Galileo's telescope showed him that venus has a large angular diameter (61 seconds of arc) when it is a crescent and a small angular diameter (10 seconds of arc) when it is nearly full. when venus is "half full," its angular size is about 59 seconds of arc. this sequence of phases and angular sizes indicates that venus:

Indicates that venus orbits closer to the sun than the earth. There are several assumptions that Galileo had to make. They are 1. The smaller the visible arc, the further away the object is. 2. When Venus is nearly full, he sees almost all of the surface of Venus that's exposed to the sun. 3. When Venus is half full, he sees half of the surface of Venus that's exposed to the sun. 4. When Venus is just a crescent, he sees almost none of Venus that's exposed to the sun. So Crescent, 61 arc seconds Large, so it's close to Earth Crescent, so can not see most of the surface that's exposed to the sun. Implies that Venus is between Earth and Sun Nearly full, 10 arc seconds. Small, so it's far from Earth Nearly full, so can see most of surface exposed to sun Implies that Venus is nearly opposite from sun as Earth (e.g. Sun is almost between Venus and the Earth) Half full, 59 arc seconds Almost as large as full, so it's a little further away, but not a whole lot Half full, so from the point of view of venus, there's a 90 degree angle between the Sun and Earth. Those observations indicate that Venus is closer to the sun than the earth is. To show why, assume Venus is farther away from the sun than the earth. If that were the case, then you would never see Venus as a Crescent. The least you would see would be half.

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.