Question
A space probe is launched into space from Earth's surface. Which graph represents the relationship between the magnitude of the gravitational force exerted on Earth by the space probe and the distance between the space probe and
the center of Earth?
the center of Earth?
Answers
GPT-4o mini
The relationship between the gravitational force exerted on the Earth by the space probe and the distance between the space probe and the center of the Earth can be described using Newton's law of universal gravitation. According to this law, the gravitational force \( F \) between two masses \( m_1 \) (Earth) and \( m_2 \) (the space probe) is given by:
\[
F = G \frac{m_1 m_2}{r^2}
\]
where:
- \( G \) is the gravitational constant,
- \( r \) is the distance between the center of the two masses.
As the distance \( r \) (from the center of the Earth to the probe) increases, the gravitational force \( F \) decreases as the inverse square of the distance. This means that if you were to plot the gravitational force against the distance from the center of the Earth, the graph would show a hyperbolic decrease.
Therefore, if you had a graph with the distance on the x-axis and the gravitational force on the y-axis, you would see a curve that starts at a certain positive value when the probe is very close to Earth and approaches zero as the distance increases towards infinity.
In conclusion, the graph representing the relationship you described would show a downward curve that approaches the horizontal axis as the distance increases.
\[
F = G \frac{m_1 m_2}{r^2}
\]
where:
- \( G \) is the gravitational constant,
- \( r \) is the distance between the center of the two masses.
As the distance \( r \) (from the center of the Earth to the probe) increases, the gravitational force \( F \) decreases as the inverse square of the distance. This means that if you were to plot the gravitational force against the distance from the center of the Earth, the graph would show a hyperbolic decrease.
Therefore, if you had a graph with the distance on the x-axis and the gravitational force on the y-axis, you would see a curve that starts at a certain positive value when the probe is very close to Earth and approaches zero as the distance increases towards infinity.
In conclusion, the graph representing the relationship you described would show a downward curve that approaches the horizontal axis as the distance increases.