# Match each statement with the law. (Some answers may be used more than once. Some may not be used...

## Question:

Match each statement with the law. (Some answers may be used more than once. Some may not be used at all.)

a. All three of Kepler's laws combined.

b. Kepler's second law of planetary motion

c. Kepler's third law of planetary motion

d. Kepler's first law of planetary motion

e. None of Kepler's laws.

i. This law places the sun at the focus of the ellipse rather than at the center.

ii. According to this law the speed of a planet would be greatest when farthest from the sun.

iii. According to this law if the semi major axis of the orbit is 8 AU's then the orbit period is 4 years.

iv. This law describes the shape of planetary orbits as ellipses.

## Kepler's laws

Before Kepler, Copernicus model was followed by scientific community, which said that the orbit of a planet around Sun is circular, with Sun at the center of circle. Kepler modified Copernicus model.

## Answer and Explanation:

**i**

First law says it **(d)**

**ii**

Second law says that the areal velocity around the sun is constant for all points on the orbit. It can also be interpreted as : The angular momentum of a planet in the orbit remains constant. So, the planet travels fastest when it is closest to the Sun.

But the second statement writes that the speed of a planet would be greatest when farthest from the sun.

This is is opposition to the second law, and so is not said by any law.

**(e)**

**iii**

Third law says that the square of orbit period of a planet is proportional to the cube of semi major axis of the orbit.

AU is the mean distance from the center of Earth to center of Sun. So, it can be taken equal to the semi major axis of orbit of Earth. Also, the orbit period of Earth around the sun is 1 year.

So, if semi major axis is 8 AU, then from third law, orbit period = {eq}1\ year\ * (8)^{\frac{2}{3}} = 4\ years {/eq}

Third law says it **(c)**

**iv**

First law says it **(d)**

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