How to calculate the comet's speed?

[jkh4]

Homework Statement

Comet moves around the sun in a very ellipical orbit around the sun. As it approach, in 1986, Comet Halley was 8.79x10^7km from the sun and moving with a speed of 54.6km/s. What will be the comet's speed be when it crosses Neptune's orbit in 2006?

length of comet from the sun = 8.79x10^7km = 8.79x10^10 m
v of comet = 54.6km/s = 54.6x10^3m/s
T = 20 years
length of neptune from the sun = 4.50x10^12m

Homework Equations

i use the equation T^2 = (4*pie*r^3)/GM and K2 + U2 = K1 + U1

The Attempt at a Solution

i first use the Kelper's rule to find M of the comet, but i don't really know if that's the right step to start with.

Thank you.

 

[OlderDan]

Make the substitutions in your conservation of energy equation and see if you really need to know the mass of the comet.

 

[jkh4]

one question, when we calculate with the K2 + U2 = K1 + U1, the M we are using, is that the mass of the sun or neptune?

 

[OlderDan]

one question, when we calculate with the K2 + U2 = K1 + U1, the M we are using, is that the mass of the sun or neptune?

The mass of Neptune does not matter. You are just using the radius of the Neptune orbit as a distance from the sun. The potential energy terms depend on the mass of the sun and the mass of the comet.

 

[jkh4]

i got the answer, thank you so much!

btw, so does that mean if for similar questions, the M is always M of sun?

 

[OlderDan]

i got the answer, thank you so much!

btw, so does that mean if for similar questions, the M is always M of sun?

If the orbit is an orbit around the sun, then the mass of the sun is involved. There are many problems involving orbits around other force centers, so M will not always be the sun's mass.