5.4 Gravitational fields

Question 1

What are gravitational field lines used for?

Answer 1

To show the direction and strength of gravitational forces between masses.

Question 2

What can field lines tell you about a field?

Answer 2

The direction of the field and the strength of the field depending on the density of the field lines.

Question 3

How do you calculate gravitational field strength?

Answer 3

g = Force / mass

Question 4

What is Newton’s law of Gravitation for two point masses?

Answer 4

Newton’s law of gravitation states that two point masses attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.

Question 5

What is Kepler’s first law?

Answer 5

Kepler’s first law states that each planet moves in an eclipse around the sun, with the sun at one focus

Question 6

What is Kepler’s second law?

Answer 6

Kepler’s second law states that a line segment joining a planet and the sun sweeps out equal areas during intervals of equal time.

This is because the speed of the planet is not constant – the planet moves faster when it is closer to the sun.

Question 7

What is Kepler’s third law?

Answer 7

Kepler’s third law states that the square of the orbital period T is proportional to the cube of the average distance r from the sun.

T³ ∝ R²

Question 8

Explain how Kepler’s third law can be derived from Newton’s Law of Gravitation.

Answer 8

Centripetal force is required to keep the planet in orbit, and this force is provided by the gravitational field of the sun.
Because of this, we can equate the formula for centripetal force with the formula for gravitational force and then rearrange for v².
mv²/r = GMm/r²
v² = GM/r
The velocity of an object in circular motion can be written as 2πr/T, so sub this in and rearrange for T.
GM/r = 4πr² / T²
T² = 4π²r³/GM

Question 9

Explain the overall shape of the field strength vs. distance graph between Earth and Mars.

Answer 9

Gravitational fields of Earth and Mars act in opposite directions.
For small 𝑟 (near Earth), Earth’s field dominates, so g is positive.
There is a neutral point where g=0, which is closer to Mars because Earth has a larger mass.
For large 𝑟 (near Mars), Mars’s field dominates, so g is negative.
Both fields follow the inverse-square law ( 𝑔 ∝ 1 / 𝑟²) which causes a curve near to either planet’s surface.