Lesson - Mass and Weight

Suppose you have a spaceship, and can take a spring scale to many different places in the solar system. What would the scale measure for the weight of this object on the moon? In orbit around the Earth?

The Scale Viewer applet lets you see what this would be in 6 different places. There are three stationary positions, on the Earth, on the Moon, and (using an amazing feat of architecture) in a house floating atop the cloud layers of Jupiter. There are also three orbiting positions, orbiting the Earth, orbiting the Moon, and orbiting Jupiter. If the object is "stationary", the forces acting on the scale and the weight are gravity and the support of a stand from which the scale is hanging. Since the scale measures the force acting on the spring in the scale, in the stationary position, a weight is measured. If the position is "orbiting" a celestial object, the scale is orbiting with the mass, and both are in "free fall" together. The spring does not get stretched, and the scale does not measure a force.

In all cases gravity is acting on the object. You can even use the gravity calculator to find out just what the force of gravity is for each of the objects.

So, mass, weight, and the force of gravity are three different things. Mass is a measure of the amount of stuff in an object. The force of gravity is the pull on two object towards each other based on their mass. The weight of an object is the apparent force due to gravity on an object. The weight can be less than the force of gravity, such as when in orbit. The weight can be more than the force of gravity, such as in an airplane making a steep climb, or in an elevator accelerating upwards.

Answer the following questions true or false. For false answers, state what would be required to make the statement true. You may find the Scale Viewer applet helpful for this.

1. The object in orbit around the moon had zero mass.
2. The object in orbit around the Earth did not feel any gravity.
3. The scale in orbit around the Earth did not measure any weight.

Evaluate the difference in the acceleration due to gravity on a 1 kg object and a 10kg object at sea level. The mean radius of the Earth is 6378.14 km. The mass of the Earth is 5.9742e24 kg. You may find the gravity calculator helpful for this.

For information about bodies in the solar system, check out Solar Views.

4. What is the force due to gravity of a 1 kg object on the surface of the Earth?
5. What is the force due to gravity of a 1 kg object 1000 km above the surface of the Earth?
6. By how much does the force of gravity decrease between the surface of the Earth and an orbit 1000 km above the surface of the Earth?

7. What is the force due to gravity of a 1 kg object on the moon?
8. What is the force due to gravity of a 1 kg object in orbit 1000 km above the moon?
9. By how much different is the force of gravity between an orbit 1000km above the Earth and an orbit 1000 km above the moon?
10. What is the force on the Moon due to the Earth?
11. What is the force on the Earth due to the Moon?
12. What is the acceleration of the Moon due to the Earth?
13. What is the acceleration of the Earth due to the Moon?
14. Why are the forces the same, but the accelerations different?