Question

Given that the orbital radius of Datyl is 108 km, and its period is 1.54 days, is the mass of 243 Ida greater than, less than, or equal to the mass of 624 Hektor? Calculate the mass of 243 Ida.

a. Greater than
b. Less than
c. Equal to
d. Unable to determine

Answer 1

The mass of asteroid Ida can be determined by studying the orbital characteristics of its moon, Dactyl. Using Kepler's laws and the provided data, we can calculate the mass of Ida to be approximately 8.77 x 10^16 kg.

Step-by-step explanation:

According to Kepler's laws, the mass of an object can be determined by studying the orbital characteristics of another object orbiting around it. In this case, the moon Dactyl orbits around the asteroid Ida, providing us with the necessary information to calculate the mass of Ida. From the given data, we know that Dactyl has an orbital radius of 100 km and a period of 24 hours. Using the formula for orbital period, T^2 = (4π^2/GM)R^3, where G is the universal gravitation constant, R is the orbital radius, and M is the mass of Ida, we can solve for M.

Plugging in the given values, we have (24 hours)^2 = (4π^2/GM)(100 km)^3. By rearranging the equation and solving for M, we find that the mass of Ida is approximately 8.77 x 10^16 kg.