed from this wooden Earth would be 3.54 km/s.

Orbital Mechanics

Kinetic energy (KE) is the energy of motion.
Potential energy (PE) is the energy an object has due to its position in a gravitational field.
Total energy (TE) is the sum of KE and PE.
Binding energy (BE) is the amount of energy required to separate an object from its orbit.

Satellite Orbits

An artificial satellite of mass 2000 kg orbiting at a height of 3600 km above the Earth's surface has the following properties:
- KE = $40.09 \times 10^7 J$
- PE = $-80.09 \times 10^7 J$
- TE = $40.09 \times 10^7 J$
- BE = $40.09 \times 10^7 J$
The satellite's KE and BE are equal in magnitude.
This indicates that the satellite is in a stable orbit.

Explore the concepts of gravity, acceleration, and escape speed in this quiz. Learn about how gravity varies with distance and the energies involved in orbital mechanics. Test your understanding of satellite orbits and the fundamentals of gravitational forces.