Question

Kepler's 3 Laws of motion describe orbital motions as ellipses. This question will test your knowledge about ellipses and help you apply Kepler's Laws to elliptical problems.

Which of the following is true about ellipses?

Check all that apply.

Check all that apply.

An ellipse has two focal points.

An ellipse has an oval shape.

An ellipse has the sum of the distances from the focal points to the surface of the ellipse is constant.

A circle is a special kind of ellipse.

Part B

Which of the following statements is true regarding an object traveling in an elliptical orbit?

Check all that apply.

Check all that apply.

The object being orbited is at one of the focal points.

There are solid objects at both of the focal point locations of the ellipse.

The orbiting object's speed varies at it moves around the elliptical orbit.

The eccentricity of the orbit refers to the flatness with a lower eccentricity corresponding to a more circular orbit.

The length of the major axis of the ellipse is the average orbital radius for calculation purposes

Part C

A newly discovered asteroid orbiting around the Sun has an eccentricity of 0.302 and a period of 11.47 years

years . What is the total distance between the two foci for this asteroid? The mass of the Sun is 1.99×10³⁰ kg

Answer 1

Solution:

The following statement about ellipses are ----

1) An ellipse has two focal points

2) An ellipse has an oval shape.

3) A circle is a special kind of ellipse.

Part-B

The following statement regarding an object travelling in an elliptical orbit -----

1) The object being orbited is at one of the focal points.

2) There are solid object at both of the focal point locations of the ellipse.

3) The orbiting object's speed varies at it moves around the elliptical orbit.

4) The eccentricity of the orbit refers to the flatness with a lower eccentricity corresponding to a more circular orbit.

Part C

Eccentricity = 0.302

So Orbit is an ellipse.

We Know that,

------(i)

Given: T = 11.47 yrs = 3.6*10^8 s

M = 1.99*10^30 kg

Substitute this values in equation(i) we get,

a = 7.58*10^11 m

Hence total distance between two foci for this asteroid is 2a = 1.516*10^12 meter [Answer]