Question

consider of the motion of the earth around the sun. assume that the earth orbit is a perfect circle and the earth moves at constant speed around the sun. the earth orbits the sun at average distance of 1.0 x10 ^11 m.
a) what is the orbital speed of the earth around the sun? Answer in m/s.
B) what is the radial acceleration of the earth around the sun?
C) what direction is acceleration pointing?

Answer 1

Answer on Question #67937 - Physics / Other

Consider of the motion of the earth around the sun. Assume that the earth orbit is a perfect circle and the earth moves at constant speed around the sun. The earth orbits the sun at average distance of $1.0 \times 10^{\wedge} 11 \, \text{m}$.

a) what is the orbital speed of the earth around the sun? Answer in m/s.

B) what is the radial acceleration of the earth around the sun?

C) what direction is acceleration pointing?

Solution:

a) From the second Newton's law

$$ma = G \frac{m M_{\text{sun}}}{R^2}$$ $$\frac{v^2}{R} = G \frac{M_{\text{sun}}}{R^2}$$

Thus, the speed of the Earth around the Sun

$$v = \sqrt{G \frac{M_{\text{sun}}}{R}} = \sqrt{6.67 \times 10^{-11} \frac{1.99 \times 10^{30}}{1.0 \times 10^{11}}} = 36432.54 \, \text{m/s}.$$

b) The radial acceleration of the Earth around the Sun

$$a = \frac{v^2}{R} = G \frac{M_{\text{sun}}}{R^2} = 6.67 \times 10^{-11} \frac{1.99 \times 10^{30}}{(1.0 \times 10^{11})^2} = 0.13 \, \text{m/s}^2.$$

c) The acceleration of the Earth has direction to the center of Sun.

**Answers:**

a) $36432.54 \, \text{m/s}$,

b) $0.13 \, \text{m/s}^2$

c) to the center of Sun.

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