Question

multiple choice question
in which location would a person experience the smallest gravitational field?

driving on a road in a car

moving underwater in a submarine

orbiting earth in a spaceship

flying over mountains in an airplane

Explanation:

Step1: Recall the formula for gravitational field

The gravitational field \(g=\frac{GM}{r^{2}}\), where \(G\) is the gravitational constant, \(M\) is the mass of the Earth, and \(r\) is the distance from the center of the Earth.

Step2: Analyze each option

• Driving on a road in a car: The distance \(r\) is approximately the radius of the Earth \(R_{E}\).
• Moving underwater in a submarine: The distance \(r\) is approximately \(R_{E}\) (depth of ocean is negligible compared to \(R_{E}\)).
• Orbiting Earth in a spaceship: The distance \(r = R_{E}+h\) (where \(h\) is the height of the orbit. For low - Earth orbit \(h\) can be a few hundred kilometers. Using \(g=\frac{GM}{r^{2}}\), as \(r\) increases, \(g\) decreases.
• Flying over mountains in an airplane: The height of the airplane (\(h_{plane}\approx 10 - 15\) km) is much less than the height of a spaceship in orbit (\(h_{orbit}\approx 100 - 1000\) km). So \(r = R_{E}+h_{plane}\) and \(g\) is larger than that for the spaceship.

Answer:

orbiting Earth in a spaceship