For a planet orbiting the sun, r p is the distance from the sun to the perihelion and r a is the distance from the sun to the aphelion. What is a planet’s orbital eccentricity if r p is equal to 0.45r a?
A. 1.45
B. 0.55
C. 0.38
D. 2.64

Where is the sun located on Earth’s elliptical orbit?
A. at the center of the two foci
B. at a focus
C. at the aphelium
D. at the perihelium

A satellite orbiting Earth at an orbital radius r has a velocity v. Which represents the velocity if the satellite is moved to an orbital radius of 4r?
A. 1/4v
B. 4v
C. 1/2v
D. 2v

1) 0.38 (C)

2) At a focus (B)

3) (1/2)v (C)

Explanation:

1) Eccentricity, e = (Ra - Rp)/(Ra +Rp)

Let r a = Ra, rp = Rp

Rp = 0.45Ra

e = (Ra - 0.45Ra)/(Ra + 0.45Ra)

e= 0.55Ra/1.45Ra

e = 55/145

e= 0.38

2) The sun is located at a focus on Earth’s elliptical orbit:

The different location in the Earth’s orbit of the Sun is determined by the perihelion and aphelion.

The perihelion is the point on earth's orbit closest to the sun while aphelion is the point on earth's orbit that is far away from the sun.

The Sun tends a little bit towards one side at a point known as the focus of an ellipse.

This out of alignment causes the planet to move either closer to or further away from the Sun every orbit.

3) initial velocity = v

radius = r

v = √(GM/r)

v = (√GM/√r)

From the expression above, Velocity is directly proportional to the inverse of square root of radius

v = 1/√r

If radius become 4r, the new velocity (V):

V = 1/√4r

V = 1/(2√r) = 1/2(1/√r)

Recall, v = 1/√r

V = (1/2)(v)

V = v/2

Hence velocity decreases as r increases.

New velocity = v/2

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.

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