A space explorer is 4.6 billion km away from a certain star, and observes that the gravitational force of attraction exerted on the spacecraft by the star is 500 N. What will the force become when the craft has approached to a position 2 billion km from the star?
what is (4.6/2)^2 * 500N
To determine the force exerted when the spacecraft moves closer to the star, we can use the inverse square law of gravity.
The inverse square law states that the force of gravity between two objects is inversely proportional to the square of the distance between their centers. Mathematically, this relationship can be expressed as:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3⋅kg^-1⋅s^-2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
In this case, the mass of the spacecraft is not given, but assuming it remains constant, we don't need to know its actual value. The mass of the star is also not relevant to this problem because we are only concerned with the force experienced by the spacecraft.
Let's denote the initial distance between the spacecraft and the star as r1 (4.6 billion km or 4.6 x 10^9 km) and the final distance as r2 (2 billion km or 2 x 10^9 km). The initial force is given as 500 N.
From the inverse square law, we can set up a proportion using the ratios of the distances squared:
(F1 / F2) = (r2^2 / r1^2)
Substituting the given values:
(500 / F2) = ((2 x 10^9)^2 / (4.6 x 10^9)^2)
Now, we can solve for F2:
F2 = 500 / ((2 x 10^9)^2 / (4.6 x 10^9)^2)
Using a calculator:
F2 ≈ 302.33 N
Therefore, when the spacecraft approaches the star to a position 2 billion km away, the gravitational force of attraction exerted on the spacecraft will be approximately 302.33 N.