A synchronous orbit is an orbit about a planet's equator that always remains above the same spot of the planet because the synchronous orbit matches the planet's rotational period. The pilot of the Mars spacecraft (which was named Cheetah 1 and had a 9556 kg mass) asked Tarzan to calculate the altitude of a synchronous orbit so they could remain over a particular geological feature on the Martian equator. Calculate the altitude above the Martian equator using the data above and Johannes Kepler's genius.

The mean distance of an asteroid from the Sun is 1.74 times that of Earth from the Sun. From Kepler's law of periods, calculate the number of years required for the asteroid to make one revolution around the Sun.

Titan has a radius of 2500.0 km and a mean density of 2.0 g/cm3. Earths moon has a radius of 1737.0 km and a mean density of 3.4 g/cm3. What is the ratio of gravitational acceleration on Titan compared to that on the moon?

Consider a spherical shell constructed from a material of density 6.1 x 103 kg/m3.  The inner radius of the shell is 4.9 x 106 m from the center, and the outer radius of the shell is 9.2 x 106 m from the center.  Calculate the magnitude of the gravitational field 13.1 x 106 m from the center of the shell, in N/kg.  Use G = 6.7 x 10-11 N m2 / kg2. (Please answer to the fourth decimal place - i.e 14.3225)

What is the escape speed from a planet of mass M = 3.1 x 1023 kg and radius R = 2.6 x 106 m? Write the answer in terms of km/s.

A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.1 × 104 m/s. The mass of the planet is M = 6.04 × 1024 kg. The mass of the satellite is m = 1.2 × 103 kg. First, find an expression for the gravitational potential energy PE in terms of G, M, m, and R.  a)Calculate the value of PE in joules.  b)Enter an expression for the total energy E of the satellite in terms of m and v.  c)Calculate the value of the total energy E in joules.

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…

The International Space Station, which has a mass of 4.94×105 kg, orbits 258 miles above the Earth's surface, and completes one orbit every 94.3 minutes. What is the kinetic energy of the International Space Station in units of GJ (109 Joules)? (Note: don't forget to take into account the radius of the Earth!) Enter answer here GJ

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.

In 2000, NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of 1.40×1016 kg and a radius of 8.20 km What is the speed of a satellite orbiting 4.90 km above the surface? What is the escape speed from the asteroid?