Sovi.AI - AI Math Tutor

Scan to solve math questions

QUESTION IMAGE

a satellite is traveling in an orbit around earth. what change would ca…

Question

a satellite is traveling in an orbit around earth. what change would cause it to experience more gravitational force from earth? orbiting closer to earths surface removing some of its mass making it orbit faster making its surface reflect the suns rays

Explanation:

Step1: Recall gravitational - force formula

The gravitational force formula is $F = G\frac{Mm}{r^{2}}$, where $F$ is the gravitational force, $G$ is the gravitational constant, $M$ is the mass of the Earth, $m$ is the mass of the satellite, and $r$ is the distance between the center of the Earth and the satellite.

Step2: Analyze each option

  • Option 1: Orbiting closer to Earth's surface means reducing $r$. Since $F$ is inversely - proportional to $r^{2}$ ($F\propto\frac{1}{r^{2}}$), a decrease in $r$ will cause an increase in $F$.
  • Option 2: Removing some of its mass ($m$) will decrease the gravitational force according to the formula $F = G\frac{Mm}{r^{2}}$ as $F$ is directly proportional to $m$ ($F\propto m$).
  • Option 3: The speed of the orbit does not directly affect the gravitational force. The gravitational force is determined by mass and distance, not speed.
  • Option 4: Making its surface reflect the Sun's rays has no relation to the gravitational force between the satellite and the Earth.

Answer:

Orbiting closer to Earth's surface