Your weight in Pounds 140 lbs Your mass (m) in kilograms 63.5 kg Mass of Earth (M) in kilograms Radius of Earth (r) meters 5.9736 x 10^24 kg 6.371 million Force of gravity calculated using the equation (in newtons force gravity pounds) 6.67 x 10^-11 x 63 x 6371000 x 6371000 / (1*2) The force of gravity between you and Earth equal to your weight? Part: Understand how the force of gravity depends on the distance between the objects points. Let’s use you and Earth as the two objects. We already know the force of gravity between you and Earth that you calculated. What would happen to this value if you increase the distance between you and Earth in the equation? In other words, would you expect the force of gravity to increase or decrease?
The Correct Answer and Explanation is:
Correct Answer:
If the distance between you and Earth increases, the force of gravity would decrease.
Explanation
Gravity is the attractive force that exists between two objects with mass. The force of gravity between two objects is given by Newton’s Law of Universal Gravitation, which is:F=G⋅m⋅Mr2F = \frac{G \cdot m \cdot M}{r^2}F=r2G⋅m⋅M
Where:
- FFF is the force of gravity (in newtons)
- GGG is the gravitational constant, approximately 6.67×10−116.67 \times 10^{-11}6.67×10−11 N·m²/kg²
- mmm is your mass (about 63.5 kg)
- MMM is the mass of Earth (about 5.9736×10245.9736 \times 10^{24}5.9736×1024 kg)
- rrr is the distance between the center of your mass and the center of Earth (usually the radius of Earth, about 6.371 million meters)
In this formula, notice that the distance rrr is in the denominator and squared. This means the force of gravity is inversely proportional to the square of the distance between you and the other object. So if you increase the distance between yourself and the center of Earth, the force of gravity does not just decrease a little—it decreases rapidly.
For example:
- If you double the distance (go to a height where you’re twice as far from Earth’s center), the force of gravity becomes one-fourth of what it was.
- If you triple the distance, the force drops to one-ninth.
This is why astronauts in orbit around Earth feel “weightless.” Even though gravity is still acting on them, they are far enough away that the force is greatly reduced.
Therefore, increasing the distance from Earth leads to a decrease in the gravitational force you feel.
