Question

Use the following information about Earth and its moon to determine the distance between them.

A 2-column table with 2 rows. Column 1 has entries Earth's mass = 6.0 times 10 superscript 24 k g; Earth's radius = 6.4 times 10 superscript 6 m. Column 2 has entries Moon's tangential speed = 1,025 m/s; Moon's mass = 7.3 times 10 superscript 22 k g.
4.6 × 106 m
3.8 × 108 m
3.9 × 1011 m

Answer 1

Use centripetal = gravitational force:

m v^2 / r = G M_e m / r^2 → r = G M_e / v^2.

Plugging in G = 6.67×10^−11, M_e = 6.0×10^24 kg, v = 1025 m/s:

r = (6.67×10^−11 × 6.0×10^24) / (1025^2)
≈ 4.002×10^14 / 1.050625×10^6
≈ 3.81×10^8 m.

So the distance is about 3.8 × 10^8 m.