Imagine an astronaut with a mass of 70 kg floating in space 10.0 m away from the center of gravity of an Apollo command module, whose mass is [tex]6.00 \times 10^{3}[/tex] kg. Determine the gravitational force acting on, and the resulting acceleration (at that instant) of both the ship and the astronaut.
Answer (2)
The gravitational force between 2 objects is G (M₁ x M₂) / R²
G = 6.67 x 10⁻¹¹ Nt-m² / kg² M₁ = 70 kg M₂ = 6 x 10³ kg R = 10
Force = (6.67 x 10⁻¹¹) (70) (6 x 10³) / (10)² = 2.8014 x 10⁻⁷ newton
The forces on the astronaut and on the module are equal. That's the 'weight' of each one, in the presence of the other one. (It's almost exactly 1 micro-ounce.)
Acceleration: F = M A ===> A = F / M
Of the astronaut:
A = (2.8014 x 10⁻⁷) / 70 = 0.000 000 004 002 m/s² (4.002 x 10⁻⁹ m/s²)
Of the command module:
A = (2.8014 x 10⁻⁷) / 6,000 = 0.000 000 000 04 669 m/s² (4.669 x 10⁻¹¹ m/s²)
The gravitational force between the 70 kg astronaut and the Apollo command module (6,000 kg) is approximately 2.8014 x 10^-7 N. This results in an acceleration of about 4.002 x 10^-9 m/s² for the astronaut and about 4.669 x 10^-11 m/s² for the command module.
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