Answer:
r = 2.031 x 10⁶ m = 2031 km
Explanation:
In order for the asteroid to orbit the planet, the centripetal force must be equal to the gravitational force between asteroid and planet:
Centripetal Force = Gravitational Force
mv²/r = GmM/r²
v² = GM/r
r = GM/v²
where,
r = radial distance = ?
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
M = Mass of Planet = 3.52 x 10¹³ kg
v = tangential speed = 0.034 m/s
Therefore,
r = (6.67 x 10⁻¹¹ N.m²/kg²)(3.52 x 10¹³ kg)/(0.034 m/s)²
<u>r = 2.031 x 10⁶ m = 2031 km</u>
The mirror formula for curved mirrors is:

where
f is the focal length of the mirror

is the distance of the object from the mirror

is the distance of the image from the mirror
The sign convention that should be used in order to find the correct values is the following:
-

: positive if the mirror is concave, negative if the mirror is convex
-

: positive if the image is real (located on the same side of the object), negative if it is virtual (located on the opposite side of the mirror)
The force of gravity the masses exert on each other. If one of the masses is doubled , the force of gravity between the objects is doubled. Increases , the force of gravity decreases.