Calculating Orbital Velocity Ratios for Planets A and B

In summary, Planet A and Planet B are in circular orbits around a distant star, with Planet A being 8.5 times farther from the star than Planet B. The ratio of their speeds, Va/Vb, cannot be determined by simply using F=1/r^2 as the force is proportional to the velocity squared divided by the radius. Therefore, the error in your thinking is assuming that the difference in forces is also the difference in velocity.
  • #1
mariners02
4
0
Planet A and planet B are in circular orbits around a distant star. Planet A is 8.5 times farther from the star than is planet B. What is the ratio of their speeds Va/Vb

This problem seems very simple, thought i could just use F=1/r^2, find the difference in forces, which would also be the difference in velocity. Can anyone explain the error in my thinking?
 
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  • #2
mariners02 said:
Planet A and planet B are in circular orbits around a distant star. Planet A is 8.5 times farther from the star than is planet B. What is the ratio of their speeds Va/Vb

This problem seems very simple, thought i could just use F=1/r^2, find the difference in forces, which would also be the difference in velocity. Can anyone explain the error in my thinking?

The problem is that the force is proportional to the velocity squared divided by the radius. Thus the velocity squared is proportional to the inverse of the radius.
 
  • #3
So i could just do V=Sqrt(1/8.5)=.35?
 

1. What is orbital velocity?

Orbital velocity is the speed at which an object must travel in order to maintain a stable orbit around another object, such as a planet or star.

2. How is orbital velocity calculated?

Orbital velocity is calculated using the formula v = √(GM/r), where v is the orbital velocity, G is the gravitational constant, M is the mass of the central object, and r is the distance between the two objects.

3. What factors affect orbital velocity?

The factors that affect orbital velocity include the mass of the central object, the distance between the two objects, and the gravitational constant. Other factors such as atmospheric drag and external forces can also impact orbital velocity.

4. What is the difference between orbital velocity and escape velocity?

Orbital velocity is the speed at which an object orbits a central object, while escape velocity is the speed at which an object can completely break free from the gravitational pull of a central object. Escape velocity is typically higher than orbital velocity.

5. Can orbital velocity be changed?

Yes, orbital velocity can be changed by altering the distance between the two objects or by changing the mass of the central object. This can be achieved through the use of thrusters or gravitational assists from other objects in space.

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