What is the average linear speed of Mercury about the Sun? (The distance from the Sun to Mercury is 5.80 1010 meters. The orbital period around the Sun is 88 days.)

Speed = circumference / time

Circumference = 2πr
= 2*π*5.8*10^10 m
= 1.16π*10^11 m

Time
= 88days * 24h/day * 60min/h * 60sec/min
=7603200 s

Speed
= distance /time
= 1.16π*10^11 / 7603200
= 47930 m/s
= 47.93 km/s

To calculate the average linear speed of Mercury about the Sun, we need to know the formula:

Average Linear Speed = Distance / Time

In this case:
Distance = The circumference of Mercury's orbit
Time = The orbital period of Mercury around the Sun

To find the circumference of Mercury's orbit, we can use the formula:
Circumference = 2 * π * radius

The radius of Mercury's orbit is half the distance from the Sun to Mercury, which is 5.80 * 10^10 meters / 2.

Now, we need to convert the orbital period from days to seconds, since the linear speed is measured in meters per second. There are 24 * 60 * 60 = 86,400 seconds in a day. Therefore, the orbital period of Mercury is 88 * 86,400 = 7,603,200 seconds.

Calculating the circumference:
Circumference = 2 * π * radius
Circumference = 2 * 3.14159 * (5.80 * 10^10 meters / 2)
Circumference = 3.14159 * 5.80 * 10^10 meters

Now that we have the circumference and the orbital period, we can find the average linear speed:
Average Linear Speed = Circumference / Time
Average Linear Speed = (3.14159 * 5.80 * 10^10 meters) / 7,603,200 seconds

By performing this calculation, you can find the average linear speed of Mercury about the Sun.