Speed at a certain distance from the sun

In summary: The velocity of the comet should be negative, but it's actually positive. This is a mistake in the homework. :(Hello! These problems of mine are due in the morning. I'm not sure whether or not I will be able to figure them out in time, but I do need to understand the process in order to prepare for my finals. So any help would be much appreciated! Thank you.
  • #1
najatau
6
0
Hello! These problems of mine are due in the morning. I'm not sure whether or not I will be able to figure them out in time, but I do need to understand the process in order to prepare for my finals. So any help would be much appreciated! Thank you.

1. Homework Statement

A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 4.6
multiply.gif
10^10 m (inside the orbit of Mercury), at which point its speed is 9.1
multiply.gif
10^4 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6
multiply.gif
10^12 m from the Sun? (This is the approximate distance of Pluto from the Sun.)
speed

Homework Equations


[/B]
KSun,f + Kcomet,f + Uf = KSun,i + Kcomet,i + Ui

The Attempt at a Solution



I set KSun to 0 for both sides since the sun isn't moving.

Then I set up this equation:

(1/2)Mv2comet final+(6.7X10-11)(1.989x1030mass of the sun)/(distance)comet final=(1/2)Mv2comet initial+(6.7X10-11)(1.989x1030mass of the sun)/(distance)comet initial

And I isolated one of the velocities:

(vfinal2/2)+((6.67x-11)((1.989x1030)/6x1012)=((1/2)(9.1x104)2)+((6.67x10-11)(1.989x1030)/4.6x1010)

vfinal=sqrt(2*((1/2)(9.1x104)2)+((6.67x10-11)-((6.67x-11)((1.989x1030)(1.989x1030)/4.6x1010))

And I got 75,656 m/s, which isn't the correct answer. :(
 
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  • #2
najatau said:
Hello! These problems of mine are due in the morning. I'm not sure whether or not I will be able to figure them out in time, but I do need to understand the process in order to prepare for my finals. So any help would be much appreciated! Thank you.

1. Homework Statement

A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 4.6
multiply.gif
10^10 m (inside the orbit of Mercury), at which point its speed is 9.1
multiply.gif
10^4 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6
multiply.gif
10^12 m from the Sun? (This is the approximate distance of Pluto from the Sun.)
speed

Homework Equations


[/B]
KSun,f + Kcomet,f + Uf = KSun,i + Kcomet,i + Ui

The Attempt at a Solution



I set KSun to 0 for both sides since the sun isn't moving.

Then I set up this equation:

(1/2)Mv2comet final+(6.7X10-11)(1.989x1030mass of the sun)/(distance)comet final=(1/2)Mv2comet initial+(6.7X10-11)(1.989x1030mass of the sun)/(distance)comet initial

The equation is wrong. Check the sign of PE.
 
  • #3
ehild said:
The equation is wrong. Check the sign of PE.
There's more wrong with the PE than just the sign.
 

Related to Speed at a certain distance from the sun

1. What is speed at a certain distance from the sun?

The speed at a certain distance from the sun refers to the velocity of an object as it orbits around the sun. This velocity is affected by the distance between the object and the sun, as well as the gravitational force between them.

2. How does distance from the sun affect speed?

The distance from the sun directly affects the speed of an object in orbit. The farther an object is from the sun, the slower its speed will be. This is because the gravitational force between the two objects decreases as distance increases, causing the object to move at a slower velocity.

3. What is the relationship between speed and orbital distance?

The relationship between speed and orbital distance is an inverse one. This means that as distance from the sun increases, the speed of the object decreases, and vice versa. This relationship is described by Kepler's Third Law of Planetary Motion.

4. Can speed at a certain distance from the sun change?

Yes, the speed at a certain distance from the sun can change. This can occur due to various factors such as the gravitational pull of other objects, changes in the object's orbit, or external forces acting upon the object.

5. How is speed at a certain distance from the sun calculated?

The speed at a certain distance from the sun can be calculated using the formula v = √(GM/r), where v is the speed, G is the gravitational constant, M is the mass of the sun, and r is the distance between the object and the sun. This formula is derived from the laws of gravity and motion.

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