Gravitational potential calculator

Worked example

Find Vg, the gravitational potential. Given: mass of the planet or star M = 5.97 × 10²⁴ kg; distance from the centre r = 6.37 × 10⁶ m; gravitational constant G = 6.67 × 10⁻¹¹ N m²/kg².

1. Write the equation
   V_g = −G M / r
2. Constants used
   G = 6.67 × 10⁻¹¹ N m²/kg²
3. Substitute the values
   V_g = −(6.67 × 10⁻¹¹) × (5.97 × 10²⁴) ÷ (6.37 × 10⁶)
4. Calculate
   V_g = −6.25116 × 10⁷ J/kg
5. Give the answer to 3 significant figures
   V_g = −6.25 × 10⁷ J/kg

Symbols and units

Gravitational potential: rearranged

• To find gravitational potential: V_g = −G M / r
• To find mass of the planet or star: M = −V_g r / G
• To find distance from the centre: r = −G M / V_g

Exam tip

Potential is the energy per kilogram needed to move a mass to infinity, so it is negative. Potential energy is mass times potential.

Common questions

What is the formula for gravitational potential?

The equation is Vg = −G M / r, where Vg is the gravitational potential (J/kg); M is the mass of the planet or star (kg); r is the distance from the centre (m); G is the gravitational constant (N m²/kg²).

What units should I use for gravitational potential?

In SI units: gravitational potential in J/kg, gravitational constant in N m²/kg², mass of the planet or star in kg, distance from the centre in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange Vg = −G M / r?

Rearranging gives these forms: to find gravitational potential: Vg = −G M / r. to find mass of the planet or star: M = −Vg r / G. to find distance from the centre: r = −G M / Vg.