Question

The radius of the earth's orbit is r = 1.5 x 10^11 m and its orbital period is T = 365.3 days. What is the radial acceleration (in m/s^2) of the earth toward the sun, assuming a circular orbit?

A. 9.84 m/s^2
B. 5.78 m/s^2
C. 0.13 m/s^2
D. 2.56 m/s^2

Answer 1

The radial acceleration of the Earth towards the Sun is approximately 5.78 m/s^2.

Step-by-step explanation:

To find the radial acceleration of the Earth towards the Sun, we can use the formula for centripetal acceleration:

a = (v^2)/r

where a is the acceleration, v is the velocity, and r is the radius of the circular orbit.

The velocity can be calculated using the formula for circumference:

v = (2 * π * r)/T

where π is a mathematical constant (approximately 3.14159), and T is the orbital period.

Substituting the values given:

r = 1.5 x 10^11 m

T = 365.3 days = 365.3 * 24 * 60 * 60 seconds

we can calculate the acceleration.

After substituting the values and performing the calculations, the radial acceleration of the Earth towards the Sun is approximately 5.78 m/s^2.