Table of Contents

Orbital Mechanics

Student Activity

Gravity's Big Reach!

1. Use the graph provided to determine the local gravitational field strength on the Earth's surface (radius 6.4 x 10³ km).

2. Use the graph provided to determine the local acceleration (due to gravity) on the Earth's surface (radius 6.4 x 10³ km).

3. Use the graph provided to determine the local gravitational field strength on the Earth's surface if the Earth's radius were to mysteriously increase to 1.0 x 10⁴ km).

4. Use the graph provided to determine the local acceleration (due to gravity) on the Earth's surface if the Earth's radius were to mysteriously increase to 1.0 x 10⁴ km).

5. Use the graph provided to determine the local gravitational field strength on the Earth's surface if the Earth's radius were to mysteriously decrease to 5.0 x 10³ km).

6. Use the graph provided to determine the local acceleration (due to gravity) on the Earth's surface if the Earth's radius were to mysteriously decrease to 5.0 x 10³ km).

7. Show by dimensional analysis that N/kg is dimensionally the same as m/s².

8. Using the expression
   g_m = GMe /r_m ²
   Determine the acceleration of the moon g_m towards the Earth (mass M_e) and where r_m is the mean distance to the Moon.

9. Calculate the local gravitational acceleration on the surface of the Moon due to the Moon's mass.

10. Calculate the local gravitational acceleration on the surface of Mars due to its mass.

G = 6,67 x 10^-11 Nm²/kg²
r_m = 3,8 x 10⁸ m (variable due to the eccentricity of the Moon's orbit)
M_e = 5,97 x 10²² kg
Mass of the Moon = 7,34 x 10²³ kg
Radius of the Moon =1,74 x 10⁶ m
Mass of Mars = 6,35 x 10²³ kg
Radius of Mars = 3,40 x 10⁶ m