### Video Transcript

What is the magnitude of the
acceleration of Venus toward the Sun, assuming a circular orbit with a radius of
1.082 times 10 to eleventh meters, and an orbital period of 0.6152 years. Use a value of exactly 365 for the
number of days in a year.

We can call this acceleration
magnitude of Venus toward the sun ๐. And if we make a sketch of the
planet Venus orbiting circularly around the sun, we know that the distance between
the center of the sun and the center of Venus is given as ๐ 1.082 times 10 to
eleventh meters. And that the planet Venus makes it
once all the way around this orbit in a period weโve called capital ๐ of 0.6152
years.

Since the planet Venus is moving in
a circular orbit, that means it will accelerate centripetally towards the center of
the circle. We recall that an objectโs
centripetal acceleration is equal to its linear speed squared divided by the radius
of the circle it moves in. Recalling further that an objectโs
speed is equal to the distance it travels divided by the time it takes to travel
that distance, we can say that the linear speed of Venus is equal to the distance it
travels the circumference of the circle two times ๐ times its radius divided by the
period ๐.

This means that the centripetal
acceleration of Venus is equal to two ๐๐ over ๐ quantity squared all divided by
the radius ๐. This simplifies to four ๐ squared
๐ over ๐ squared. Since weโre given both the radius
๐ and the period ๐, we have all the information we need. But before we plug in and solve for
๐, we like to convert the period ๐ from units of years to units of seconds.

To make that conversion, weโll take
๐, which is given in years, multiply it by the number of days in a year multiply
that by the number of hours in a day and multiply that by the number of seconds in
an hour. This then will give us a time value
in units of seconds.

With the radial distance ๐ plugged
into our expression, weโre already to calculate ๐. When we do, we find a value of
1.135 times 10 to the negative two meters per second squared. Thatโs the magnitude of the
center-seeking acceleration of the planet Venus as it moves in its circular
orbit.