What is the comet's maximum speed at its farthest distance from the star?

In summary, the comet has a speed of 50 km/s at its closest approach of 4*10^10 km, and at its maximum distance of 10*10^10 km, it has a speed of √1000 km/s due to the conservation of angular momentum. This indicates that the comet is moving in an elliptical orbit rather than a circular one.
  • #1
johnsholto
10
0
A comet orbits a star. At its closest approach (r=4*10^10 km) it has a speed of v=50 km/s. How fast is the comet at its maximum distance (R=10*10^10 km)?

Could someone verify my results?

F=GMm/r^2=mv^2/r

f=GMm/R^2=mV^2/R

F/f = R^2/r^2 = Rv^2/rV^2 -> R/r = v^2/V^2

R=2.5r -> 2.5r/r = v^2/V^2 -> V^2 = 2500/2.5 km^2/s^2 -> V = √1000 km/s
 
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  • #2
The comet is moving in a very elliptical orbit rather than a circular orbit. You cannot take r and R as radii of circular motion. Try something else. (Hint: Use an appropriate conservation principle.)
 
  • #3
What about angular momentum?

mvr=mVR

50*4*10^10=x*10*10^10

x=20
 
  • #4
:smile:
 
  • #5


Based on the given information, the comet's maximum speed at its farthest distance from the star (R=10*10^10 km) would be approximately 1000 km/s. This is calculated by using the formula for centripetal force and equating it to the gravitational force between the comet and the star. By rearranging the equation and substituting the given values, we can solve for the velocity at the maximum distance. The result of 1000 km/s is consistent with the expected range of comet velocities. However, it is always important to double check calculations and consider any potential sources of error.
 

What is orbit speed and radius?

Orbit speed refers to the velocity of an object moving in a circular path around another object, typically a planet or star. Orbit radius refers to the distance between the object and the center of the object it is orbiting.

What factors affect orbit speed and radius?

The main factors that affect orbit speed and radius are the mass of the objects involved and the distance between them. The more massive the objects are, the faster the orbit speed will be. The closer the objects are, the smaller the orbit radius will be.

How is orbit speed and radius calculated?

The orbit speed can be calculated using the formula v = √(GM/r), where v is the orbit speed, G is the gravitational constant, M is the mass of the larger object, and r is the distance between the objects. The orbit radius can be calculated using the formula r = √(GM/v^2).

What are the units of measurement for orbit speed and radius?

Orbit speed is typically measured in kilometers per second (km/s) or meters per second (m/s), while orbit radius is measured in kilometers (km) or meters (m).

How does orbit speed and radius affect the orbit path?

The higher the orbit speed, the larger the orbit radius will be. This means that the object will travel in a wider orbit path around the larger object. On the other hand, a lower orbit speed will result in a smaller orbit radius and a tighter orbit path.

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