Question

Asteroid 253 Maitice is one of several that hidve been wished Part A u) space. probes. This asterold is roughic eptherical with a dinmeter of 53 km. The ree oil accelariation at the sutace is: What is the asteroid's misss? 9.9×10

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Express your answer with the appropriate units. X Incorrect: Try Again; 5 attempts remaining

Answer 1

The mass of asteroid 253 Maitice can be calculated using the formula g = G×m/r². With a surface gravitational acceleration of 9.9×10⁻⁷ m/s² and a radius of 26.5 km, the mass of the asteroid is found to be 4.876×10¹¹ kg.

Step-by-step explanation:

To find the mass of the asteroid 253 Maitice, we can use the formula for gravitational acceleration at the surface of a spherical object.

The formula is g = G×m/r², where g is the acceleration due to gravity, G is the gravitational constant (6.674×10⁻¹¹ m³/kg·s²), m is the mass of the asteroid, and r is the radius of the asteroid. Given that the acceleration due to gravity on the asteroid is 9.9×10⁻⁷ m/s² and the diameter of the asteroid is 53 km (which means the radius r is 26.5 km or 26,500 m), we can rearrange the formula to solve for mass (m = g×r²/G).

Plugging in the values, we find: m = (9.9×10⁻⁷ m/s²) × (26,500 m)² / (6.674×10⁻¹¹ m³/kg·s²) = 4.876×10¹¹ kg, which is the mass of the asteroid 253 Maitice.