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

AI Thread Summary
The discussion centers on calculating a comet's speed at its farthest distance from a star, given its speed at closest approach. The initial speed at a distance of 4 x 10^10 km is 50 km/s. A user attempts to apply gravitational and centripetal force equations but is advised to consider angular momentum conservation instead. By applying the conservation of angular momentum, the comet's speed at a distance of 10 x 10^10 km is determined to be 20 km/s. The conversation emphasizes the importance of using the correct principles for elliptical orbits.
johnsholto
Messages
9
Reaction score
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
 
Physics news on Phys.org
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.)
 
What about angular momentum?

mvr=mVR

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

x=20
 
:smile:
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Extra speed necessary to orbit at 970 km
Replies
8
Views
2K
Potential Energy and raising a satellite from Earth into a Circular Orbit
Replies
5
Views
2K
What Is the Speed of the Comet at a Different Distance?
Replies
17
Views
3K
Velocity required to escape the solar system
Replies
15
Views
1K
Calculating Orbital Velocity and Radius Using Energy Conservation
Replies
3
Views
2K
Finding r of a Jovian-synchronous orbit and escape velocity
Replies
7
Views
2K
A comet at its closest approach to the Sun
Replies
1
Views
2K
Find the speed of a satellite at a distance R from Earth
Replies
39
Views
4K
Centripetal Acceleration of Satellite
Replies
7
Views
2K
From circular orbit to elliptical orbit
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top