Astronomy 105 Homework 1 Complete Solution

Question: #756

Astronomy 105 Homework 1

Answer all question on a separate sheet. Please be as neat as you can. Show all
work, including units. Circle your final answer clearly.

Part I - Getting to Space
There is no obvious boundary between where the Earth’s atmosphere ends and space begins. But
since this is a class about sending people into space, let us use the the definition that the United
States designates people who travel above an altitude of 80 km (80,000 meters) as astronauts.
In order to throw and object, straight up, to a height h, you have to throw it with a velocity v:
v =
q
2gh
where g is the acceleration due to gravity of the Earth (g = 9.8 m/s2). The velocity v is measured
in meters per second (m/s) and the height h is in meters (m). Air resistance is ignored.
1 (5 pts) Calculate how fast you have to throw someone, straight up, to make them an astronaut.
2 (3 pts) Express your calculated speed in miles-per-hour. 1 m/s = 2.24 mph.
3 (2 pts) The fastest airplane (really rocket-plane)
was the X-15 with a top speed of about 4,000 mph.
Could the X-15 go to space?
The rocket equation can be rewritten to find how much payload we can lift if we are given a value

for Part II - Staying in Space.
Getting to space is easy(ish). Staying in space is hard.
The Earth is a sphere (almost). This means that as you travel horizontally across the surface, the
surface continuously curves downwards. The Earth is really big so the curve is very slight.
For every 3,570 meters you walk, the Earth
curves downward by 1 meter.
The time is takes an object to fall from a height h is:
t =
s
2h
g
where t is measured in seconds (s), h is in meters (m), and g is 9.8 m/s2. Again, air resistance is
ignored.5 (5 pts) Calculate how long is takes an object to fall from a height of 1 meter.If you can throw an object horizontally, fast enough, so that is goes 3,570
meters before it falls 1 meter, that object will never hit the surface of the
Earth. This is the definition of an object in orbit.
6 (10 pts) Calculate how fast you have to throw a person horizontally, so that they are in orbit
around the Earth.
7 (3 pts) Express your answer in miles per hour
8 (2 pts) Can the X-15 go into orbit?
9 (5 pts) How does the speed needed to orbit compare to the speed needed to get a person to space?
10 (5 pts) Calculate the Payload Fraction of a rocket that is just able to
make a person orbit the Earth. Assume that u = 2,300 m/s