Question

1. the gravitational force of attraction between the sun and an asteroid travelling in an orbit of radius 4.14 x 10¹¹ m is 4.62 x 10¹⁷ n. what is the mass of the asteroid? a 1.45 x 10⁹ kg b. 4.08 x 10⁹ kg c. 4.71 x 10¹⁶ kg d. 6.00 x 10²⁰ kg

Explanation:

Step1: Use the formula for gravitational force

The formula for gravitational force is \(F = G\frac{Mm}{r^{2}}\), where \(F\) is the gravitational force, \(G = 6.67\times10^{- 11}\space Nm^{2}/kg^{2}\) (universal gravitational constant), \(M = 1.99\times10^{30}\space kg\) (mass of the Sun), \(m\) is the mass of the asteroid, and \(r\) is the radius of the orbit. We need to solve for \(m\). Rearranging the formula for \(m\) gives \(m=\frac{F r^{2}}{G M}\).

Step2: Substitute the given values

We are given \(F = 4.62\times10^{17}\space N\), \(r = 4.14\times10^{11}\space m\), \(G = 6.67\times10^{-11}\space Nm^{2}/kg^{2}\), and \(M = 1.99\times10^{30}\space kg\).
Substitute these values into the formula:

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Answer:

B. \(4.08\times 10^{9}\space kg\)