Question

The constellation Canis Minor has a binary star system consisting of Procyon A and Procyon B. Procyon A, at 3×1030kg, has 2.5 times the mass of Procyon B; and they are roughly 2×1012m apart. How does the force on Procyon A from Procyon B compare to the force on Procyon B from Procyon A?

Answer 1

This question involves the concepts of Newton's Law of Gravitation and mass.

The force on Procyon A from Procyon B will be "equal" to the force on Procyon B from Procyon A, which has a value of "3.75 x 10²⁶ N".

Applying Newton's Law of Gravitation, we can find the force on Procyon A from Procyon B, which is equal to the force on Procyon B from Procyon A:

$F=\frac{Gm_1m_2}{r^2}$

where,

F = force = ?

G = universal gravitational constant = 6.67 x 10⁻¹¹ N.m²/kg²

m₁ = mass of Procyon A = 3 x 10³⁰ kg

m₂ = mass of Procyon B = (2.5)(3 x 10³⁰ kg) = 7.5 x 10³⁰ kg

r = distance between them = 2 x 10¹² m

Therefore,

$F=\frac{(6.67\ x\ 10^{-11}\ N.m^2/kg^2)(3\ x\ 10^{30}\ kg)(7.5\ x\ 10^{30}\ kg)}{(2\ x\ 10^{12}\ m)^2}$

F = 3.75 x 10²⁶ N

Learn more about Newton's Law of Gravitation here:

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