Question: What is the free-body diagram for the Earth in its roughly circular orbit around the Sun?

The only interaction is gravity --- the Sun exerts a gravitational force on the Earth that points toward the Sun.

Knowing the distance to the Sun and how long it takes the Earth to orbit the Sun, we can calculate the acceleration the Earth is experiencing.

r = 150 million km = 1.5 x 10¹¹ m

T = 1 year = π x 10⁷ s

v

=

2π r T

=

2π (1.5 x 1011) π x 107

=

30000 m/s

=

30 km/s

ac

=

v2 r

=

(3 x 104) 2 1.5 x 1011

=

9 x 108 1.5 x 1011

=

6 x 10-3 m/s2

Pretty small, but just right to keep us in orbit.