Students will learn to use Newton's Universal Law of Gravity equation to solve problems. They will also learn how the acceleration of gravity on Earth is calculated and a bit about gravitational fields in general.
Key Equations

FG=Gm1m2r2 ; the force of gravity between an object with massm1 and another object of massm2 and a distance between them ofr . 
G=6.67×10−11 Nm2/kg2 ; the universal constant of gravity  Some data needed for the problems:

The radius of Earth is
6.4×106 m 
The mass of Earth is about
6.0×1024 kg 
The mass of Sun is about
2.0×1030 kg 
The EarthSun distance is about
1.5×1011 m 
The EarthMoon distance is about
3.8×108 m
 When using the Universal Law of Gravity formula and the constant
G above, make sure to use units of meters and kilograms.  The direction of the force of gravity is in a straight line between two objects. It is always attractive.
 Newton invented calculus in order to prove that for a spherical object (like Earth) one can assume all of its mass is at the center of the sphere (thus in his formula, one can use the radius of Earth for the distance between a falling rock and Earth).
 Newton's Laws apply to all forces; but when he developed them only one was known: gravity. Newton's major insight  and one of the greatest in the history of science  was that the same force that causes objects to fall when released is also responsible for keeping the planets in orbit.
Universal Gravity
Any two objects in the universe, with masses
Here is an illustration of this law for two objects, for instance the earth and the sun:
Gravity on the Earth's Surface
On the surface of a planet  such as earth  the
We can do this because the quantity in braces only has constants; we can combine them and call their product
We call the quantity
Simulation
Gravity and Orbits (PhET Simulation)
Time for Practice
 Use Newton’s Law of Universal Gravitation to explain why even though Jupiter has 300 times the mass of the earth, on the “surface” of Jupiter you’d weigh only 3 times what you weigh on earth. What other factor has to be considered here?
 Prove
g is approximately10 m/s2 on Earth by following these steps: Calculate the force of gravity between a falling object (for example an apple) and that of Earth. Use the symbol
mo to represent the mass of the falling object.  Now divide that force by the object’s mass to find the acceleration
g of the object.  Calculate the force of gravity between the Sun and the Earth. (sun mass
=2.0×1030 kg; average distance from sun to earth = 150 million km)
 Calculate the force of gravity between a falling object (for example an apple) and that of Earth. Use the symbol
 Calculate the gravitational force that your pencil or pen pulls on you. Use the center of your chest as the center of mass (and thus the mark for the distance measurement) and estimate all masses and distances.
 If there were no other forces present, what would your acceleration be towards your pencil? Is this a large or small acceleration?
 Why, in fact, doesn’t your pencil accelerate towards you?
 Mo and Jo have been traveling through the galaxy for eons when they arrive at the planet Remulak. Wanting to measure the gravitational field strength of the planet they drop Mo’s lava lamp from the top deck of their spacecraft, collecting the velocitytime data shown below.
velocity (m/s)  time (s) 

0  0 
3.4  1.0 
7.0  2.0 
9.8  3.0 
14.0  4.0 
17.1  5.0 
(a) Plot a velocitytime graph using the axes above. Put numbers, labels and units on your axes. Then draw a bestfit line (use a ruler) and use that line to find the gravitational field strength of Remulak. Explain below how you did that.
(b) Mo and Jo go exploring and drop a rock into a deep canyon – it hits the ground in 8.4 s. How deep is the canyon?
(c) If the rock has a mass of 25 g and makes a hole in the ground 1.3 cm deep, what force does the ground exert to bring it to a stop?
(d) Mo and Jo observe the shadows of their lava lamps at different positions on the planet and determine (a la Eratosthenes, the Greek astronomer, around 200 B.C.) that the radius of Remulak is 4500 km. Use that and your result for
Answer to 5
5a.
5b.
5c.
5d.