Consider a planet that is a uniform sphere of radius R that has a narrow radial tunnel extending toward its center. Let Få be the gravitational force on an object on the planet's surface. How far down the tunnel should the object be lowered such that the gravitational force is then 0.800F? O0.200R 0.850R O 0.217R 0.451R 0.333R 0.100R 0.125R 0.912R O 0.750R 0.400R

A satellite in geostationary orbit (also called synchronous orbit) appears to remain stationary in the sky as seen from any particular location on the planet.  a.) In the future, there will be need for satellites in synchronous orbit around Mars to aid colonies. At what altitude would such a satellite need to be above the surface of Mars?Assume that the mass of Mars is 6.39 × 10^23 kg, the length of the Martian solar day (i.e., sol) is 24h 39m 35s, the length of the sidereal day is 24h 37m 22s, and the equatorial radius is 3396 km. (Hint: if you haven’t had a physics class before, you can find this by using the fact that the acceleration of an object in circular motion either as v2/r, where v and r are the velocity and radius of the orbit, or as 4Pi 2r/T2 , where T is the period. Use this second equation and Mathematical Insight 4.5 on p. 131 to find r for T=1 day. Make sure to use values for Mars nstead of Earth, as necessary. Alternatively, you can calculate the answer using Newton’s…

Consider a planet that has two layers.  There is a core, which has density 9.9 x 103 kg/m3 and radius 3.9 x 106 m, and then there is a crust, which has density 4.9 x 103 kg/m3 and sits on top of the core.  The planet has a total radius of 16.9 x 106 m.  Calculate the acceleration due to gravity at the surface of this planet, in N/kg.  Use G = 6.7 x 10-11 N m2/ kg2.   (Please answer to the fourth decimal place - i.e 14.3225)

One of your summer lunar space camp activities is to launch a 1090 kg rocket from the surface of the Moon. You are a serious space camper and you launch a serious rocket: it reaches an altitude of 227 km. What gain in gravitational potential energy does the launch accomplish? The mass and radius of the Moon are 7.36×10^22 kg and 1740 km, respectively.