Table of Contents

Orbital Mechanics

Student Activity

Gravity's Big Reach!: Answer Key

1. Use the graph provided to determine the local gravitational field strength on the Earth's surface (radius 6.4 x 10³ km).
   
   ANS: 9.8 N/kg
   
   

2. Use the graph provided to determine the local acceleration (due to gravity) on the Earth's surface (radius 6.4 x 10³ km).
   
   ANS: 9.8 m/s²
   
   

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).
   
   ANS: 3.9 N/kg
   
   

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).
   
   ANS: 3.9 m/s²
   
   

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).
   
   ANS: 15.2 N/kg
   
   

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).
   
   ANS: 15.2 m/s²
   
   

7. Show by dimensional analysis that N/kg is dimensionally the same as m/s².
   
   ANS: a newton is a unit of force i.e. mass x acceleration dimensionally
   N = kg·m/s² therefore N/kg = (kg m/s²)/kg = m/s²

   Q.E.D.

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.
   
   ANS: 2.75 x 10^-3 m/s²
   
   

9. Calculate the local gravitational acceleration on the surface of the Moon due to the Moon's mass.
   
   ANS: 1.71 m/s²
   
   

10. Calculate the local gravitational acceleration on the surface of Mars due to its mass.
    
    ANS: 3.69 m/s²
    
    

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