Satellite geostationary orbit?

Yes, you're right. The satellite can't stay directly above Canberra. It could stay above the equator north of Canberra. By the way -- the mass of the satellite shouldn't enter into the solution. If it was 100 kg, 200 kg, 5000 kg -- it would still have the same orbit.

Yes, you're right. The satellite can't stay directly above Canberra. It could stay above the equator north of Canberra. By the way -- the mass of the satellite shouldn't enter into the solution. If it was 100 kg, 200 kg, 5000 kg -- it would still have the same orbit.

I think you also detected an issue about the wording or phrasing in this question. A geostationary satellite must be over the equator, as you noted. If a satellite passes directly overhead Canberra, it cannot be a geostationary orbit, and will move around the sky both north-south and east-west. The position would trace out an ellipse, at best. Also, with an inclination of at least 37 degrees, the satellite orbit will precess over time as well. The mass of the satellite has nothing to do with the problem -- it just distracts. If there were no atmosphere, a satellite orbiting the earth at a distance of one earth radius has a period of just a bit over 84 minutes. To have a period of 1440 minutes, that is 17.14 times longer. Kepler says the ratio of the periods is equal to the ratio of the semi-major axes raised to the 3/2 power. So... the orbit must be 6.65 earth radius units in its semi-major axis. Its altitude above the surface is then 5.65 earth radius units. Multiply that by the radius of the earth 6380 kilometers, and you get 36037 km above the surface. (same basic number you had from the center of the earth, but the problem asked for height above the surface) That would be the height above the equator. It would be a good bit farther away from Canberra. Draw a sketch of the problem, and you will see the satellite distance from Canberra can be found by applying geometry and trigonometry to calculate the extra distance.

A geostationary orbit (or Geostationary Earth Orbit - GEO) is a geosynchronous orbit directly above the Earth's equator (0° latitude), with a period equal to the Earth's rotational period and an orbital eccentricity of approximately zero. The satellite orbits in the direction of the Earth's rotation, at an altitude of 35,786 km (22,236 mi) above ground, producing an orbital period equal to the Earth's period of rotation, known as the sidereal day. All GEO satellites are directly above the Equator.

You're right about the geosynchronous orbit radius. You are also right in saying that a geosynchronous satellite must orbit in the equatorial plane and therefore can't ever be directly above Canberra. Although the effect of the satellite's mass on the orbital period isn't QUITE zero, it is so tiny as to be negligible, so you really don't need that information.

You are correct that it is impossible to be stationary over any place not on the equator. So the best you can do is to be over Lat: 0° 0’ and Long: 149° 08’E. Your radius looks about right.

You're right about the geosynchronous orbit radius. You are also right in saying that a geosynchronous satellite must orbit in the equatorial plane and therefore can't ever be directly above Canberra. Although the effect of the satellite's mass on the orbital period isn't QUITE zero, it is so tiny as to be negligible, so you really don't need that information.

A geostationary orbit (or Geostationary Earth Orbit - GEO) is a geosynchronous orbit directly above the Earth's equator (0° latitude), with a period equal to the Earth's rotational period and an orbital eccentricity of approximately zero. The satellite orbits in the direction of the Earth's rotation, at an altitude of 35,786 km (22,236 mi) above ground, producing an orbital period equal to the Earth's period of rotation, known as the sidereal day. All GEO satellites are directly above the Equator.

You are correct that it is impossible to be stationary over any place not on the equator. So the best you can do is to be over Lat: 0° 0’ and Long: 149° 08’E. Your radius looks about right.