Gravity Problems

This is just a shorter version of the word doc (attached below) that we use in our online course. The activity is setup as a quiz in Canvas with multiple attempts so the students can come back to it an retake it while studying. You can, of course, add as many different problems as you'd like.

Introduction

Within a year of Galileo's death, in 1642, Isaac Newton was born in the English countryside. During his life he created Calculus (independently, and simultaneously, with Leibniz) and made fundamental contributions in physics--all of which are still taught today!

Whether or not the apple actually fell on Newton's head may never be known; however, his observing objects falling to the Earth led him to extend that knowledge to the possibility that the force that caused the apple to fall might extend to the Moon. And, if the force extended to the Moon, why not the Sun? Newton assumed that the force of gravity diminished as the inverse of the distance squared, and without any additional physics he was able to derive Kepler's Laws! He had made a stunning connection between apples and the motions of the planets, and shown that science had power in explaining the Universe.

As you will soon see, gravity plays a rather large role in this course. We will use the equation you learned in this week's lesson to describe the surface gravity on a world, tidal forces between worlds, resonances, the formation of satellites and rings, and the tidal heating of worlds in the Solar System. We’ll start today with the straightforward calculation of the surface gravity of a world and how changing basic properties, like the world’s mass and radius, influence the surface gravity you would feel on the surface of that world. We will modify our use of the equation given below as we progress throughout the course so get good at using it now - you will become very familiar with it.

Goals

This self-check is designed to give you some practice solving the types of gravity problems you are likely to encounter throughout the first half of this course. This is about the only math you will ever have to do on an exam in this class. Make sure you understand how to solve these problems in your sleep! Bug me for help if you are having trouble with them.

Procedure

Newton’s Law of Universal Gravitation, or the gravitational force of a world, is represented by the following equation:

F g = G M m R 2

For the purposes of this worksheet, Fg represents the surface gravity of the world in Newtons (N). M is the mass of the world in kilograms (kg) and m is the mass of the object on the surface of the world in kilograms (kg). R is the radius of the world in meters (m). G is the gravitational constant, approximately equal to 6.67 x 10-11 Nm2kg-2. If you are interested about the details of the above formula feel free to ask me about it. You'll only be responsible for the simplified version of this equation that I introduced in the lesson presentation and you'll use it to solve the problems: