Question

The asteroid Toro has a radius of about 5.00m.

Part A
Assuming that the density of Toro is the same as that of the earth (5.50 g/cm^s ), find its total mass.

Part B
Find the acceleration due to gravity at its surface.

Part C
Suppose an object is to be placed in a circular orbit around Toro, with a radius just slightly larger than the asteroid's radius. What is the speed of theobject?

For part A I tried finding the volume of the asteroid and I got (4/3)πr^2

(4/3)π5^3=524 then I used Mass=Volume*Density and got 2879.8

which was wrong. this is due tonight by 10pm. Please help. this is my first question, and I intend to help out as well... please help.

Answer 1

You are on the track for part A. However, you need to take a closer look at the units that you are using. When you solve for the volume of theasteroid, you get a volume in m³. However, the density is given to you in g/cm³. You must convert one of them so that they areeither both in m³ or cm³. Also, check what unit it wants your answer in, probably either grams or kilograms.

For part B, we will use the universal gravitation equation. F_g =, where Fg is force ofgravity, G is the universal gravitation constant (6.67x10-11 ) , m₁ andm₂ are the masses of the two objects in question, and r is the radius between the centers of mass for the two masses. Be careful, make surethat your masses are in kilograms and that your radius is in meters since it must match with the units of the gravitation constant. Let's callm₁ the mass of the asteroid and m₂ the mass of another object under the influence of the asteroid's gravitational field. We canset F_g = m₂a, and notice that m₂ will cancel out on both sides and we will be left with the acceleration due togravity at the whatever given distance from the center of the asteroid. To find the acceleration due to gravity at the surface, simply plug in thedistance from the surface to the center of the asteroid for r. Remember to check the units!

For part C, we also need to take into account the centripetal force. We know that F_c = , where v is thetangential velocity. We know that in the case of an object orbiting another, the centripetal force is provided entirely by the force of gravity. Inotherwords, F_c = F_g. By setting the equations for Fc and Fg equal to each other, we can solve for the v necessary to maintainorbit. Again notice that m₂ will cancel out from both equations since m2 would be plugged into the equation for F_c. This showsthat the velocity necessary to maintain an orbit does NOT depend on the mass of the object in orbit.

Hope this helped!