11.2. Gravitational Potential

• What is the definition of gravitational potential?

  Potential energy per unit mass
• Compare and contrast gravitational potential and gravitational field strength.

  1️⃣ Definition: Potential energy per unit mass vs. Force per unit mass

  2️⃣ Type: Scalar vs. Vector

  3️⃣ Relationship to distance: Decreases with increasing distance for both

  4️⃣ Units: J/kg vs. N/kg
• What is the formula for gravitational potential in terms of G, M, and r?

  V = -GM/r
• Gravitational potential is positive because energy is released to escape the field.

  False
• The formula for gravitational field strength is g = GM/r².

  True
• Gravitational potential is a scalar quantity.
• The gravitational constant G defines the strength of gravity.
• Match the property with its description:

  Gravitational Potential ↔️ Scalar

  Gravitational Field Strength ↔️ Vector

  Negative Sign ↔️ Energy needed to escape field
• As the mass of the attracting object increases, the gravitational potential becomes more negative.


  True
• What is the formula for escape velocity?

  v_{escape} = \sqrt{\frac{2GM}{r}}</latex>
• Match the velocity with its description:

  Orbital Velocity ↔️ Velocity to maintain stable orbit

  Escape Velocity ↔️ Velocity to escape gravitational field

  Gravitational Potential ↔️ Potential energy per unit mass
• Gravitational potential is always negative
• What is the unit of gravitational potential?

  J/kg
• The unit of gravitational potential helps quantify energy changes in gravitational fields.


  True
• Match the distance with the corresponding gravitational potential.

  10⁷ m ↔️ -3.34 × 10⁸ J/kg

  2 × 10⁷ m ↔️ -1.67 × 10⁸ J/kg
• Gravitational potential is negative because energy is needed to move an object away from the gravitational source
• What is the formula for gravitational potential?

  $V =$$- \frac{GM}{r}$
• What are the units of gravitational potential?

  J/kg
• Gravitational potential is negative because energy is needed to move an object away from the gravitational source.

  True
• Gravitational potential is inversely proportional to the distance from the center of mass.
• Higher orbits have lower orbital velocities because the gravitational potential is less negative.


  True
• In gravitational fields, total mechanical energy is conserved.

  True
• Gravitational potential is a vector quantity.

  False
• Gravitational potential increases with increasing distance from the source.

  False
• The formula for gravitational potential is V = U/m
• Gravitational potential decreases with increasing distance
• What does the unit J/kg represent for gravitational potential?

  Potential energy per unit mass
• What is the value of the gravitational constant G in the formula for gravitational potential?

  6.674 × 10⁻¹¹ N⋅m²/kg²
• The negative sign in the gravitational potential formula indicates the energy needed to escape the field.


  True
• What does the variable 'M' represent in the gravitational potential formula?

  Mass of attracting object
• How does the mass of the attracting object affect gravitational potential?

  Directly proportional
• Summarize the influence of mass and distance on gravitational potential.

  Mass increases, V increases; Distance increases, V decreases
• Escape velocity is the minimum velocity needed to escape a gravitational field.