# Planetary Gravitation

1. Jan 3, 2009

### Raynor.Jim

Ok I got most of them but am having trouble on a few of them.

The question is:

The Sojourner rover vehicle shown in the sketch above was used to explore the surface of Mars as part of the Pathfinder mission in 1997. Use the data in the tables below to answer the questons that follow.

Mars Data: Radius: 0.53 X Earth's radius (Earth radius: 6.37E6) Sojourner Data: Mass of Sojourner vehicle: 11.5 kg
Mass: 0.11 X Earth's mass (Earth mass: 5.98E24) Wheel diameter: 0.13 meters
Stored energy available: 5.4 x 10E5 J
Power required for driving under average conditions: 10 W
Land speed: 6.7 x 10E-3 m/s

A. Determine the acceleration due to gravity at the surface of Mars in terms of g, the acceleration due to gravity at the surface of Earth. I got 3.8 M/S
B. Calculate Sojourner's weight on the surface of Mars. I got 3.02
C. Assume that when leaving the Pathfinder spacecraft Sojourner rolls down a ramp inclined at 20 degrees to the horizontal. the Ramp must be lightweight but strong eough to support Sojourner. Calculate the minimum normal force that mus be supplied by the ramp. I got 41 <-- not sure

having trouble with:

D. What is the net force on Sojourner as it travels across the Martian surface at constant velocity? Justify your answer.
E. Determine the maximum distance that Sojourner can travel on a horizontal Martian surface using its stored energy.
F. Suppose that 0.010% of the power for driving is expended against atmospheric drag as Sojourner travels on the Martian surface. Calculate the magnitude of the drag force.

Any help is appreciated.

EDIT: I cant fix it, Wheel diameter: 0.13 meters
Stored energy available: 5.4 x 10E5 J
Power required for driving under average conditions: 10 W
Land speed: 6.7 x 10E-3 m/s

are under Sojourner Data.

Last edited: Jan 3, 2009
2. Jan 3, 2009

### Gib Z

For A) Your answer is incorrect, your answer must be in terms of g! You should know the quantity you want is $$g_{Mars} = \frac{GM_{Mars}}{r^2_{Mars}}$$. You can express M and r of Mars as ratios of the values for Earth - substitute them in and simplify. You will get some constant times the expression on the RHS, except with the Subscripts of Earth instead. Then you will have it.

B) Are you sure? W = mg. m = 11.5 kg and your value of g from Q A) dont seem to match up to give 3.02. And you should state units!

C) Draw a free body diagram. The normal force is applied to the craft perpendicular from the surface. For it to support its weight, which is a strictly downwards vertical force, the vertical component of the Normal force must be equal in magnitude. Split your normal force into components and equate. If you used the value of W from your previous question I would try it again.

D) What do the words constant velocity imply? What is Newtons Second Law?

E) We use the equation E=Pt where E is energy, P is power and t is time. You know the power and Energy available, so you can work out how long it will run. You also know its land speed.

F) Well, $W = Pt = Fs$ and since we know know the distance it travels, the time it took for that and the power it consumed for it, we can solve for the average force that was applied to it to make this motion happen. This force is however, the sum of the Total Automotive force against the Drag force. Also remember 0.1% of the Power went to overcoming this force.

EDIT: I really shouldn't have given you any help actually, you have to show us some of your working!!!

3. Jan 4, 2009

### Raynor.Jim

I did the work I just didn't type it... If you want to know I can type it here:

G X Mass of mars (I got this by: 0.11 X Earth mass)
///////////////////
Radius of Mars ( I got this by: 0.53 X Earth Radius)

which gave me: 6.67E-11 X 6.578E23
//////////////////////// = 3.8493651
3376100 (squared)

whoops, I messed up on B, W = mg
(11.5)(3.8) = 43.7 kg