Calculating Orbit Velocity Around a Star

In summary, the conversation discusses the implementation of Newton's universal gravity law in a 2D space orbiter game. The speaker has successfully created a circular orbit using this law, but is having trouble creating an asteroid belt. They have tried various calculations, including multiplying velocity by r^-2, but it is not working. After receiving help, they realize that their vectors were rotated incorrectly and are able to resolve the issue.
  • #1
Chetic
8
0
I'm toying with the idea of making a little 2D space orbiter game so I've implemented Newton's universal gravity law into this little app. It works really well, even.

The problem I'm having is when I want to create an asteroid-belt. I spawn little asteroids randomly around an area around the sun and give them a starting velocity vector v that is based on their position relative to the sun. Then I rotate v 90 degrees by multiplying with a transformation matrix.

After that I'm just guessing basically. Though I have tried many different ideas based on some calculations. At the moment I multiply v by r^-2 (where r is the distance to the center of the sun) but that sure isn't it. Help?
 
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  • #2


An object is in circular orbit when its centripetal acceleration is equal to the gravitational acceleration:
[tex]\frac{v^2}{r} = \frac{G M}{r^2}[/tex]
solving for v:
[tex] v = \sqrt{\frac{G M}{r}}[/tex]
 
  • #3


Hah! It works!
Now the problem turned out to be that my vectors were rotated incorrectly, but your answer helped me realize what wasn't wrong so thank you very much!

Here's a li'l pic of it at the moment:
http://img814.imageshack.us/img814/3983/gasim.png"
 
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Related to Calculating Orbit Velocity Around a Star

1. How is orbit velocity around a star calculated?

The orbit velocity around a star is calculated using the equation v = √(GM/r), where v is the velocity, G is the gravitational constant, M is the mass of the star, and r is the distance between the star and the object orbiting it.

2. What units are used for calculating orbit velocity?

The units used for calculating orbit velocity are meters per second (m/s) for velocity, kilograms (kg) for mass, and meters (m) for distance. The gravitational constant, G, is measured in the units of cubic meters per kilogram per second squared (m3/kg/s2).

3. How does the mass of the star affect orbit velocity?

The mass of the star has a direct effect on the orbit velocity. The higher the mass of the star, the greater the gravitational pull, which results in a higher orbit velocity for a given distance. This means that objects orbiting a more massive star will have to move faster to maintain their orbit compared to objects orbiting a less massive star.

4. What is the significance of the distance from the star in calculating orbit velocity?

The distance from the star is an important factor in calculating orbit velocity because it affects the strength of the gravitational force between the star and the orbiting object. The closer the object is to the star, the stronger the gravitational pull, resulting in a higher orbit velocity. However, as the distance increases, the gravitational force decreases, causing a decrease in orbit velocity.

5. Is the orbit velocity constant for all objects orbiting the same star?

No, the orbit velocity is not constant for all objects orbiting the same star. The orbit velocity depends on the mass and distance of the object from the star. Objects with a higher mass or closer distance will have a higher orbit velocity compared to objects with a lower mass or farther distance.

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