1. Universal Gravitation

2. Key Ideas By the end of this unit you should know and understand:
Kepler’s 3 Laws of planetary motion
Newtonian Gravitation
Gravitational Force
Free Fall
Gravitational Field Intensity
Geosynchronous Orbits
Newtonian Gravity as evidence of Dark Matter

3. Isaac Newton (1642-1727) The ultimate “nerd”
Able to explain Kepler’s laws
The Three Laws of Motion 3

4. Newton – Science in Reverse
Newton used his ideas on motion (Three Laws) along with the data that was already available from Brahe and Kepler to come up with …

5. Universal Gravitation
Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of the masses and inversely proportional to the square of the distance
between them.

6. Relating it to Newton’s Laws of Motion
The force that mass 1 exerts on mass 2 is equal and opposite to the force mass 2 exerts on mass 1
The forces form a Newton’s third law action-reaction
Gravitational forces are exerted
from an object’s centre of mass (think back to torque and balance).

7. Fg = force of gravity (N)
G = universal gravitational constant (Nm2/kg2)
= 6.67 x 10-11
m1, m2 = masses (kg)
R = distance between the centres of masses (m) 7

8. What about the equation for weight?
How are these two things related???

9. How does this relate to Newton’s Laws of Motion?
3rd Law: Equal and opposite reaction forces.

10. Question - If an apple weighs 1N at distance 1d, as in the diagram at left, what will be its weight at a distance of 4d?
Inverse square relationship:
Answer: 1/d2 = 1/(4d)2 = 1/16 N
1/16 N

11. Example 1
A 65.0 kg astronaut is walking on the surface of the Moon, which has a mass of 7.35 x 1022 kg and a mean radius of
1.74 x 103 km. What is the weight of the astronaut?
105 N

12. Page 580
Questions 1 to 8
7 and 8 are more challenging

13. Some Hints…
The “r” value is sometimes given as d or distance of separation between two objects.
If the altitude is given, you must add the altitude to the radius of the planet (etc) to get the actual orbital radius.

14. Satellites
All satellites orbit in circular motion. (Still follows Kepler’s First Law of Planetary Motion as circles are special cases of ellipses).

15. Example 2
Find the mass of the Sun using Earth’s orbital radius (on formula sheet: x 1011 m) and period of revolution (on formula sheet: days).
HINT: Remember to use correct units!
1.97 x 1030 kg