PHY C8: Graphs of Φ-r and g-r between Two Masses and Escape Velocity

How is the potential (Φ) at a point between two masses determined?

As the algebraic sum (scalar addition) of the individual potentials from each mass.

How is the field strength (g) at a point between two masses determined?

As the vector sum (vector addition) of the individual field strengths from each mass.

What is Escape Velocity (Escape Speed)? (Definition)

The minimum speed needed for a body to just escape from the gravitational influence of a massive body to infinity.

What is the energy requirement for a body to just escape to infinity?

Its total energy store (ET) at infinity must be zero (ET = EP + EK = 0, with EP=0 and EK=0 at infinity).

What happens if a body's total energy store is greater than zero?

It will go beyond infinity and completely escape the massive body's gravitational field.

What is the formula for Escape Velocity (V_min)?

V_min = √(2GM/R).

Does Escape Velocity depend on the mass of the body being projected?

No, it is independent of the mass of the body.

What is the Escape Velocity for Earth?

Approximately 11.2 km s⁻¹.

What is the Problem-Solving Technique for Escape Velocity problems?

Analyze by considering energy stores and transfers (conservation of energy).