Worksheet: The Gravitational Field Inside Planets

In this worksheet, we will practice calculating the magnitude of the acceleration due to gravity at a point inside of a planet.

Q1:

Which of the following relations shows how the local acceleration due to gravity, π‘Ž , at any point outside or inside a planet varies with the density of the planet, 𝜌 , if the planet has a constant density throughout?

  • A π‘Ž ∝ 𝜌 
  • B π‘Ž ∝ 𝜌 
  • C π‘Ž ∝ 1 𝜌
  • D π‘Ž ∝ 𝜌
  • E π‘Ž ∝ 1 𝜌 

Q2:

What is the acceleration due to gravity at a distance of 0.15 𝑅  from Earth’s center of mass? Assume that Earth is a perfect sphere with a radius 𝑅 = 6 , 3 7 0  km and a constant density of 5,510 kg/m3. Give your answer to 3 significant figures.

Q3:

What is the acceleration due to gravity at the center of Earth?

Q4:

What is the acceleration due to gravity at a distance from Earth’s center of mass that is equal to half the Earth’s radius? Assume that Earth is a perfect sphere with a radius of 6,370 km and a constant density of 5,510 kg/m3. Give your answer to 3 significant figures.

Q5:

The figure shows how the acceleration due to gravity inside and outside of a planet varies along two spatial dimensions. The planet has a constant density. At which of the five points shown in the figure is the acceleration due to gravity zero?