How to calculate the comet's speed?

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In summary, the conversation involves calculating the speed of a comet when it crosses Neptune's orbit in 2006, given its distance and speed when approaching the sun in 1986. Kepler's rule and the conservation of energy equation are used to solve the problem, with the mass of the sun being the relevant factor.
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jkh4
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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.
 
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  • #2
Make the substitutions in your conservation of energy equation and see if you really need to know the mass of the comet.
 
  • #3
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?
 
  • #4
jkh4 said:
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.
 
  • #5
i got the answer, thank you so much!

btw, so does that mean if for similar questions, the M is always M of sun?
 
Last edited:
  • #6
jkh4 said:
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.
 

1. How do I calculate the comet's speed using its orbital period and distance from the sun?

To calculate the comet's speed, you will need to use the formula: speed = distance/time. First, you will need to convert the orbital period into seconds. Then, divide the distance from the sun by the orbital period in seconds to get the comet's speed in meters per second.

2. Can I calculate the comet's speed using its velocity and acceleration?

Yes, you can calculate the comet's speed using the formula: speed = velocity + (acceleration x time). You will need to know the initial velocity of the comet and the acceleration it experiences.

3. What units should I use to measure the comet's speed?

The standard unit for speed is meters per second (m/s). However, you can also use other units such as kilometers per hour (km/h) or miles per hour (mph).

4. How can I determine the comet's speed if I only have its distance from the sun and the time it takes to complete one orbit?

If you have the distance from the sun and the orbital period, you can use the formula for orbital speed: speed = 2πr/ T. In this formula, r represents the distance from the sun, and T is the orbital period in seconds. This will give you the comet's speed in meters per second.

5. Is there a difference between the comet's speed and its velocity?

Yes, speed and velocity are slightly different concepts. Speed is a scalar quantity that only measures how fast an object is moving, while velocity is a vector quantity that measures both the speed and direction of an object's movement. When calculating the comet's speed, you will only be looking at the magnitude of its movement, not its direction.

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