Gravitation — small g vs capital G, Weight, and Escape Velocity

The Chapter Where One Letter Costs You Marks

Gravitation gives away marks — provided you never confuse G with g. They are not the same quantity, they do not share units, and one of them changes from place to place while the other does not.

• ›G, the universal gravitational constant, is a fixed number of nature: 6.67 × 10⁻¹¹ N m² kg⁻². It is the same on Earth, on the Moon, and in the farthest galaxy.
• ›g, the acceleration due to gravity, is roughly 9.8 m s⁻² at Earth's surface — but it is different at the poles and the equator, different on a mountain, different in a mine shaft, and about one-sixth as much on the Moon.

The second idea worth fixing early is mass versus weight. Mass is the amount of matter in a body and never changes. Weight is a force, W = mg, and changes wherever g changes. An astronaut carries the same mass to the Moon and weighs a sixth as much there.

Every question in this chapter is one of those two distinctions dressed in numbers.

1. If the distance between two bodies is doubled, the gravitational force of attraction between them becomes—

2. What is the approximate value of the universal gravitational constant G, together with its correct SI unit?

3. At which of the following places is the value of the acceleration due to gravity, g, the greatest?

4. The escape velocity from the surface of the Earth is approximately—

5. A body weighs 60 N on the surface of the Earth. Taking the acceleration due to gravity on the Moon as one-sixth of that on the Earth, what will the body weigh on the Moon?

6. What is the relation between the escape velocity vₑ from a planet's surface and the orbital velocity v₀ of a satellite revolving very close to that surface?

7. An astronaut inside a space station orbiting the Earth appears to float. The correct reason is that—

8. At a depth equal to half the radius of the Earth, the value of the acceleration due to gravity becomes—