Question

The radius of Mercury's orbit is r = 5.79 x 1010 m and its orbital period is T=88 days. What is the

magnitude of the orbital velocity for the planet around the sun, assuming a circular orbit?
A. 7.21 x 103 m/s
B. 8.45* 104 m/s
C. 4.79 x 104 m/s
D. 5.32 x 104 m/s

Answer 1

To determine the orbital velocity of Mercury, first, the orbital period is converted to seconds, then the circumference of the orbit is calculated, and finally, the velocity is found using the formula v = 2πr/T. Mercury's orbital velocity is approximately 4.74 x 104 m/s.

Step-by-step explanation:

To calculate the magnitude of the orbital velocity for the planet Mercury in its circular orbit around the Sun, we can use the formula for orbital velocity, which is the circumference of the orbit divided by the orbital period: v = 2πr/T.

First, we need to convert the orbital period from days to seconds since the radius is given in meters:

• T = 88 days × 24 hours/day × 3600 seconds/hour = 7,603,200 seconds

Next, we use the radius r given as 5.79 x 1010 m to find the circumference:

• Circumference (C) = 2π(5.79 x 1010 m)

Now we calculate the velocity:

• v = C/T = 2π(5.79 x 1010 m) / 7,603,200 s

When you calculate that out, you will find that the velocity of Mercury in its orbit around the Sun is approximately 4.74 x 104 m/s, which is closest to the given option C, 4.79 x 104 m/s.