Planetary fields

Question 1

State the condition of r for Newton’s Law of Gravitation

Answer 1

R must be equal or greater than the radius of the sphere

Question 2

Explain why r must be greater than or equal to the radius of mass M

Answer 2

Newton’s Law of Gravitation assumes the mass is a point, if r is less than the radius of M then we are inside the mass where gravitational effects are different

• g is zero at the center of a sphere
• r represents distance from the center

Question 3

Describe the shape of the graph of g against r

Answer 3

g increases linearly with r until r=R at a maximum value
Beyond r=R it decreases hyperbolically
- approaches 0 as r increases
- drops sharply outside the mass

Question 4

Describe the shape of the graph of V against r

Answer 4

Hyperbola that approaches 0 as r approaches infinity and tends to negative infinity as r approaches the mass

Question 5

What is the significance of the gradient of the V-r graph?

Answer 5

The gradient at any point is equal to -g where g is the GFS at that point

Question 6

Define escape velocity

Answer 6

The minimum velocity an object must be given to escape from the planet when projected vertically from the surface

Question 7

Show how to derive both escape velocity equations

Answer 7

Check notes