1. Newton’s Law of Universal Gravitation:
N3L states…
Newton’s Law of Universal Gravitation:

2. Example: You, Earth and the Person next to you…
Take your weight in pounds and divide by 2.2 to obtain your mass in kg.
Determine your weight in Newton’s.
Calculate the force of gravity between you and the Earth assuming that you are
on the surface of the Earth.
If the force of gravity between you and the Earth is mutual, why is it that when you jump out of an airplane, you fall to Earth and the Earth doesn’t seem to fall towards you?
What is the Earth’s acceleration towards you? Is this something that you would notice?
What order of magnitude is the force of gravitational attraction between you and a person 1m away?

3. Example: You and the Earth again…
Relationships : understanding the mathematical relationships amongst the variables leads to better understanding and quicker calculations.
Example: You and the Earth again…
Lets say you were on a planet that had twice the mass of Earth but had the same radius. Would you weigh more, less or the same? If so by how much?
b) What would the force of gravity be on this planet if your mass doubled because you ate so much? Compare this to your weight on Earth.
Use the law of gravitation to determine what you would weigh on the moon.
d) Given your weight on the moon, what must be the acceleration due to gravity on the moon?
Fg(N)
Mass (kg)

4. Relationships : INVERSE SQUARE LAW
Patent Pending: BUTTER GUN
Q: What does an 80kg person weigh on surface of the Earth?
Q: What would this person weigh 6.37 x 106m above Earth’s surface?
r r r
Q: What would be the acceleration due to gravity be at a point where an 815kg satellite weighs N?
Q: If the Earth’s radius is considered 1r, what is the radius of the satellites orbit in terms of r?

5. Relationships : INVERSE SQUARE LAW
2m1 = Fg
2m1 , 3m2 = Fg
2r = Fg
2r , 2m1 = Fg
1/3r , 2m1 , 2m2 = Fg
Q: The force of gravity between the Earth and the moon is x 1020N. How far away is the moon and what would the moon weigh on Earth?

6. Gravitational Field Strength =
The radius of Mars is x 106m and its mass is
6.4 x 1023kg…
What is Gravitational Field Strength near the surface of Mars?
Compare the mass and weight of an 80kg astronaut on the surface of Mars versus being 3 Mars radii away .
How far from the center of Mars would the astronaut have to be in order to have the same weight as they would on Earth?

7. Mass M is orbited by mass m with linear speed v.
Determine the following in terms of (G, M, v)
The distance between their centers?
The magnitude of m’s acceleration?

8. Which of the following is the closest to the force of the sun on the Earth?

9. Given the radius of the Earth as found earlier in the year using clever geometry, the acceleration due to gravity found by dropping an object and the gravitational constant determined by Cavendish, the mass of the Earth can be calculated. Do it.

10. Newton’s Law of Universal Gravitation
The magnitude of the gravitational constant G can be measured in the laboratory. This is the Cavendish experiment.

11. Gravitational Mass vs Inertial Mass

12. The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. Derive two expressions for the speed of one of these satellites in terms of ( g, r ) & (G, M, r)

13. The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical mile = km = 6076 ft]
Determine the speed of these satellites.
(b) Determine the period of these satellites.

14. Determine the speed of the Hubble Space Telescope orbiting at a height of 598km above the Earth’s surface

15. Determining the Mass of a Black Hole!
The Hubble telescope has detected the light being emitted from different regions of galaxy M87.

16. Determining the Mass of a Black Hole!
From characteristics of this light, astronomers have determined an orbiting speed of 7.5 E5 m/s for matter located at a distance of 5.7 E17 m from the center of the galaxy.
Find the mass of the object located at the galactic center.
b) Given that the mass of our sun is 2.0 E30 kg, how many Solar Masses is this equivalent to?

17. Space Stations : ISS

18. The ISS maintains an orbit with an altitude of between 330 km (205 mi) and 435 km (270 mi) by means of
reboost maneuvers using the engines of the Zvezda module or visiting spacecraft.
What is the average speed of the ISS?
How many orbits does it makes in 24 hours?

19. Geosynchronous Orbits

20. A geostationary orbit is a type of geosynchronous orbit in which the orbiting satellite stays directly above one point on the Earth. What is the only latitude that this can occur?

21. Geosynchronous Orbits: Determine the altitude above Earth’s surface for a satellite to be ‘geosynchronous’.

22. Geosynchronous Orbits: Determine the speed
of a ‘geosynchronous’ satellite

23. Geosynchronous Orbits: How is the speed of a satellite related to the radius?
Use the relation above and your knowledge of ratios to
determine the speed of satellite orbiting 200km above
surface of Earth?

24. Space Stations & Artificial Gravity: A space laboratory is rotating to create artificial gravity. Its period of rotation is chosen so the outer ring (rA= 2150m) simulates the acceleration due to gravity on earth (9.80 m/s^2). What should be the radius rB of the inner ring, so it simulates the acceleration due to gravity on the surface of Mars (3.72 m/s^2)?