Asteroid's orbital radius and speed

In summary, the conversation discusses calculating the orbital radius and speed of an asteroid with a period of 5 Earth years in the asteroid belt between Mars and Jupiter. A formula using the universal gravitational constant and the mass of the sun is suggested, with a correction to the calculation of the period. The method for calculating the orbital radius and speed is deemed correct.
  • #1
guru
38
0
somebody help me start this question

The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 5 Earth years. What is the asteroid's orbital radius and speed?

Thanks!
 
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  • #2
I believe you need the mass of the sun, unless you are allowed to give your answer as a function of that variable. Use this formula:
[tex]T=\frac{2\pi r^{\frac{3}{2}}}{\sqrt{Gm_{sun}}}[/tex]
where G is the universal gravitational constant and T is the orbital period.
 
  • #3
is this right

Sirus said:
I believe you need the mass of the sun, unless you are allowed to give your answer as a function of that variable. Use this formula:
[tex]T=\frac{2\pi r^{\frac{3}{2}}}{\sqrt{Gm_{sun}}}[/tex]
where G is the universal gravitational constant and T is the orbital period.
will the period be 31536000s. if it is, is this right:
r=[T*(sqrt(GM_sun)/2pi)]^(2/3)
[ 31536000*sqrt(6.67*10^(-11)*(1.99*10^(30)))/(2*pi)]^(2/3)
 
  • #4
Check your period calculation again. Your method looks correct.
 
  • #5
Sirus said:
Check your period calculation again. Your method looks correct.
opps
31536000*5?
 

1. What is an asteroid's orbital radius?

An asteroid's orbital radius is the distance between the center of the asteroid and the center of the object it is orbiting, such as a planet or the sun. It is typically measured in astronomical units (AU), which is the average distance between the Earth and the sun.

2. How is an asteroid's orbital radius calculated?

An asteroid's orbital radius is calculated using Kepler's Third Law of Planetary Motion, which states that the square of the orbital period of a planet or asteroid is directly proportional to the cube of its average distance from the sun.

3. What is the average orbital radius of an asteroid in our solar system?

The average orbital radius of an asteroid in our solar system is approximately 2.8 AU, or 2.8 times the distance between the Earth and the sun.

4. How does an asteroid's orbital radius affect its speed?

An asteroid's orbital radius and speed are inversely proportional, meaning that as the orbital radius increases, the speed decreases and vice versa. This is due to the conservation of angular momentum, as the asteroid must travel a longer distance in the same amount of time, resulting in a slower speed.

5. Can an asteroid's orbital radius change over time?

Yes, an asteroid's orbital radius can change over time due to various factors such as gravitational interactions with other objects in the solar system or collisions with other asteroids. However, these changes are usually small and occur over long periods of time.

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