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

[johnsholto]

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

 

[TSny]

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.)

 

[johnsholto]

What about angular momentum?

mvr=mVR

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

x=20

 

[TSny]