1. Gravity Physics 6A Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

2. GRAVITY
Any pair of objects, anywhere in the universe, feel a mutual attraction due to gravity.
There are no exceptions – if you have mass, every other mass is attracted to you, and you are attracted to every other mass. Look around the room – everybody here is attracted to you!
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

3. Use this formula to find the magnitude of the gravity force.
Any pair of objects, anywhere in the universe, feel a mutual attraction due to gravity.
There are no exceptions – if you have mass, every other mass is attracted to you, and you are attracted to every other mass. Look around the room – everybody here is attracted to you!
Newton’s law of gravitation gives us a formula to calculate the attractive force between 2 objects:
m1 and m2 are the masses, and r is the center-to-center distance between them
G is the gravitational constant – it’s tiny: G≈6.674*10-11 Nm2/kg2
Use this formula to find the magnitude of the gravity force.
Use a diagram or common sense to find the direction. The force will always be toward the other mass. m1 r
F2 on 1 m2
F1 on 2
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

4. Find the net gravitational force on planet H (the middle one).
Example:
Three planets are aligned as shown. The masses and distances are given in the diagram.
Find the net gravitational force on planet H (the middle one).
1012 m
3 x 1012 m
Planet of the Apes:
mass=6 x 1024 kg
Planet Hollywood:
mass=6 x 1020 kg
Daily Planet:
mass=3 x 1025 kg
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

5. Find the net gravitational force on planet H (the middle one).
Example:
Three planets are aligned as shown. The masses and distances are given in the diagram.
Find the net gravitational force on planet H (the middle one).
1012 m
3 x 1012 m
Planet of the Apes:
mass=6 x 1024 kg
Planet Hollywood:
mass=6 x 1020 kg
Daily Planet:
mass=3 x 1025 kg
We should start by defining our coordinate system.
Let’s put the origin at planet H and say positive is to the right.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

6. Find the net gravitational force on planet H (the middle one).
Example:
Three planets are aligned as shown. The masses and distances are given in the diagram.
Find the net gravitational force on planet H (the middle one).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
mass=6 x 1024 kg
Planet Hollywood:
mass=6 x 1020 kg
Daily Planet:
mass=3 x 1025 kg
We can also draw the forces on planet H in our diagram.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

7. Find the net gravitational force on planet H (the middle one).
Example:
Three planets are aligned as shown. The masses and distances are given in the diagram.
Find the net gravitational force on planet H (the middle one).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
mass=6 x 1024 kg
Planet Hollywood:
mass=6 x 1020 kg
Daily Planet:
mass=3 x 1025 kg
Our formula will find the forces (we supply the direction from looking at the diagram):
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

8. Find the net gravitational force on planet H (the middle one).
Example:
Three planets are aligned as shown. The masses and distances are given in the diagram.
Find the net gravitational force on planet H (the middle one).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
mass=6 x 1024 kg
Planet Hollywood:
mass=6 x 1020 kg
Daily Planet:
mass=3 x 1025 kg
Our formula will find the forces (we supply the direction from looking at the diagram):
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

9. Find the net gravitational force on planet H (the middle one).
Example:
Three planets are aligned as shown. The masses and distances are given in the diagram.
Find the net gravitational force on planet H (the middle one).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
mass=6 x 1024 kg
Planet Hollywood:
mass=6 x 1020 kg
Daily Planet:
mass=3 x 1025 kg
Our formula will find the forces (we supply the direction from looking at the diagram):
This is negative because the force points to the left
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

10. Find the net gravitational force on planet H (the middle one).
Example:
Three planets are aligned as shown. The masses and distances are given in the diagram.
Find the net gravitational force on planet H (the middle one).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
mass=6 x 1024 kg
Planet Hollywood:
mass=6 x 1020 kg
Daily Planet:
mass=3 x 1025 kg
Our formula will find the forces (we supply the direction from looking at the diagram):
This is negative because the force points to the left
This is positive because the force points to the right
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

11. Find the net gravitational force on planet H (the middle one).
Example:
Three planets are aligned as shown. The masses and distances are given in the diagram.
Find the net gravitational force on planet H (the middle one).
1012 m
3 x 1012 m
FApes on H
FDP on H
Planet of the Apes:
mass=6 x 1024 kg
Planet Hollywood:
mass=6 x 1020 kg
Daily Planet:
mass=3 x 1025 kg
Our formula will find the forces (we supply the direction from looking at the diagram):
This is negative because the force points to the left
This is positive because the force points to the right
Net force is to the left
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB
Add the forces to get the net force on H:

12. GRAVITY m Rplanet One more useful detail about gravity:
The acceleration due to gravity on the surface of a planet is right there in the formula.
Here is the gravity formula, modified for the case where m is the mass of an object on the surface of a planet. m
Rplanet
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

13. GRAVITY
One more useful detail about gravity:
The acceleration due to gravity on the surface of a planet is right there in the formula.
Here is the gravity formula, modified for the case where m is the mass of an object on the surface of a planet.
We already know that Fgrav is the weight of the object, and that should just be mg (if the planet is the Earth) m
Rplanet
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

14. GRAVITY
One more useful detail about gravity:
The acceleration due to gravity on the surface of a planet is right there in the formula.
Here is the gravity formula, modified for the case where m is the mass of an object on the surface of a planet.
We already know that Fgrav is the weight of the object, and that should just be mg (if the planet is the Earth) m
Rplanet
This part is g
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

15. Kepler’s Laws
1st Law: The orbits of the planets are elliptical, with the sun at one focus of the ellipse.
a=Semi-major axis
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

16. Kepler’s Laws
2nd Law: A line from the sun to a given planet sweeps out equal areas in equal times.
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB

17. Kepler’s Laws
3rd Law: The periods of the planets are proportional to the 3/2 power of the major axis length.
Here is a formula:
Radius of orbit (assuming circular instead of elliptical)
Mass of central object – orbiting mass does not matter
Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB