ОГН_10_grade_Satellites

Satellites andspeed of the orbiting object

Objectives

Describe motion of spacecraft;

Analyse circular orbits in inverse square law fields by relating the gravitational force to the centripetal acceleration it causes;

If you drop a stone, it will fall in a straight-line path to the ground below. If you move your hand, the stone will land farther away. What would happen if the curvature of the path matched the curvature of Earth?

If you toss the stone horizontally with the proper speed, its path will match the surface curvature of the asteroid.

How fast would the stone have to be thrown horizontally for it to orbit Earth?
A stone dropped from rest accelerates 10 m/s2 and falls a vertical distance of 5 meters during the first second.
In the first second, a projectile will fall 5 meters below the straight-line path it would have taken without gravity.

In circular orbit, the speed of a satellite is not changed by gravity.
Compare a satellite in circular orbit to a bowling ball rolling along a bowling alley.
Gravity acting on the bowling ball does not change its speed.
Gravity pulls downward, perpendicular to the ball’s motion.
The ball has no component of gravitational force along the direction of the alley.

The speeds of the bowling ball and the satellite are not affected by the force of gravity because there is no horizontal component of gravitational force.

The satellite is always moving at a right angle (perpendicular) to the force of gravity.
It doesn’t move in the direction of gravity, which would increase its speed.
It doesn’t move in a direction against gravity, which would decrease its speed.
No change in speed occurs—only a change in direction

Assuming the orbits are circular.
Gravity causes the centripetal force

This is the speed of the orbiting object

1. The speed of the earth in orbit around the sun:

m1 = mass of the sun = 1.99 x 1030 kg
r = distance between Sun and Earth = 1.49 x 1011m
G = 6.6742 x 10-11 m3kg-1s-2

2. The time for the earth to orbit around the sun:

Newton was right again – 1 Year